A fuzzy soft set based approximate reasoning method¹

Article type: Research Article

Authors: Qin, Keyun^{a; *} | Yang, Jilin^b | Liu, Zhicai^a

Affiliations: [a] College of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, China | [b] College of Fundamental Education, Sichuan Normal University, Chengdu, Sichuan, China

Correspondence: [*] Corresponding author. Keyun Qin, College of Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan, China. Tel.: +86 15208391856; Fax: +86 28 87600764; E-mail: [email protected].

Note: [1] This work has been partially supported by the National Natural Science Foundation of China (Grant Nos. 61473239, 61175044), the Fundamental Research Funds for the Central Universities of China (Grant No. 2682014ZT28), and the open research fund of key laboratory of intelligent network information processing, Xihua University (szjj2014-052).

Abstract: Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool for dealing with uncertainties. This paper is devoted to the discussion of fuzzy soft set based approximate reasoning. First, based on fuzzy implication operators, the notion of fuzzy soft implication relation between fuzzy soft sets is introduced. The composition method of fuzzy soft implication relations is provided. Second, Triple I methods for fuzzy soft modus ponens (FSMP)and fuzzy soft modus tollens (FSMT) are investigated. Computational formulas for FSMP and FSMT with respect to left-continuous t-norms and its residual implication are presented. At last, the reversibility properties of Triple I methods are analyzed.

Keywords: Fuzzy set, soft set, fuzzy soft implication relation, triple I method, left-continuous t-norm

DOI: 10.3233/JIFS-16088

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 1, pp. 831-839, 2017