A study of Bipolar valued shadowed set theory and its application in decision-making problems

Bipolar-Valued Fuzzy Sets (BVFS) capture positive and negative information, yet their high computational cost hampers large-scale decision problems. We fuse BVFS with shadowed-set theory to create Bipolar-Valued Shadowed Sets (BVSHS) that discretize the membership range into three crisp regions, positive, negative, and shadow, via two automatically learnt thresholds. This research provides formal definitions of complement, union, intersection, null, absolute, and subset operators and proves algebraic closure. The BVSHS reduction algorithm is tested on a paint-selection problem involving ۱۰ experts, ۴ paint types, ۵ criteria, and benchmarked against the original BVFS approach. BVSHS reduced memory footprint and runtime. In the paint-selection task, both BVFS and BVSHS identified the same optimal paint type (P₃), but BVSHS reached this conclusion with only three discrete evaluations per alternative instead of full interval computations. BVSHS delivers a lightweight, mathematically rigorous, and decision-accurate alternative to BVFS for bipolar information processing; it is particularly suited for real-time or resource-constrained applications.

کلیدواژه ها:

Fuzzy Sets ، Bipolar valued fuzzy sets ، Shadowed sets ، Bipolar valued shadowed sets