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

In this article, we study the inconsistency of a system of max-product fuzzy relational equations and of a system of max-Lukasiewicz fuzzy relational equations. For a system of max-min fuzzy relational equations A Boxminmax x = b and using the L_∞ norm, (Baaj, 2023) showed that the Chebyshev distance Delta = infc ∈ C Vert b - c Vert, 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 max-product fuzzy relational equations and that associated to the second member of a system of max-Lukasiewicz fuzzy relational equations.