On Consistency of Redundancy Deduction of Linguistic Fuzzy Rules

Abstract

Eliminating the redundant rules in a given system of fuzzy rules is important in fuzzy inference. A high number of seemingly very similar rules can be then reduced and the system is thus simple, comprehensible and adjustable for the users of the rules. This paper focuses on the redundancy of a special type of linguistic fuzzy rules that contain linguistic evaluative expressions. Recently, we have approached to generalize the existing criteria for detecting redundant linguistic fuzzy rules. It is important to mention that the elaboration of the redundancy criteria is initiated by the identification of the socalled investigated pairs, which are the pairs of two rules in which one rule is suspicious from redundancy with respect to another one. Principally, for a given investigated pair, we may use the established criteria to derive the redundancy or non-redundancy of the rule which is suspicious from redundancy. In this paper, we use the most recent generalized criteria and show that the deduction for the redundancy or non-redundancy of a certain rule is consistent when this rule belongs to different investigated pairs.