Generalizations of (U, N)-implications derived from commutative semi-uninorms and pseudo-uninorms

Article type: Research Article

Authors: Li, Zhen-Bo^{a; b} | Liu, Hua-Wen^{a; *}

Affiliations: [a] School of Mathematics, Shandong University, Jinan, Shandong, P.R. China | [b] School of Statistics, Shandong University of Finance and Economics, Jinan, Shandong, P.R. China

Correspondence: [*] Corresponding author. Hua-Wen Liu, School of Mathematics, Shandong University, Jinan, Shandong 250100, P.R. China. Tel.: +86 531 88364652; Fax: +86 531 88365550; E-mail: [email protected].

Abstract: In this paper, two classes of generalized (U, N)-implications derived from commutative semi-uninorms and pseudo-uninorms are investigated. Then some properties of UI,N operations derived from implications are explored. Last the necessary and sufficient conditions such that a (UCS, N)-operation (or (UP, N)-operation) is an implication are given out.

Keywords: Fuzzy connective, fuzzy implication, (U_S, N)-implication, commutative semi-uninorm, pseudo-uninorm

DOI: 10.3233/IFS-151693

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 5, pp. 2177-2184, 2015