Practical Inference With Systems of Gradual Implicative Rules

Abstract

A general approach to practical inference with gradual implicative rules and fuzzy inputs is presented. Gradual rules represent constraints restricting outputs of a fuzzy system for each input. They are tailored for interpolative reasoning. Our approach to inference relies on the use of inferential independence. It is based on fuzzy output computation under an interval-valued input. A double decomposition of fuzzy inputs is done in terms of α-cuts and in terms of a partitioning of these cuts according to areas where only a few rules apply. The case of 1-D and 2-D inputs is considered, as well as higher dimensional cases. An application to a cheese-making process illustrates the approach.

Fuzzy rule base ensemble generated from data by linguistic associations mining

“…[35,4]. As the PbLD stems from the implicative rules [40,41] and not from the Mamdani-Assilian ones (details can be found below), the defuzzification cannot use principles similar to the Center-Of-Gravity defuzzification but has to focus on sets of elements with maximal membership degrees. In principle, this defuzzification is a combination of First-Of-Maxima (FOM), Mean-Of-Maxima (MOM) and Last-Of-Maxima (LOM) that are applied based on the classification of the inferred output fuzzy set.…”

On Perception-based Logical Deduction and Its Variants

“…The maximum in (3) then expresses accumulation of data [2]. For further sources related to the interpretability and interpretation of such systems, we refer to [4,5,6].…”

“…, R n }. 5 The following conventions will be kept throughout the rest of this paper: We will denote by N n the set {1, . .…”

Parameter optimization of a fuzzy inference system using the FisPro open source software

“…The difference of nature between conjunctive and implicative rules impacts rule combination: while several conjunctive rules are combined disjunctively (as they widen the scope of a single rule), implicative rules are combined conjunctively, because several constraints lead to a more restricted feasible set of allowed situations than a single constraint. All details can be found in [19]. Implicative rules are ususally designed by experts.…”