Development of a Compensatory Algebraic Operator for Fuzzy Matrices Based on the Arithmetic Mean (SAM)

Abstract

In this research, we introduce a new, more balanced approach called the Substitution Arithmetic Mean (SAM) operator. In fuzzy matrix theory, the standard Max-Min operator has a well-known problem; it consistently focuses on the smallest values, which causes the data to fade away or decay toward zero when we perform multiple operations. The introduction of a new (SAM) uses a compensatory logic that allows stronger data points to support weaker ones' loss. Through mathematical proofs and examples, we show that our (SAM) operator performs better than classical methods and keeps the data's meaning intact, which makes it a more reliable tool for real-world decision making.