Chebyshev distances associated to the second members of systems of Max-product/Lukasiewicz Fuzzy relational equations

Abstract

In this article, we study the inconsistency of a system of -product fuzzy relational equations and of a system of -Lukasiewicz fuzzy relational equations. For a system of - fuzzy relational equations A x = b and using the L∞ norm, (Baaj, 2023) showed that the Chebyshev distance = ∈fc ∈ C b - c , where C is the set of second members of consistent systems defined with the same matrix A, can be computed by an explicit analytical formula according to the components of the matrix A and its second member b. In this article, we give analytical formulas analogous to that of (Baaj, 2023) to compute the Chebyshev distance associated to the second member of a system of -product fuzzy relational equations and that associated to the second member of a system of -Lukasiewicz fuzzy relational equations.