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    Fully bipolar fuzzy linear systems: bounded and symmetric solutions in dual form
    (Springer nature, 2025) Muhammad, Ghulam; Allahviranloo, Tofigh; Hussain, Nawab; Mrsic, Leo
    The aim of this article is to develop a new and simple technique to determine the approximate fuzzy solution of the fully bipolar fuzzy linear system of equations (BFLSEs) AU = eta, where U and eta are the triangular bipolar fuzzy vectors and A is either the crisp or fuzzy matrix. The solution of the proposed system is extracted in two fold. First, we obtain the crisp solution of the proposed system. To achieve this, we solve the BFLSEs using(-1,1)-cut expansion. Second, we assign unknown symmetric parameters to each row of this crisp system in(-1,1)-cut expansion. Thus, this system will transform into a system of interval equations. The unknown symmetric parameters corresponding to each element of a bipolar fuzzy vector are obtained by solving such an interval system of equations. Additionally, we demonstrate that the bounded and symmetric solutions (B&SSs) of the fully BFLSEs will reside within the tolerable solution set (TSS) and in the controllable solution set (CSS), respectively. To enhance the novelty of the proposed technique, we present several theorems that serve as a formal foundation for our approach. Furthermore, a numerical example is provided to demonstrate the effectiveness and validity of the proposed technique.
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    Multicriteria Group Decision Making Based on TODIM and PROMETHEE II Approaches with Integrating Quantum Decision Theory and Linguistic Z Number in Renewable Energy Selection
    (Multidisciplinary Digital Publishing Institute (MDPI), 2024) Mandal, Prasenjit; Mrsic, Leo; Kalampakas, Antonios; Allahviranloo, Tofigh; Samanta, Sovan
    Decision makers (DMs) are often viewed as autonomous in the majority of multicriteria group decision making (MCGDM) situations, and their psychological behaviors are seldom taken into account. Once more, we are unable to prevent both positive and negative flows of varying alternative preferences due to the nature of attributes or criteria in complicated decision-making problems. However, DMs’ perspectives are likely to affect one another in complicated MCGDM issues, and they frequently use subjective limited rationality while making decisions. The multicriteria quantum decision theory-based group decision making integrating the TODIM-PROMETHEE II strategy under linguistic Z-numbers (LZNs) is designed to overcome the aforementioned problems. In our established technique, the PROMETHEE II controls the positive and negative flows of distinct alternative preferences, the TODIM method manages the experts’ personal regrets over a criterion, and the quantum probability theory (QPT) addresses human cognition and behavior. Because LZNs can convey linguistic judgment and trustworthiness, we provide expert LZNs for their viewpoints in this work. We determine the criterion weights for each expert after first obtaining their respective expert weights. Second, to represent the limited rational behaviors of the DMs, the TODIM-PROMETHEE II approach is introduced. It is employed to determine each alternative’s dominance in both positive and negative flows. Third, a framework for quantum possibilistic aggregation is developed to investigate the effects of interference between the views of DMs. The views of DMs are seen in this procedure as synchronously occurring wave functions that affect the overall outcome by interfering with one another. The model’s efficacy is then assessed by a selection of renewable energy case studies, sensitive analysis, comparative analysis, and debate. © 2024 by the authors.