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On the unique solvability of fuzzy relational equations

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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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Authors and Affiliations

  1. Department of Industrial Engineering, Tsinghua University, Beijing, 100084, China

    Pingke Li

  2. Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC, 27695-7906, USA

    Shu-Cherng Fang

Authors
  1. Pingke Li
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  2. Shu-Cherng Fang
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Correspondence to Pingke Li.

Additional information

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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