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

01/30/2023

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by   Ismaïl Baaj, et al.

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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 _min^max x = b and using the L_∞ norm, (Baaj, 2023) showed that the Chebyshev distance Δ = inf_c ∈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 max-product fuzzy relational equations and that associated to the second member of a system of max-Lukasiewicz fuzzy relational equations.