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Uniqueness of solutions to fuzzy relational equations regarding Max-av composition and strong regularity of the matrices in Max-av algebra

The second author is supported by the China Scholarship Council (Grant No. 201506060121) and Fundamental Research Funds for Central Universities in China. The fifth author is supported by the National Natural Science Foundation of China (Grant No. 11771008) and the Natural Science Foundation of Shandong Province in China (Grant Nos.: ZR2015FM014, ZR2015AL010 and ZR2017MA005).
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  • The problem of solving a fuzzy relational equation plays an important role in fuzzy systems. In this paper, we investigate the uniqueness of solutions of fuzzy relational equations regarding Max-av composition through the relationship between minimal solutions and minimal coverage. A method for verifying the strong regularity of matrices in fuzzy Max-av algebra is proposed in the paper.

    Mathematics Subject Classification: Primary: 34A07; Secondary: 49N60.


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