Affiliations: School of Sciences, Zhejiang Sci-Tech University, Hangzhou, China | School of Information, Zhejiang Sci-Tech University, Hangzhou, China
Note: [] Corresponding author. Daowu Pei, School of Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, China. E-mail: [email protected]
Abstract: Recently, quantitative logic is proposed and used to build new frameworks of approximate reasoning. In the current paper, fuzzy reasoning is investigated from the perspective of quantitative logic. Based on the basic concepts of quantitative logic and detailed analysis of the formal solutions of several models of fuzzy reasoning, we discuss the transformation situations of truth degrees from premises to conclusions through the triple I based fuzzy reasoning, and several estimations of truth degrees of inference conclusions are obtained. In addition, the current paper proposes the theory of the deviation of formulas as a rational improvement to quantitative logic. Several common used t-norms and the corresponding residuated implications are investigated from the perspective of the truth degrees and deviations of quantitative logic. Thus, a new assessment criterion of suitability of t-norms and residuated implications for fuzzy reasoning is developed.
Keywords: Fuzzy logic, fuzzy reasoning, quantitative logic, truth degree, deviation
