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.
Similar content being viewed by others
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
Czogała E, Drewniak J (1984) Associative monotonic operations in fuzzy set theory. Fuzzy Sets Syst 12:249–269
Czogała E, Drewniak J, Pedrycz W (1982) Fuzzy relation equations on a finite set. Fuzzy Sets Syst 7:98–101
Di Nola A, Sessa S (1983) On the set of solutions of composite fuzzy relation equations. Fuzzy Sets Syst 9 (3):275–285
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
Drewniak J (1984) Fuzzy relation equations and inequalities. Fuzzy Sets Syst 14:237–247
Drewniak J (1989) Fuzzy relation calculus. Uniwersytet Śląski, Katowice
Drewniak J, Kula K (2002) Generalized compositions of fuzzy relations. Int J Uncertain Fuzziness Knowl Based Syst 10:149–163
Fernández MJ, Gil P (2004) Some specific types of fuzzy relation equations. Inform Sci 164(1–4):189–195
Goguen JA (1967) L-fuzzy sets. J Math Anal Appl 18:145–174
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
Higashi M, Klir GJ (1984) Resolution of finite fuzzy relation equations. Fuzzy Sets Syst 13:65–82
Klement EP, Mesiar R, Pap E (2000) Triangular norms. Kluwer, Dordrecht
Miyakoshi M, Shimbo M (1985) Solutions of composite fuzzy relational equations with triangular norms. Fuzzy Sets Syst 16:53–63
Pedrycz W (1982) Fuzzy relational equations with triangular norms and their resolutions. BUSEFAL 11:24–32
Pedrycz W (1993) S-T fuzzy relational equations. Fuzzy Sets Syst 59:189–195
Sanchez E (1976) Resolution of composite fuzzy relation equations. Inform Control 30:38–48
Shieh BS (2007) Solutions of fuzzy relation equations based on continuous t-norms. Inform Sci 177(19):4208–4215
Stamou GB, Tzafestas SG (2001) Resolution of composite fuzzy relation equations based on Archimedean triangular norms. Fuzzy Sets Syst 120(3):395–407
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
Zhang Ch, Lu ChJ, Li DY (2006) On perturbation properties of fuzzy relation equations. J Fuzzy Math 14:53–63
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-009-0481-6