Abstract
The solution set of a consistent system of fuzzy relational equations with max-min composition can be characterized by one maximum solution and a finite number of minimal solutions. A polynomial-time method of O(mn) complexity is proposed to determine whether such a system has a unique minimal solution and/or a unique solution, where m, n are the dimensions of the input data. The proposed method can be extended to examining a system of fuzzy relational equations with max-T composition where T is a continuous triangular norm.
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This research has been sponsored by the United States National Science Foundation Grant #DMI-0553310.
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Li, P., Fang, SC. On the unique solvability of fuzzy relational equations. Fuzzy Optim Decis Making 10, 115–124 (2011). https://doi.org/10.1007/s10700-011-9100-y
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DOI: https://doi.org/10.1007/s10700-011-9100-y