Interval-valued fuzzy inference based on aggregation functions

Abstract

Generalized modus ponens (GMP) and generalized modus tollens (GMT), as two basic patterns of approximate reasoning, aim to acquire some reasonable imprecise conclusions from a collection of imprecise premises using some inference rules. To solve the GMP and GMT problems under interval-valued fuzzy setting, an interval-valued A-compositional rule of inference (ACRI) method and quintuple implication principle (QIP) method with interval-valued implication generated by A under any partial order are presented in this paper, where A is an interval-valued aggregation function. In order to develop these methods, we firstly discuss interval-valued negation generated by an interval-valued aggregation function with any partial order. Some properties of interval-valued implications generated by interval-valued aggregation functions with an arbitrary order are then analyzed. We further investigate the ACRI method and quintuple implication principle (QIP) method with interval-valued implication generated by interval-valued aggregations to solve the interval-valued fuzzy modus ponens (IFMP) and interval-valued fuzzy modus tollens (IFMT). Finally, two examples are implemented to illustrate our proposed approaches using some special interval-valued aggregation functions.