Abstract
Fuzzy relational equations play an important role in fuzzy set theory and fuzzy logic systems. To compare and evaluate the accuracy and efficiency of various solution methods proposed for solving systems of fuzzy relational equations as well as the associated optimization problems, a test problem random generator for systems of fuzzy relational equations is needed. In this paper, procedures for generating test problems of fuzzy relational equations with the sup- $${\mathcal{T}}$$ composition are proposed for the cases of sup- $${\mathcal{T}_M}$$ , sup- $${\mathcal{T}_P}$$ , and sup- $${\mathcal{T}_L }$$ compositions. It is shown that the test problems generated by the proposed procedures are consistent. Some properties are discussed to show that the proposed procedures randomly generate systems of fuzzy relational equations with various number of minimal solutions. Numerical examples are included to illustrate the proposed procedures.
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