Asian Journal of Current Research

This study compares the behaviour of the max-min, max-product, and max-average composition operators in a symmetric fuzzy relation. The work focuses on whether these operators preserve symmetry under self-composition and how their resulting membership values differ. To support the comparison, the manuscript first outlines the relevant concepts of fuzzy sets, fuzzy relations, fuzzy equivalence relations, and the three composition operators. It then applies each operator to the same symmetric fuzzy relation represented by a 3 × 3 membership matrix. The theoretical discussion shows that max-min, max-product, and max-average self-compositions preserve symmetry when the original fuzzy relation is symmetric. The numerical example further demonstrates that the operators generate different membership strengths despite retaining the same structural property. In the example, max-product produces comparatively weaker indirect membership values, max-average produces stronger values, and max-min gives a balanced outcome. These findings indicate that the selection of a composition operator affects the strength of inferred fuzzy relationships, although it does not change the preservation of symmetry in the examined case. The comparison is therefore useful for identifying how different operators process indirect associations within the same relation matrix. The study provides a concise comparative account of the three composition methods for symmetric fuzzy relation analysis.