Noncommutative symmetric difference operators for fuzzy logic

Article type: Research Article

Authors: Dai, Songsong^a | Cheng, Wentao^{b; *}

Affiliations: [a] School of Electronics and Information Engineering, Taizhou University, Taizhou, China | [b] School of Mathematics and Computation Science, Anqing Normal University, Anqing, China

Correspondence: [*] Corresponding author. Wentao Cheng, School of Mathematics and Computation Science, Anqing Normal University, Anqing 246133, China. E-mail: chengwentao@aqnu.edu.cn.

Abstract:  This paper introduces noncommutative symmetric difference operators for fuzzy logics. Structures and properties of these operators are investigated. Finally, pseudo-quasi-metric and pseudo-metric are constructed on [0,1] based on the noncommutative symmetric differences.

Keywords: Noncommutative symmetric difference, t-norm, difference operator, pseudo-quasi-metric

DOI: 10.3233/JIFS-190400

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 6, pp. 8005-8013, 2019