Approximation abilities of perception-based logical deduction

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology, 2015

We present and analyze inference method called Perception-based Logical Deduction (PbLD) aimed at the treatment of fuzzy IF-THEN rules as linguistically expressed genuine logical implications. Besides the original PbLD, we propose a new balancing variant of PbLD, introduce both variants with fuzzy inputs and study them from the point of view of the interpolativity property.

International Journal of Intelligent Systems, 2004

In this article, we return to the problem of the derivation of a conclusion on the basis of fuzzy IF–THEN rules. The so-called Mamdani method is well elaborated and widely applied. In this article, we present an alternative to it. The fuzzy IF–THEN rules are here interpreted as genuine linguistic sentences consisting of the so-called evaluating linguistic expressions. Sets of fuzzy IF–THEN rules are called linguistic descriptions. Linguistic expressions derived on the basis of an observation in a concrete context are called perceptions. Together with the linguistic description, they can be used in logical deduction, which we will call a perception-based logical deduction. We focus on semantics only and confine ourselves to one specific model. If the perception-based deduction is repeated and the result interpreted in an appropriate model, we obtain a piecewise continuous and monotonous function. Though the method has already proved to work well in many applications, the nonsmoothness of the output may sometimes lead to problems. We propose in this article a method for how the resulting function can be made smooth so that the output preserves its good properties. The idea consists of postprocessing the output using a special fuzzy approximation method called F-transform. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 1007–1031, 2004.

International Journal of Industrial Mathematics, 2015

This paper deals with one problem that needs to be addressed in the emerging field known under the name computing with perceptions. It is the problem of describing, approximately, a given fuzzy set in natural language. This problem has lately been referred to as the problem of retranslation. An approaches to dealing with the retranslation problem is discussed in the paper, that is based on a pre-defined set of linguistic terms and the associated fuzzy sets. The retranslation problem is discussed in terms of two criteria validity and informativeness.

Soft Computing - A Fusion of Foundations, Methodologies and Applications, 2004

This paper presents an approach to approximate reasoning over a set of IF-THEN rules called fuzzy logic deduction. It understands IF-THEN rules as linguistically expressed logical implications and interprets them inside formal logical theory. Methodology and some properties are presented.

Soft Computing, 1999

This paper presents a new linguistic approximation algorithm and its implementation in the frame of fuzzy logic deduction. The algorithm presented is designed for fuzzy logic deduction mechanism implemented in Linguistic Fuzzy Logic Controller (LFLC).

1986

The generalized modus ponens is a fuzzy logic pattern of reasoning that permits to make inferences with rules having imprecision both in their antecedent and consequent parts. Though it is a very powerful approximate reasoning tool (from a theoretical point of view), this technique may result in unacceptably slow executions if inappropriately implemented. There are several ways to avoid the inefficiency bottleneck. One of them, that is the object of this paper, consists in introducing an approximation technique focussing only of what is semantically important. This approximation technique is conceived so as to be used in situations where the dependency between two given variables is described via a collection of rules. Moreover, this paper addresses the problem in the setting having the main features that follow: the possibility distributions involved in facts and rules are continuous (the referential is the real line), normalized, unimodal and expressed by parametrized functions; only single antecedent rules are considered; the rules are consistent and it is assumed that their antecedents and consequents do not overlap too much; the deduction process is based on the ‘min’ conjunction and Gödel implication operators. The ultimate goal of this work is to render the generalized modus ponens technique usable in practical deduction systems.

International Journal of Intelligent Systems, 1998

M. Ying proposed a propositional calculus in which the reasoning may be approximate by allowing the antecedent clause of a rule to match its premise only approximately. The aim of this note is to relate Ying's proposal to an extension principle for closure operators proposed by the authors. In this way it is possible to show that, in a sense, w Ying's apparatus can be reduced to a fuzzy logic as defined by Pavelka J. Pavelka, ''On fuzzy logic I. Many valued rules of inference,''

2016

We present and analyze inference method called Perception-based Logical Deduction (PbLD) aimed at the treatment of fuzzy IF-THEN rules as linguis-tically expressed genuine logical implications. Be-sides the original PbLD, we propose a new balanc-ing variant of PbLD, introduce both variants with fuzzy inputs and study them from the point of view of the interpolativity property.

Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1990

Mathematical Principles of Fuzzy Logic, 1999