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Properties of \(\text{max-}*\) fuzzy relation equations

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Abstract

We extend the result of Zhang et al. (J Fuzzy Math 14:53, 2006), who discussed the finite fuzzy relation equations with max–min and max–prod composition. In this article, the \(\text{max-}*\) composition is used for wide family of operations \(*\). In particular, families of solutions of two relation equations are compared.

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References

  • Birkhoff G (1967) Lattice theory. AMS Coll Publ 25, Providence, RI

  • Bour L, Lamotte M (1988) Equations de relations floues avec la composition conorme-norme triangulaires. BUSEFAL 34:86–94

    MATH  Google Scholar 

  • Czogała E, Drewniak J (1984) Associative monotonic operations in fuzzy set theory. Fuzzy Sets Syst 12:249–269

    Article  MATH  Google Scholar 

  • Czogała E, Drewniak J, Pedrycz W (1982) Fuzzy relation equations on a finite set. Fuzzy Sets Syst 7:98–101

    Google Scholar 

  • Di Nola A, Sessa S (1983) On the set of solutions of composite fuzzy relation equations. Fuzzy Sets Syst 9 (3):275–285

    Article  MathSciNet  MATH  Google Scholar 

  • Di Nola A, Sessa S, Pedrycz W (1983) Energy and entropy measures of fuzziness of solutions of fuzzy relation equations with continuous triangular norms. BUSEFAL 12:60–71

    MATH  Google Scholar 

  • Drewniak J (1984) Fuzzy relation equations and inequalities. Fuzzy Sets Syst 14:237–247

    Article  MathSciNet  MATH  Google Scholar 

  • Drewniak J (1989) Fuzzy relation calculus. Uniwersytet Śląski, Katowice

    MATH  Google Scholar 

  • Drewniak J, Kula K (2002) Generalized compositions of fuzzy relations. Int J Uncertain Fuzziness Knowl Based Syst 10:149–163

    Article  MathSciNet  MATH  Google Scholar 

  • Fernández MJ, Gil P (2004) Some specific types of fuzzy relation equations. Inform Sci 164(1–4):189–195

    Article  MathSciNet  MATH  Google Scholar 

  • Goguen JA (1967) L-fuzzy sets. J Math Anal Appl 18:145–174

    Article  MathSciNet  MATH  Google Scholar 

  • Han SC, Li SC, Wang JY (2006) Resolution of finite fuzzy relation equations based on strong pseudo-t-norms. Appl Math Lett 19(8):752–757

    Article  MathSciNet  MATH  Google Scholar 

  • Higashi M, Klir GJ (1984) Resolution of finite fuzzy relation equations. Fuzzy Sets Syst 13:65–82

    Article  MathSciNet  MATH  Google Scholar 

  • Klement EP, Mesiar R, Pap E (2000) Triangular norms. Kluwer, Dordrecht

    MATH  Google Scholar 

  • Miyakoshi M, Shimbo M (1985) Solutions of composite fuzzy relational equations with triangular norms. Fuzzy Sets Syst 16:53–63

    Article  MathSciNet  MATH  Google Scholar 

  • Pedrycz W (1982) Fuzzy relational equations with triangular norms and their resolutions. BUSEFAL 11:24–32

    MATH  Google Scholar 

  • Pedrycz W (1993) S-T fuzzy relational equations. Fuzzy Sets Syst 59:189–195

    Article  MathSciNet  Google Scholar 

  • Sanchez E (1976) Resolution of composite fuzzy relation equations. Inform Control 30:38–48

    Article  MATH  Google Scholar 

  • Shieh BS (2007) Solutions of fuzzy relation equations based on continuous t-norms. Inform Sci 177(19):4208–4215

    Article  MathSciNet  MATH  Google Scholar 

  • Stamou GB, Tzafestas SG (2001) Resolution of composite fuzzy relation equations based on Archimedean triangular norms. Fuzzy Sets Syst 120(3):395–407

    Article  MathSciNet  MATH  Google Scholar 

  • Wang XP, Xiong QQ (2005) The solution set of a fuzzy relational equation with sup-conjunctor composition in a complete lattice. Fuzzy Sets Syst 153(2):249–260

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang Ch, Lu ChJ, Li DY (2006) On perturbation properties of fuzzy relation equations. J Fuzzy Math 14:53–63

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The support of the grant the University of Information Technology and Management in Rzeszów, Poland is kindly announced. The authors are grateful to the reviewers for their valuable comments and suggestions, which helped to improve the final version of the paper.

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Authors and Affiliations

  1. Institute of Mathematics, University of Rzeszów, Al. Rejtana 16a, 35–310, Rzeszow, Poland

    Józef Drewniak

  2. University of Information Technology and Management, Al. Sucharskiego 2, 35–225, Rzeszow, Poland

    Zofia Matusiewicz

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  1. Józef Drewniak
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  2. Zofia Matusiewicz
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Correspondence to Józef Drewniak.

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Drewniak, J., Matusiewicz, Z. Properties of \(\text{max-}*\) fuzzy relation equations. Soft Comput 14, 1037–1041 (2010). https://doi.org/10.1007/s00500-009-0481-6

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  • DOI: https://doi.org/10.1007/s00500-009-0481-6

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