Spectrum of Operational Research focuses on advancing operational research, management science and analytics through theoretical insights, developments and real-world case studies. The material published is of high quality and relevance, written in a manner that makes it accessible to this wide-ranging readership. Spectrum of Operational Research is an international peer-reviewed journal covering the main aspects of operational research and analytics and providing a source of information for applied scientists. The journal explores interactions of operational research, management science, and analytics with other relevant disciplines. Spectrum of Operational Research aims at this important task by providing a venue for high-quality scientific papers that contribute significantly to the field of operational research, management science and analytics. The material published is of high quality and relevance, written in a manner that makes it accessible to a wide-ranging readership. Papers reporting original theoretical and/or practice-oriented research or extended versions of the already published conference papers are all welcome. The scope of the journal covers the whole spectrum of decision science. Papers for publication are selected through a double-blind peer-review process to ensure originality, relevance, and readability. In doing that, the objective is not only to keep the quality of published papers high but also to provide a timely, thorough, and balanced review process. General Journal guidelines for authors Spectrum of Operational Research publishes research articles, reviews, short communications, and case studies. Research articles must include: motivation for the work, an adequate overview of the representative work in the field including up-to-date references, a clear statement of the novelty in the presented research, suitable theoretical background, one or more examples to demonstrate and discuss the presented ideas and, finally, conclusions. Short communications are usually 4-7 pages long, research articles and case studies 8-14 pages, while reviews can be longer. Page number limits are not strict and, with appropriate reasoning, the submitted articles can also be longer or shorter. Authors are requested to follow the Spectrum of Operational Research guidelines and strictly format their manuscripts as per the article template that is available here. If extensions of previously published conference papers are submitted, Editors will check if sufficient new material has been added to fulfill the journal standards and qualify the submission for the review process. The added material must have not been previously published. New results are desired but not necessarily required; however, the submission should contain expansions of key ideas, examples, elaborations, etc. of the conference submission. Aims and Scope: The principal aim of the journal is to bring together the latest research and development in various fields of decision science. We would like to highlight that papers should refer to Aims and scope, but they are not limited to. Publication Frequency: One issue per year is published online, but processed and accepted papers, with full bibliographic data, are added to the issue continuously over the whole year. Open Access: This is an open-access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. eISSN (Online): 3042-1470 Publication fee: There is no submission charge or publication fee. Publication in SOR is free of charge for the authors. Publisher: Scientific Oasis, Tekeriška 28a, 11000 Belgrade, Serbia, Email: office@scientificoasis.org Indexing: Google Scholar; ROAD; COBISS; Crossref; doiSerbia;
A Systematic Comparative Review of Compromise Ranking Methods in Multi-Criteria Decision Making
MCDM has become a relevant framework for solving complex decision problems in which there are several conflicting criteria. Compromise ranking methods are one of the most important groups of methods in the MCDM family because they identify solutions that balance individual satisfaction and group utility while minimizing individual dissatisfaction and group regret. This study provides a systematic comparative study of the major compromise ranking methods, such as VIKOR, TOPSIS, COPRAS, MOORA, MULTIMOORA, and MOOSRA. The review is conducted using the PRISMA methodology and supplemented by bibliometric analysis in order to assess publication trends, prevailing subjects, the most popular journals, country representation, and emerging research areas. The study also investigates the methodological principles, normalization processes, computational complexity, robustness, sensitivity behaviour, ranking stability, and the capabilities of the methods to handle uncertainty. The results show that VIKOR is effective in providing explicit compromise solutions by balancing utility and regret, whereas MULTIMOORA is robust and shows superior ranking consistency because of its inherent multi-perspective structure. MOORA and MOOSRA are simpler methods that are computationally efficient and scalable for large-scale decision problems, whilst TOPSIS and COPRAS are intuitive and practical ranking methods. The review further reveals the expanding use of compromise ranking techniques in conjunction with fuzzy systems, artificial intelligence, machine learning, and real-time decision-support systems to address uncertainty and subjective weighting. Furthermore, the application analysis across engineering, energy, finance, healthcare, supply chain, sustainability, transportation, and intelligent systems demonstrates the wide range of applications of compromise ranking methods. In general, this research lays a solid groundwork for the future development of intelligent and adaptive MCDM systems.
Copyright (c) 2026 Arkyadeep Sarkar, Shankha Shubhra Goswami, Dhiren Kumar Behera (Author) https://creativecommons.org/licenses/by/4.0
Complex Pythagorean Fuzzy Aczel–Alsina Weighted Heronian Mean Operators and Their Applications in MCDM
Aggregation operators serve as fundamental mathematical tools for synthesizing multiple inputs into a single representative output. In this study, we introduce a family of aggregation operators (AOs) tailored to the framework of complex Pythagorean fuzzy sets (CPyFSs). Owing to their superior ability to capture both amplitude and phase information, CPyFSs offer enhanced flexibility in modeling uncertainty and vagueness, making them highly suitable for real-world decision-making problems. Motivated by these advantages, this paper develops several novel AOs within the CPyFS environment to address multi-attribute decision-making (MADM) problems more effectively. To further enhance the flexibility and robustness of the proposed operators, Aczél–Alsina (AA) operational laws are incorporated. In particular, we propose the complex Pythagorean fuzzy Aczél–Alsina Heronian mean (CPyFAAHM) operator and the complex Pythagorean fuzzy Aczél–Alsina geometric Heronian mean (CPyFAAGHM) operator, which integrate AA operations with Heronian mean and geometric Heronian mean structures. We investigate the key mathematical properties of the proposed operators, including their structural characteristics and aggregation behavior. Additionally, weighted versions of these operators are developed to accommodate the varying importance of decision attributes. Based on these operators, a MADM methodology is constructed for decision-making under the CPyFS framework. Finally, the effectiveness and practicality of the proposed approach are demonstrated through a numerical example, followed by a comparative analysis with existing MADM methods under complex Pythagorean fuzzy information, highlighting its superiority and applicability.
Copyright (c) 2026 Javeria Gul, Hua Zhu, Bushra Naz, Ziad Khan, Rashid Jan, Fawad Hussain, Imran Qureshi (Author) https://creativecommons.org/licenses/by/4.0
A Comprehensive Review: The Novel Weighting Methods For Multi-Criteria Decision-Making (MCDM)
In Multi-Criteria Decision-Making (MCDM), the importance of the criteria, interpreted relative to each other, defines a key factor that directly determines the accuracy, transparency, and reliability of the final assessment. In the past ten years, there have been tremendous changes in the fields of computational intelligence, uncertainty modelling, and multi-faceted decision frameworks, and the number of novel weighting approaches has gone beyond the constraints of traditional subjective and objective models. This paper provides an in-depth overview of these new methods, including current subjective schemes, objective models derived from data, integrations, fuzzy and probabilistic developments, and artificial intelligence weighting schemes. The review identifies how these methods help enhance robustness, minimize bias, improve uncertainty management, and enable flexibility when faced with complex situations by analyzing peer-reviewed articles published between 2010 and 2025. Comparative reflections are used to identify the methodological strengths, practical limitations, and implementation issues of each group of these weighting strategies. Another important area is the increasing popularity of explainability, universal benchmarking, and big-data integration as key future trends, which are highlighted in the review. On balance, the current research summarizes the dynamic nature of weighting procedures and contributes useful insights regarding their use by researchers, practitioners, and policymakers in search of more reliable and intelligent decision support systems.
Artificial intelligence in decision making
Copyright (c) 2026 Arkyadeep Sarkar, Shankha Shubhra Goswami (Author) https://creativecommons.org/licenses/by/4.0
Aggregation of Expert Ranking Opinions Using Multi-Criteria Decision-Making Methods
This paper investigates the application of multi-criteria decision-making methods (MCDM) for the aggregation of expert opinions related to ranking, considering the weight coefficients of the experts' competencies. Measurement Alternatives and Ranking according to Compromise Solution (MARCOS), Complex Proportional Assessment (COPRAS), Additive Ratio Assessment (ARAS), and Combined Compromise Solution (CoCoSo) methods, which are traditionally used to select the optimal alternative in MCDM, are applied in this study for the purpose of aggregating the ranks given by experts. The validity of the results was confirmed by comparison with the Einstein weighted arithmetic average (EWAA), Hamacher weighted arithmetic aggregation (HWAA), Ordered Weighted Averaging (OWA), and Ordered Weighted Geometric (OWG) operators, where identical ranks were obtained. The conducted sensitivity analysis based on a Monte Carlo simulation confirms that classical MCDM methods provide stable and reliable results under conditions of perturbations of expert weights and ranks, while aggregation operators show significantly lower robustness and consistency. The aforementioned shows that MCDM methods can be a reliable and practical tool for group decision-making, i.e., the aggregation of expert opinions, with the advantage of generating final ranks without additional post-analysis.
Copyright (c) 2026 Dusko Tesic, Dragan Pamučar, Darko Božanić, Gülay Demir, Adis Puška (Author) https://creativecommons.org/licenses/by/4.0
Fuzzy Logic Base Large-Scale Urban Traffic Signal Optimization Using Circular Complex Pythagorean Fuzzy Sets and Intelligent Hybrid Machine Learning
Large-scale urban traffic networks operate under highly dynamic, nonlinear, and uncertain conditions, where fluctuating traffic demand, incomplete sensor data, and unpredictable driver behavior make real-time signal optimization a complex decision-making challenge. To address these issues, this study introduces the concept of Circular Complex Pythagorean Fuzzy Sets (CrC-PFS) for modeling uncertainty in urban traffic signal control problems. The proposed CrC-PFS framework extends classical Pythagorean fuzzy sets, Complex Pythagorean fuzzy sets, and circular Pythagorean fuzzy environments by providing greater flexibility in representing membership, non-membership, and hesitation degrees under periodic and time-varying traffic patterns. To enhance computational capability, we establish refined algebraic operational laws for CrC-PFS, including direct sum, direct product, and scalar multiplication operators based on generalized t-norm and t-conorm structures. In addition, Circular Complex Pythagorean fuzzy weighted averaging and ordered weighted aggregation operators are developed to integrate multiple traffic performance indicators such as queue length, delay time, saturation flow, and emission levels within a multi-criteria decision-making framework. Furthermore, an intelligent hybrid machine learning mechanism is incorporated to dynamically learn traffic flow patterns and adapt signal timing strategies in large-scale urban networks. By integrating fuzzy uncertainty modeling with predictive learning algorithms, a robust optimization framework is constructed for adaptive traffic signal coordination. The experimental findings demonstrate that the proposed model significantly improves traffic efficiency, reduces congestion levels, and enhances overall network resilience, thereby supporting sustainable and uncertainty-aware urban transportation management.
Circular Complex Pythagorean fuzzy sets fuzzy set
Copyright (c) 2026 Kaleem Ullah, Noor Rehman, Abbas Ali (Author) https://creativecommons.org/licenses/by/4.0
Integrating Artificial Intelligence for Sustainable Development: A Fuzzy Decision-Making Approach
Artificial Intelligence (AI) is reshaping various sectors and offers powerful potential to support sustainable development goals (SDGs) across Africa. Nevertheless, its full adoption remains restricted by context-specific challenges within the region, which hinder its large-scale implementation. This study applies a fuzzy simple weight calculation (F-SIWEC) method to systematically assess strategies for optimizing AI for sustainable development (SD) in Africa. Data were collected from four domain experts who evaluated six strategies, and the adopted method was then applied to determine the relative importance of each strategy. The results reveal that infrastructure and connectivity, human capital and AI literacy, and regulatory frameworks and ethical guidelines constitute the three most important strategies to optimize AI for SD on the continent. The study makes a meaningful contribution to the decision sciences and management literature by offering practical insights for legal experts, technologists, representatives from civil society, and policymakers, and concludes by outlining clear avenues for future research.
Copyright (c) 2026 Mouhamed Bayane Bouraima (Author) https://creativecommons.org/licenses/by/4.0
Emerging Trends and Research Insights in Fuzzy Multi-Criteria Decision-Making Applications for Logistics Location Selection: A Comprehensive Bibliometric Analysis (1982-2025)
Selecting an appropriate location is a pivotal decision in logistics. Multi-Criteria Decision-Making (MCDM) methods have gained considerable attention for their effectiveness in identifying optimal logistics sites. This paper explores the evolution, applications, and prospects of Fuzzy MCDM methods in logistics location selection. Through an extensive bibliometric analysis of 35,566 relevant papers sourced from the Web of Science (WoS) database spanning 1982 to 2025, this study uncovers key trends, influential authors, major institutions, and the geographical distribution of research contributions, employing tools such as VOSviewer 1.6.20. The findings indicate that China has established itself as the leading country in terms of published papers. At the same time, Edmundas Kazimieras Zavadskas emerges as the most prolific author in this bibliometric review. The United Kingdom is highlighted for its robust international co-authorship networks. Additionally, King Abdulaziz University is recognized as a significant institution fostering global collaborations, with Zavadskas noted as a central figure in the author collaboration network. Moreover, the journal IEEE Access is the most frequently cited publication outlet for related work. Commonly used key terms among authors include decision making, machine learning, and fuzzy logic. The findings also indicate that the most frequently discussed topics related to the United Nations Sustainable Development Goals (SDGs) are Industry, Innovation and Infrastructure, followed by Sustainable Cities and Communities and Well-being and Health. This study offers a comprehensive overview of research on Fuzzy MCDM methods for logistics location selection, providing valuable insights for future research directions in this rapidly evolving field.
Copyright (c) 2026 Emre Kadir Özekenci, Kübra Topcuoglu Onat, Süreyya Yilmaz Özekenci (Author) https://creativecommons.org/licenses/by/4.0
Data-Driven Large-Cap US Stock Price Forecasting Using a Hybrid MCDM-Machine Learning Approach
This study investigates the enhancement of stock price forecasting for the large-cap sector of the U.S. market through the integration of objective weights derived from multi-criteria decision-making (MCDM) methods. Due to the inherent complexities and volatility of stock markets, traditional forecasting approaches often struggle to provide accurate predictions. In this research, MCDM techniques such as EW, SD, MEREC, SECA, CRITIC, CILOS, and WENSLO are applied to assign appropriate weights to various input features, thereby improving the predictive capabilities of stock price models. The proposed methodology utilizes historical stock price data alongside objectively determined weights to train advanced machine learning models, including transformer neural networks. The findings of this study demonstrate that the application of MCDM weighting techniques to input features significantly enhances the forecasting performance of the transformer neural network model. This research not only contributes to the field of stock price prediction but also offers a framework for applying objective feature-weighting methods in various financial forecasting contexts.
Copyright (c) 2026 Mehmet Ozcalici, Nazli Ersoy, Dragan Pamucar (Author) https://creativecommons.org/licenses/by/4.0
Fuzzy Compromise Approach for Solving Stochastic Multi-objective q-Rung Orthopair Fuzzy Linear Programming Problem
The model considered in this study is a multi-objective linear programming (MOLP) model under uncertainty, in which the coefficients of the objective functions are represented by q-rung orthopair fuzzy numbers (q-ROFNs), while the right-hand side constraint parameters are treated as probabilistic quantities. The random variables are assumed to follow known probability distributions and are characterized by specified means and variances. By employing an appropriate score function and considering several probability distributions, namely Gamma, log-normal, and exponential distributions, the initial probabilistic q-rung orthopair fuzzy (q-ROF) MOLP problem is transformed into an equivalent deterministic MOLP model. The Zimmermann methodology with linear membership degrees (MDs) is then applied to represent the preferences of the decision-maker and obtain a satisfactory compromise solution. A numerical example is provided to demonstrate the applicability and efficiency of the proposed methodology. The study concludes with final observations and suggestions for future research.
Copyright (c) 2026 Sultan S. Alodhaibi, Hissah Ibrahim Almuzini, Hamiden Abd El-Wahed Khalifa (Author) https://creativecommons.org/licenses/by/4.0
A Systematic Review of integrated GIS and MCDM methodology for Wind Farm Site Selection: Trends, Methods, and Criteria
Wind energy has emerged as one of the most promising renewable energy sources and a sustainable alternative to conventional fossil fuels. However, selecting suitable locations for wind farms is a complex process that depends on several factors, including social, technological, economic, and environmental aspects. Over the past decade, academics have increasingly employed combinations of Geographic Information Systems (GIS) and Multi-Criteria Decision-Making (MCDM) techniques to address the challenges of wind farm location selection. This tendency is reflected in the significant number of scholarly papers on the subject. To give researchers a state-of-the-art perspective and a thorough understanding of current approaches, a comprehensive review of 147 studies published between 2015 and 2025 was carried out. A constructed taxonomy that encompasses GIS software, application fields, uncertainty treatment, MCDM techniques, spatial resolution in GIS, and site selection criteria was used to classify the examined studies. The most popular MCDM techniques for criterion weighting and ranking of alternatives are the Analytical Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods. An examination of the criteria reveals that wind speed, slope, land use, distance from transmission lines, road proximity, environmental restrictions, and social acceptance are the most frequently considered factors during wind farm site selection. Identifying research gaps, improving modelling techniques, and facilitating well-informed decision-making in future wind energy development initiatives are all made possible by these classifications and insights.
Copyright (c) 2026 Emhemed Algazel, Ibrahim Badi (Author) https://creativecommons.org/licenses/by/4.0
Quantifying Multi-Cause Psychological Disorder Risk Through an Advanced Mathematical Model Using Intuitionistic Pentagonal Fuzzy Logic
The evaluation of psychological disorders is a very complicated and sensitive area of study, where emotions, thoughts, and the mental states of different patients are analyzed on the basis of questionnaires and observational techniques. The identification and analysis of people's mental states, emotions, and behaviors are difficult and limited with the aid of conventional approaches since the data gathered from these factors appear to be vague, uncertain, and imprecise. To demonstrate this information systematically, we have proposed a comprehensive mathematical model able to deal with indeterminate and imprecise data, utilizing Intuitionistic Pentagonal Fuzzy Numbers (IPnFNs). To create a coherent mathematical framework, IPnFNs integrate five values of membership and non-membership functions of any constraint, providing an innovative numerical framework that effectively explains the assessment of diagnosis and the patient's condition. The research study analyzes several key psychiatric disorders, such as childhood psychiatric problems, hormonal changes, social stress, cognitive distortions, anxiety, and traumatic life events, as the main factors. The proposed technique provides psychologists with a thorough and clear picture of the issue by depicting the patient's mental health numerically. The research is significantly helpful in cases where the symptoms of psychological illness are not obvious or the patient's information is imprecise or confusing. Furthermore, a comparative analysis of various patients can be developed using the proposed technique, assisting in assessing severity and diagnosis preferences. This mathematical method shows that the use of IPnFNs can be a reliable and scientific method in the evaluation of psychological disorders. This approach is significantly applicable in educational counseling and clinical psychology, where it is a daily routine for individuals to deal with imprecise and inconsistent data in mental health issues while making decisions.
Intuitionistic Pentagonal Fuzzy Framework
Copyright (c) 2025 Aiman Ishtiaq, Khadija Tul Kubra, Anns Uzair, Awais Ali (Author) https://creativecommons.org/licenses/by/4.0
Prioritizing MSMEs based on Technology Adoption Capabilities: A Fuzzy SAW-COPRAS Approach
Emerging economies have started focusing on micro, small, and medium enterprises (MSMEs) as they see a lot of potential in these businesses. Quite often, these sectors are unorganized, but there is a significant contribution to the economy from them. Industry 4.0 has emphasized automation and encouraged the use of technologies. In this context, upskilling and reskilling are required. At the ground level, such technological adoptions are not direct, and the implementation of such technologies incurs challenges that affect the process of adoption. This paper presents a combined decision approach for the prioritization of MSMEs based on technology adoption capabilities. It must be noted that the presented framework attempts to prioritize MSMEs based on their ability to handle technology adoption issues. Notably, every MSME undergoes a transition in social, economic, and environmental contexts when shifting to technology-driven solutions. To facilitate the process and aid in better understanding, this paper puts forward a combined decision approach. First, the technology adoption factors are presented based on a literature review and discussions with MSME stakeholders. Later, Fuzzy SAW is used to determine the weights of tech-adoption criteria. These weights signify the relative importance of each criterion. Likewise, Fuzzy COPRAS is used to assign priority values to MSMEs. We consider the simple and straightforward procedure along with its ability to understand the criteria type before making a decision. Implications are discussed to support policymakers. A case example from India is considered to determine the usefulness of the proposed model. The results indicate that the top three criteria are lack of skillset (T5), infrastructure mismatch (T6), and high initial cost (T7), which are used to prioritize MSMEs.
Copyright (c) 2025 Kattur Soundarapandian Ravichandran, Durga Nandhini (Author) https://creativecommons.org/licenses/by/4.0
Research on the Redefined Square Root Interval-valued Normal Pythagorean Fuzzy Multi-Attribute Decision-Making Model Based on Aggregation Operators
In this paper, we construct new multiple attribute decision-making (MADM) problems using the redefined square root interval-valued normal Pythagorean fuzzy set (RSIVNPFS). The interval-valued Pythagorean fuzzy sets (IVPFSs) and square root PFSs are extended by the square RSIVNPFS. We introduce RSIVNPF weighted averaging (RSIVNPFWA), RSIVNPF weighted geometric (RSIVNPFWG), generalized RSIVNPFWA (RSGIVNPFWA), and generalized RSIVNPFWG (RSGIVNPFWG). Idempotence, boundedness, commutativity, and monotonicity in algebraic operations are all satisfied by RSIVNPFSs. We develop an algorithm for dealing with MADM problems using the aggregation operators (AOs). The applications of the Euclidean distance (ED) and the Hamming distance (HD) are described using examples from everyday scenarios. We also compare several suggested and current models to show the validity and applicability of the models. Our objective is to compare expert opinions with the criteria in order to determine the best option and to demonstrate the superiority and validity of the suggested AOs.
Copyright (c) 2025 Murugan Palanikumar, Nasreen Kausar (Author) https://creativecommons.org/licenses/by/4.0
Sustainable Urban Development: q-Rung Orthopair Fuzzy MCDM with Generalized Power Prioritized Yager Aggregation
In light of accelerating urbanization and the intensifying challenges of climate change, ensuring sustainability and resilience in urban environments has become a strategic imperative. This study introduces an innovative methodology that combines Multi-Criteria Decision Making (MCDM) with q-rung orthopair fuzzy Yager aggregation operators (q-ROFYAOs) to address the multifaceted complexities of sustainable urban development. The paper proposes novel Yager operations grounded in Yager t-norms within the framework of q-rung orthopair fuzzy sets (q-ROFSs). Utilizing these foundations, two advanced aggregation operators are formulated: the q-Rung Orthopair Fuzzy Generalized Power Prioritized Yager Weighted Average Operator (q-ROFGPOPRYWA) and the q-Rung Orthopair Fuzzy Generalized Power Prioritized Yager Weighted Geometric Operator (q-ROFGPOPRYWG). These operators satisfy essential mathematical properties, including idempotency, monotonicity, and boundedness, ensuring consistency and reliability in decision-making contexts. To demonstrate the practical relevance of the proposed approach, the operators are embedded within an MCDM framework and applied to a real-world case study on sustainable urban planning. The analysis encompasses sensitivity testing, comparative evaluations, and performance assessments, offering comprehensive insights into the robustness of the method. Finally, the paper provides a critical evaluation of the advantages and limitations of the proposed operators, underscoring their effectiveness in promoting urban resilience and minimizing environmental impact within complex decision-making environments.
Copyright (c) 2026 Subramanian Petchimuthu, Balakrishnan Palpandi, K Rajakumar, Fathima Banu M (Author) https://creativecommons.org/licenses/by/4.0
Stochastic Models for Autonomous Systems and Robotics
The field of robotics is rapidly evolving with the development of autonomous systems capable of operating in dynamic and uncertain environments. A key challenge is ensuring that these systems can reliably make decisions and execute tasks despite inherent uncertainties. Stochastic modeling provides a crucial mathematical framework to address these uncertainties by incorporating randomness and variability in system behavior and external conditions. This paper explores the role of stochastic models in autonomous systems, particularly in navigation, decision-making, and task execution, and how they integrate with artificial intelligence and machine learning to enhance system robustness and adaptability. A case study on autonomous vehicles (AVs) demonstrates the application of stochastic models, highlighting the use of Markov Decision Processes (MDPs) for path planning, Kalman filters for sensor fusion, and Monte Carlo methods for probabilistic localization. Through detailed mathematical and computational analyses, we show how these stochastic methods help AVs navigate uncertain urban environments, improving decision-making and overall system performance.
Copyright (c) 2026 Shankha Shubhra Goswami, Surajit Mondal (Author) https://creativecommons.org/licenses/by/4.0
Sustainable Supplier Selection Based on a Comparative Decision-Making Approach Under Uncertainty
Nowadays, due to the increasing awareness of sustainability and green issues worldwide, companies are forced to implement sustainable projects in their supply chain (SC) to maintain and increase their competitive advantage. To enhance business performance and gain a competitive edge, it is crucial to select green and sustainable suppliers in the supply chain, as they play a vital role in executing sustainable projects. Therefore, this research was conducted to select sustainable suppliers in the SC. Initially, a list of indicators for selecting sustainable suppliers was extracted, and these indicators were adjusted and finalized using the fuzzy Delphi technique. Also, the Step-wise Weight Assessment Ratio Analysis (SWARA) technique was used for weighting, and the Fuzzy Weighted Aggregates Sum-Product Assessment (F-WASPAS) technique was used for prioritizing suppliers. In addition, the robustness of the findings was examined using a comparative analysis of different decision methods in a fuzzy environment. The weighting results showed that the product price, transportation cost, and green design and purchasing indicators were of the highest importance, respectively. Moreover, the results of the supplier ranking revealed that the first supplier had the highest priority.
Copyright (c) 2026 Seyyed Jalaladdin Hosseini Dehshiri (Author) https://creativecommons.org/licenses/by/4.0
Analysis of Innovation Performance of South- Eastern European Countries in Transition Economies: An Application of the Entropy-Based ARTASI Method
Innovation performance has emerged as a crucial policy concern for nations undergoing institutional change and economic restructuring. Using a novel hybrid multi-criteria decision-making (MCDM) framework, this study assesses the innovation capacities of five transition economies in South-Eastern Europe: Albania, Bosnia and Herzegovina, Montenegro, North Macedonia, and Serbia. Although the Global Innovation Index (GII) is widely regarded as a comprehensive benchmarking tool, its aggregated scoring system often obscures contextual subtleties, particularly in smaller or less-studied economies. To address these limitations, this study combines the ARTASI ranking model with objective weighting methods—Entropy and CRITIC—providing a transparent, flexible, and reproducible evaluation framework. The results indicate that output-oriented indicators—such as Knowledge and Technology Outputs, Market Sophistication, and Creative Outputs—are the most significant factors in differentiating national innovation performance. Among the analyzed countries, Serbia leads the regional ranking, followed by North Macedonia and Montenegro, while Albania and Bosnia and Herzegovina exhibit notable output-related deficiencies. Robustness checks—including sensitivity analysis and cross-validation with alternative MCDM techniques—confirm the model's stability and reliability. Beyond addressing a geographic gap in the innovation literature, this study offers a methodologically refined approach to innovation evaluation. The proposed framework can serve as a foundation for comparative research in similar socioeconomic contexts and guide evidence-based policymaking in transition economies.
Copyright (c) 2026 Gökhan Çobanoğulları, Kübra Daldiran, Bünyamin Daldiran (Author) https://creativecommons.org/licenses/by/4.0
A Study for Application of Decision Making Model in a Public Organization
Decision-making can be regarded as an outcome of mental processes leading to the selection of a course of action among numbers of alternatives available at a point of time. Each decision making process produces a final choice and the output will be an action or an opinion of choice (Decision Making). Decision making is, however, only a step in planning, even when it is taken quickly, with little thoughts and information or when it effects action for few minutes only. Everyone takes decision daily in his life for every course of action. Seldom there is a chance to judge a course of action in isolation, as every decision has to gear up other plans. In public organization consensus can be a goal, not a mandate for public decision-making. Public policies are the mixture of our values and opinions, technical knowledge and abilities, and political set up. These are the views often conflict with one another, but when they differ from the individual views, generate disregard for the opinions and perspectives of others.
Copyright (c) 2026 Divanshu Mittal (Author) https://creativecommons.org/licenses/by/4.0
Enhancing Web Security Through Complex Cubic q-Rung Orthopair Fuzzy Information
Over the past two decades, the evolution of web services has profoundly transformed communication and information technologies. As computer programs that facilitate data exchange and interoperability between applications via the Internet, web services play a pivotal role in enabling seamless interactions and information access. However, despite their advantages, these platforms also introduce significant security risks. This study leverages the novel framework of Complex Cubic q-Rung Orthopair Fuzzy Sets (CCuqROFS) to model and address these security threats effectively. Unlike conventional models, CCuqROFS provides a robust structure that incorporates membership (M) and non-membership (NM) degrees, offering a more precise representation of uncertainty. Through illustrative examples, we introduce key concepts such as Complex Cubic q-Rung Orthopair Fuzzy Relations (CCuqROFR), the Cartesian product of CCuqROFSs, and various forms of CCuqROFRs. For the first time in fuzzy set theory, this work systematically examines the relationships between different security threats and countermeasures in web services. The proposed methodologies demonstrate how robust security measures can mitigate the impact of these threats. Finally, a comparative analysis underscores the advantages of our strategies, providing valuable insights for enhancing web service security.
Complex cubic q-rung orthopair fuzzy set
Complex cubic q-rung orthopair fuzzy relations
Copyright (c) 2026 Shoukat Hussain (Author) https://creativecommons.org/licenses/by/4.0
Investigation of Threats to Data States in Data Loss Prevention Using the Concept of Complex Linear Diophantine Fuzzy Relations
In today's digital age, many operational decisions in businesses rely on data sources, enabling organizations to enhance productivity, make informed decisions, and gain competitive advantages. However, businesses also face data breaches involving sensitive information—such as financial records, intellectual property, and customer personal data—which may be compromised inadvertently. These threats can often be mitigated by implementing robust cybersecurity measures, such as Data Loss Prevention (DLP), to ensure proper monitoring and control of all organizational data, enforce policies without exceptions, and prevent unauthorized data transfers or rule violations. Despite these measures, uncertainties remain regarding the efficacy of identifying threats at various stages of data loss to mitigate their adverse effects through effective cybersecurity. To address this, this paper introduces Complex Linear Diophantine Fuzzy Relations (CLDFRs). For the first time in fuzzy set theory, we analysed the relationships between various threats and components of DLP-based data loss solutions. Additionally, we present the concept of Hasse diagrams for Complex Linear Diophantine Fuzzy Sets and Relations to examine different cybersecurity methods and procedures. This approach helps determine the most effective strategy based on Hasse diagram analysis. Furthermore, after applying specific constraints to the decision-making process, the optimal cybersecurity approach is selected. Finally, a comparative analysis demonstrates the advantages of the proposed methods.
Complex Linear Diophantine Fuzzy Relation
Copyright (c) 2026 Sami Ullah Khan, Abdul Nasir, Malaika Marwat (Author) https://creativecommons.org/licenses/by/4.0
Evaluation of Purchasing Process in Solar Energy Investment Projects via SIWEC Methodology
Solar energy investments involve financial and technological commitments aimed at generating electricity or heat from sunlight. Direct electricity production is achieved through solar panels, while concentrated sunlight produces high-temperature energy. The importance of solar energy investments can be assessed from multiple perspectives. These projects reduce carbon emissions by decreasing reliance on fossil fuels. Solar energy investments are becoming increasingly vital, particularly in alignment with energy transition and sustainable development goals. In short, solar energy is a sustainable and environmentally friendly power source. It also enhances energy access in rural areas through off-grid energy production. To identify the critical factors influencing procurement performance in solar energy investments, a novel decision-making model is proposed, incorporating the SIWEC technique. The findings reveal that strategy definition is the most crucial aspect of the procurement process in solar energy investments. A common digital platform should be implemented across all company units to improve coordination in project and procurement processes. This platform enables real-time tracking of business plans, ensuring timely service delivery and more effective project risk management. Additionally, robust project management software should be utilized to monitor all stages of solar energy projects. Such tools help streamline supply processes, meet material requirements on time, and optimize costs. Potential disruptions in project planning can be identified early through digital systems, further reducing operational expenses. A transparent, data-driven supplier evaluation and selection process should be established to identify the most suitable suppliers for solar energy investments. Supplier performance must be monitored, evaluated, and reviewed periodically. Selecting the right supplier enhances project quality and overall efficiency.
Copyright (c) 2026 Enes Şimşek, Serkan Eti, Serhat Yüksel, Hasan Dinçer (Author) https://creativecommons.org/licenses/by/4.0
Fundamental Characteristics and Applicability of the RADAR Method: Proof of Ranking Consistency
This paper presents a mathematical explanation of one of the Multi-Attribute Decision-Making (MADM) methods—the Ranking based on Distance and Range (RADAR) method—along with its modified variant, RADAR II. Through mathematical proofs, the influence of each step of the method on the final ranking of alternatives is analyzed. The methods are tested on three numerical examples with varying criterion weights. The robustness of the methods, as well as their fundamental characteristics, is demonstrated. A comparative analysis reveals that although both methods prioritize alternatives based on their stability across all criteria—particularly the most important ones—the RADAR II method is somewhat more rigorous and stringent, whereas the original RADAR method is more flexible and yields more objective results.
Copyright (c) 2026 Nikola Komatina, Dragan Marinkovic, Matej Babič (Author) https://creativecommons.org/licenses/by/4.0
Interpretable Robust Multicriteria Ranking with TODIM in Generalized Orthopair Fuzzy Settings
The endeavor to align TODIM (an acronym in Portuguese for interactive and multicriteria decision making) with prospect theory has given rise to the development of several variant methods, including power TODIM, exponential TODIM, and logarithmic TODIM. However, these existing methods fail to address high-order uncertainty within generalized orthopair fuzzy environments. To overcome this limitation, we propose an interpretable robust TODIM approach tailored for generalized orthopair fuzzy settings. First, we extend these TODIM methods to accommodate generalized orthopair fuzzy settings, integrating them into a unified framework. Second, we introduce a set of robustness analysis measures for the extended TODIM method, accounting for simultaneous uncertainty in criteria weights, value function coefficients, and the membership and non-membership degrees of generalized orthopair fuzzy sets. Third, we develop a programming model to determine representative criteria weights based on these robustness analysis measures, followed by an approach to recommend an interpretable and robust ranking within the extended TODIM framework. Finally, we present an illustrative example to demonstrate the application of this interpretable and robust TODIM approach, accompanied by a comparative analysis to highlight its advantages.
Copyright (c) 2026 Wenkai Zhang, Hengxia Gao (Author) https://creativecommons.org/licenses/by/4.0
A Study on DEMATEL Approach Under Uncertainty Environments
A fuzzy set is a mathematical construct that assigns a membership grade to each element within a universe of discourse, representing the degree to which the element belongs to the set. This approach extends classical binary logic by allowing continuous values between 0 and 1, making it a natural framework for handling uncertainties and vague concepts often expressed in natural language. Fuzzy sets are particularly powerful in modelling real-world scenarios where ambiguity and imprecision are inherent, such as in human decision-making, linguistic expressions, and complex systems. This paper introduces a novel application of fuzzy logic by proposing a fuzzy Decision Making Trial and Evaluation Laboratory (DEMATEL) method. DEMATEL is a well-established technique used to analyse cause-and-effect relationships within complex systems. Still, its traditional form relies on crisp values, which may not adequately capture the inherent uncertainties in real-world data. Our proposed method integrates triangular fuzzy numbers into the DEMATEL framework, enabling the representation and analysis of data with imprecision and vagueness. Specifically, we apply the fuzzy DEMATEL approach to study the cause-and-effect relationships among factors affecting transgender individuals, a population often marginalized and underrepresented in research. By leveraging triangular fuzzy numbers, our method provides a more nuanced and realistic representation of the uncertainties and complexities in the data. This approach not only enhances the accuracy of the analysis but also offers a meaningful way to interpret vague or subjective information, ultimately contributing to more informed decision-making and policy development for transgender communities.
Decision Making Trial and Evaluation Laboratory
Copyright (c) 2026 Saraswathi Appasamy (Author) https://creativecommons.org/licenses/by/4.0
Sustainable Urban Transportation: Key Criteria for a Greener Future
A sustainable transportation network has become increasingly critical for society as urban growth, environmental challenges, and transport system inefficiencies intensify. The seamless application of multi-criteria decision analysis (MCDA) as an analytical framework enables the identification, weighting, and ranking of key sustainability criteria across economic indicators, environmental factors, and social sustainability measures. The Fuzzy Logarithm Methodology of Additive Weights (F-LMAW) serves as an analytical tool to evaluate, weigh, and rank these criteria under uncertain conditions. In this study, F-LMAW—incorporating Triangular Fuzzy Numbers (TFNs)—is applied to assess sustainable transport criteria across different sustainability dimensions. The analysis integrates expert surveys, current literature, and findings from completed transportation projects to introduce five new sustainability criteria. The results reveal that safety, health, and greenhouse gas emissions are the most critical sustainability factors. Furthermore, transportation system design should prioritize human well-being and environmental protection. While economic factors, particularly infrastructure costs, remain essential, they must be evaluated alongside long-term operational sustainability requirements. This research provides a structured approach to help authorities systematize transportation funding decisions, optimize resource allocation, and integrate sustainable practices into urban transport systems.
Copyright (c) 2026 Kiana Nayeb-Pashaei, Sahand Vahabzadeh, Amin Hosseinian-Far, Saeid Jafarzadeh Ghoushchi (Author) https://creativecommons.org/licenses/by/4.0
Fuzzy SIWEC and Fuzzy RAWEC Methods for Sustainable Waste Disposal Technology Selection
Rapid industrialization, population growth, and poor waste management have led to significant environmental and economic challenges. These issues underscore the need for effective disposal technologies to mitigate public health risks, reduce greenhouse gas emissions, and promote resource recovery. This study aims to determine the most suitable sustainable solid waste disposal technology for the planned Çivril Solid Waste Disposal Facility in Denizli Province. To evaluate eight disposal alternatives: landfilling (A₁), composting (A₂), biomethanization (A₃), incineration (A₄), gasification (A₅), plasma treatment (A₆), pyrolysis (A₇), and refuse-derived fuel (RDF) (A₈), we employed fuzzy-based Multi-Criteria Decision-Making (MCDM) methods: the Simple Weight Calculation (SIWEC) and Ranking Alternatives with Weights of Criterion (RAWEC). Twelve criteria, including environmental impact, legal compliance, and operational costs, were weighted using Fuzzy SIWEC, while the alternatives were ranked using Fuzzy RAWEC. The results identified composting (A₂) as the most suitable technology, whereas RDF (A₈) performed the worst. Validation through comparison with other MCDM methods (F-TOPSIS, F-SAW, F-MABAC, and CORASO) demonstrated high consistency. Sensitivity analysis confirmed that composting (A₂) and gasification (A₅) maintained stable rankings across different scenarios, while the rankings of other methods varied depending on decision-maker preferences. The integrated use of fuzzy-based SIWEC and RAWEC provides a reliable and systematic framework for sustainable waste management decision-making.
Copyright (c) 2026 Ali Katranci, Nilsen Kundakci, Kevser Arman (Author) https://creativecommons.org/licenses/by/4.0
Shadowed Offset: Integrating Offset and Shadowed Set Frameworks for Enhanced Uncertainty Modeling
Uncertainty‑handling frameworks—including Fuzzy Sets, Intuitionistic Fuzzy Sets, Hyperfuzzy Sets, Neutrosophic Sets, HyperNeutrosophic Sets, Soft Sets, Rough Sets, and Plithogenic Sets—have become fundamental tools for modeling imprecision and vagueness across diverse application domains. Classical fuzzy sets extend traditional set theory by assigning each element a membership degree within the unit interval [0,1], thereby capturing graded inclusion. To represent under‑ and over‑membership, many of these theories have been enriched with offset concepts that allow membership values to fall outside this canonical range. Shadowed sets complement these developments by employing two thresholds to partition the membership spectrum into three regions—excluded, included, and indeterminate—providing a compact mechanism for residual uncertainty. Despite the complementary strengths of offset and shadowed approaches, a unified formalism integrating both has not yet been explored. In this paper, we introduce the novel concept of the Shadowed Offset, which extends the shadowed‑set paradigm by permitting off‑interval membership while preserving tripartite thresholding. We present a rigorous mathematical definition of Shadowed Offsets, derive their fundamental properties, and illustrate their behavior through representative examples. The proposed construct offers a more flexible and expressive framework for complex uncertainty, and we conclude by outlining promising directions for future research.
Copyright (c) 2025 Takaaki Fujita (Author) https://creativecommons.org/licenses/by/4.0
Decision-Making Framework for Urban Transportation Using Linear Diophantine Fuzzy Z-numbers with Dombi Aggregation, TOPSIS and VIKOR Methods
This study proposes an innovative approach to decision-making under uncertainty, using Pakistan’s urban transportation issues—particularly in cities like Karachi, Lahore, and Islamabad—as a case study. These cities face severe traffic congestion, demanding more effective strategies for infrastructure planning. We introduce a Linear Diophantine Fuzzy Z-Numbers (LDFZN) framework that captures membership and non-membership grades alongside the degree of reliability, addressing key limitations of traditional fuzzy systems by simultaneously considering uncertainty and confidence. Within this framework, we develop three decision-making methods: an LDFZN Dombi Weighted Averaging operator that aggregates expert opinions while accounting for their reliability; an adapted VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method for multi-criteria compromise solutions under LDFZN settings; and a modified Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) tailored for LDFZN-based scenarios. These tools are applied to real-world transportation challenges in Pakistan, demonstrating their effectiveness in managing uncertainty and expert-based confidence levels. The results outperform conventional models in decision robustness and clarity under uncertain conditions. This work contributes significantly to the theoretical and practical advancement of fuzzy mathematics, extending uncertainty modeling and providing practical solutions not only for transportation but also for various fields requiring informed decision-making with imprecise and unreliable data.
Copyright (c) 2025 Rukhshanda Anjum, Muhammad Umar Mirza, Nasreen kausar, Rabia Ali (Author) https://creativecommons.org/licenses/by/4.0
Remote Sensing-Based Evaluation of Lake Area Dynamics: A Quantitative Assessment for Environmental Management in Turkey
This research employs remote sensing techniques and advanced image processing algorithms to analyze lake level changes. The study focuses on two major lakes in Turkey, Burdur and Salda, using satellite imagery from 2000 to 2024. The primary objective is to investigate spatial and temporal surface area changes over a one-year period. A key step in the process involves identifying water pixels in infrared band images through binarization and image processing, enabling accurate measurements of lake sizes and shapes. The results were evaluated using three criteria: R², RMSE, and MAPE. Findings showed that Burdur Lake experienced a 1.47% decrease, while Salda Lake had a smaller decline of 0.307% in 2024, attributed to drought and water resource availability.
Copyright (c) 2026 Shahryar Ghorbani, Dragan Pamucar (Author) https://creativecommons.org/licenses/by/4.0
Solution of Fuzzy System of Linear Equation Under Different Fuzzy Difference Ideology
Fuzzy arithmetic includes distinctive notions regarding differences between fuzzy numbers, which impact the defining characteristics of fuzzy-valued calculus. In this article, we consider the Hukuhara and generalized Hukuhara differences of fuzzy numbers for solving systems of linear equations under fuzzy-rule uncertainty within an analytical framework. Moreover, the discussion of solutions in parametric form includes existence and uniqueness criteria. Numerical examples and graphical representations are provided to illustrate the proposed theory.
Copyright (c) 2024 Payel Sing, Mostafijur Rahaman, Sankar Prasad Mondal Sankar (Author) https://creativecommons.org/licenses/by/4.0