An extension of several properties for fuzzy t-norm and vague t-norm

Article type: Research Article

Authors: Wang, Haohao | Li, Wei | Yang, Bin^{; *}

Affiliations: College of Science, Northwest A&F University, Yangling, PR China

Correspondence: [*] Corresponding author. Bin Yang, College of Science, Northwest A&F University, Yangling, 712100, PR China. E-mail: binyang0906@nwsuaf.edu.cn.

Abstract: Rosenfeld defined a fuzzy subgroup of a given group as a fuzzy subset with two special conditions and Mustafa Demirci proposed the idea of fuzzifying the operations on a group through a fuzzy equality and a fuzzy equivalence relation. This paper mainly focuses on fuzzy subsets and vague sets of monoids with several extended algebraic properties. Firstly, we generalize some algebraic properties of t-norms to fuzzy t-norms, this allows for a broader analysis and classification of fuzzy t-norms, enabling their wider application. Furthermore, we explore specific research on the properties of vague t-norms. Finally, selected conclusions about fuzzy t-norms are extended to bounded lattices.

Keywords: t-norm, t-conorm, uninorm, nullnorm, aggregation function, fuzzy monoid, vague monoid

DOI: 10.3233/JIFS-231401

Journal: Journal of Intelligent & Fuzzy Systems, vol. 46, no. 3, pp. 6881-6891, 2024