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Keywords:
fuzzy relational equations; inconsistency; optimal approximation; mixed integer linear programming
fuzzy relational equations; inconsistency; optimal approximation; mixed integer linear programming
Summary:
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 Łukasiewicz 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.
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