Kybernetika 62 no. 4, 735-754, 2026

A note on resolving inconsistency of fuzzy relational equations on \Lukasiewicz algebra

Pingke LiDOI: 10.14736/kyb-2026-4-0735

Abstract:

The inconsistency of fuzzy relational equations is frequently encountered when modelling an inference system with fuzzy logic. A polynomial-time direct search procedure is designed to resolve the inconsistency for fuzzy relational equations on {\L}ukasiewicz algebra by minimizing the maximum absolute deviation to the right-hand side vector. Alternatively, a reformulation approach is proposed by minimizing instead the sum of absolute deviations. It results in a polynomial-sized mixed integer linear programming problem and hence, may be readily solved with the aid of an off-the-shelf optimization solver. This reformulation approach is flexible in nature and can be adjusted to deal with some other problems related to the inconsistency of fuzzy relational equations.

Keywords:

fuzzy relational equations, mixed integer linear programming, inconsistency, optimal approximation

Classification:

08A72, 15B15, 90C11

paper.pdf

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