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 rul...

In this paper we will investigate which fuzzy/linguistic rules are redundant in systems of such rules called linguistic descriptions. We present a formal definition of redundancy and show that rules which are seemingly redundant can be in fact indispensable. These results apply for IF-THEN rules which use evaluative linguistic expressions (e.g., small, very big, etc.) and inference method calle...

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.

A fuzzy cognitive map is a graphical means of representing arbitrary complex models of interrelations between concepts. The purpose of this paper is to describe a dynamic/adaptive fuzzy cognitive map based on the random neural network model. Previously, we have developed a random fuzzy cognitive map and illustrated its application in the modeling of processes. The adaptive fuzzy cognitive map c...

A fuzzy cognitive map is a graphical means of representing arbitrarily complex models of interrelations between concepts. The purpose of this paper is to describe a fuzzy cognitive map based on the random neural network model called the random fuzzy cognitive map, and to illustrate its application in the modeling of process. This model is based on the probability of activation of the neurons/co...

fuzzy logic, 67algebraic semantics, 53approximate reasoning, 6axiomatic extensions of MTL, 56 Bellman, R., 21bipolar possibilistic logic, 93BL logic, 51 canonical chain, 66canonical completeness, 66canonical extension, 83Carnap, R., 3comparative truth, 63compositionality, 29computational complexity, 73core fuzzy logic, 58 De Finetti B., 3degre...

The paper develops fuzzy attribute logic, i.e. a logic for reasoning about formulas of the form A ⇒ B where A and B are fuzzy sets of attributes. A formula A ⇒ B represents a dependency which is true in a data table with fuzzy attributes iff each object having all attributes from A has also all attributes from B, membership degrees in A and B playing a role of thresholds. We study axiomatic sys...

Received (received date) Revised (revised date) Preselection of rules is an algorithm which chooses one rule from linguistic description of some process. This rule is then used for inference instead of the whole description. This article studies properties of preselection and proposes use of measures of resemblance for choosing the rule which best ts the observation.

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

An important notion of inconsistency occurring in the theory of IF-THEN rules is discussed. We propose a definition of it in the frame of fuzzy logic deduction and show some properties.