Chebyshev distances associated to the second members of systems of
Max-product/Lukasiewicz Fuzzy relational equations
- URL: http://arxiv.org/abs/2302.08554v1
- Date: Mon, 30 Jan 2023 09:18:20 GMT
- Title: Chebyshev distances associated to the second members of systems of
Max-product/Lukasiewicz Fuzzy relational equations
- Authors: Isma\"il Baaj
- Abstract summary: We study the inconsistency of a system of $max$-product fuzzy relational equations and of a system of $max$-Lukasiewicz fuzzy relational equations.
We 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 relational fuzzy equations.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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 $A
\Box_{\min}^{\max} x = b$ and using the $L_\infty$ norm, (Baaj, 2023) showed
that the Chebyshev distance $\Delta = \inf_{c \in \mathcal{C}} \Vert b - c
\Vert$, where $\mathcal{C}$ 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.
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