On the unique solvability of fuzzy relational equations |
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Authors: | Pingke Li Shu-Cherng Fang |
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Institution: | (1) Operations Research Program, North Carolina State University, Raleigh, NC 27695-7913, USA;(2) Department of Industrial Engineering, North Carolina State University, Raleigh, NC 27695-7906, USA |
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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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Keywords: | |
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