An Algebraic Composition Operator on Intuitionistic Fuzzy Soft Set Evaluations for Multi-Evaluator Decision-Making

In multi-evaluator decision-making, it is important not only to aggregate fuzzy information but also to preserve the structural and algebraic properties of each evaluation. This paper proposes a binary composition operator between evaluators, each represented as an Intuitionistic Fuzzy Soft Set (IFSS), where every evaluator is treated as a full parametric fuzzy object. The composition uses the Einstein product for membership degrees and the Einstein sum for non-membership degrees. The proposed operator is proven to satisfy four key algebraic properties: closure, associativity, identity, and commutativity. These properties make the model suitable for structured evaluation processes, whether applied sequentially or in parallel. The final result remains within the IFSS domain and can be interpreted using a symbolic score (µ − ν). A simple case study on system selection demonstrates how this approach supports collective evaluation in a lightweight and transparent manner while maintaining the fuzzy semantics of the original input.