Indian Journal of Science and Technology

Abstract

Objective: To introduce a new concept in the realm of fuzzy number theory, the "Trigonal Fuzzy Number" or "30-gonal Fuzzy Number." Unlike conventional fuzzy numbers with fixed and rigid membership functions, Trigonal Fuzzy Numbers present a versatile and adaptive framework for representing and managing uncertainty. Method: The study delves into the effective utilization of "Alpha Cuts" as a precise tool for quantifying and navigating uncertainty levels within Trigonal Fuzzy Numbers. Furthermore, it showcases essential arithmetic operations, including addition, subtraction, and multiplication, performed on Trigonal Fuzzy Numbers using Alpha Cuts, thus extending the boundaries of fuzzy arithmetic. Findings: This innovative approach demonstrates real-life applications across various domains, emphasizing its practicality and potential to revolutionize decision-making processes under uncertain conditions. The presented framework not only enriches fuzzy number concepts but also serves as a valuable asset for addressing real-world problems characterized by imprecision and ambiguity. Novelty: Innovatively, the article demonstrates the real-life applications of this novel approach in various domains, illustrating its practicality and potential for revolutionizing decision-making processes under uncertain conditions. The presented framework is not only conceptually enriching but also offers a valuable asset for addressing real-world problems where imprecision and ambiguity are inherent, thereby bridging the gap between theoretical fuzzy number concepts and practical decision support systems.

Keywords: Trigonal Fuzzy Numbers, Alpha Cuts, Fuzzy Arithmetic, Uncertainty Management, Decision Making