On the characterizations of fuzzy XNOR connectives

Article type: Research Article

Authors: He, Xingxing^{a; *} | Li, Yingfang^b | Qin, Keyun^a | Meng, Dan^b

Affiliations: [a] School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, China | [b] School of Economics Information Engineering, Southwestern University of Finance and Economics, Chengdu, Sichuan, China

Correspondence: [*] Correspondence author. Xingxing He, School of Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan, China. Tel.: +86 13808003779; Fax: +86 028 87600764; E-mail: x.he@home.swjtu.edu.cn.

Abstract: The fuzzy XNOR connective, as the dual construction of the fuzzy symmetric difference operator, has been defined and discussed by Li, Qin and He [18]. The aim of this paper is to give a systematic investigation of properties and structures of fuzzy XNOR connectives. The main results are: (1) It is proved that the biresiduation of a t-norm is indeed a fuzzy XNOR connective. (2) The structures and properties for biresiduations and two canonical constructions of fuzzy XNOR connectives given in [18] are examined. The associativity of fuzzy XNOR connectives is specially investigated. (3) Three additional ways of constructing fuzzy XNOR connectives are proposed.

Keywords: Symmetric difference operator, equivalence operator, fuzzy XNOR connective, t-Norm, t-Conorm, fuzzy negation

DOI: 10.3233/JIFS-16845

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2733-2745, 2017