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Fuzzy relational equations with min-biimplication composition

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Abstract

This paper discusses fuzzy relational equations with min-biimplication composition where the biimplication is the biresiduation operation with respect to the Łukasiewicz t-norm. It is shown that determining whether a finite system of fuzzy relational equations with min-biimplication composition has a solution is NP-complete. Moreover, a system of such equations can be fully characterized by a system of integer linear inequalities and consequently its solution set can be expressed in the terms of the minimal solutions of this system of integer linear inequalities.

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Authors and Affiliations

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

    Pingke Li

  2. Department of Management Science and Engineering, Zhejiang University, Hangzhou, 310058, Zhejiang, China

    Qingwei Jin

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  1. Pingke Li
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  2. Qingwei Jin
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Correspondence to Qingwei Jin.

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Li, P., Jin, Q. Fuzzy relational equations with min-biimplication composition. Fuzzy Optim Decis Making 11, 227–240 (2012). https://doi.org/10.1007/s10700-012-9122-0

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  • DOI: https://doi.org/10.1007/s10700-012-9122-0

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