Logical foundation of symmetric implicational methods for fuzzy reasoning

Article type: Research Article

Authors: Dai, Songsong^{; *}

Affiliations: School of Electronics and Information Engineering, Taizhou University, Taizhou, China

Correspondence: [*] Corresponding author. Songsong Dai, School of Electronics and information engineering, Taizhou University, Taizhou 318000, China. Tel.: +86 15867670861; Fax: +86 0576 88661937; E-mail: ssdai@tzc.edu.cn.

Abstract: The symmetric implicational methods for fuzzy reasoning characterizes the solution B* (A*) of the formula (A → 1B) → 2 (A* → 1B*) for the fuzzy modus ponens (fuzzy modus tollens), where →1 and →2 are two different implications. In this study, we provide a predicate formal representation of the solution for the symmetric implicational methods based on the LΠ formal logic system, including detailed logic proofs. We bring the symmetric implicational methods within a logical framework and provide a sound logic foundation for the symmetric implicational methods of fuzzy reasoning.

Keywords: Fuzzy reasoning, symmetric implicational method, LΠ logic

DOI: 10.3233/JIFS-191998

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 1, pp. 1089-1095, 2020