One of the most popular methods of knowledge representation are the fuzzy rules. One of the ways of representation of fuzzy rules is the functional representation. From over eight decades a number of different fuzzy implications have been described, e.g. [5]-[9]. This leads to the following question: how to choose the proper function among basic fuzzy implications. This paper is a continuation ...

Fuzzy Mathematical Morphology aims to extend the binary morphological operators to grey-level images. In order to define the basic morphological operations fuzzy erosion, dilation, opening and closing, we introduce a general method based upon fuzzy implication and inclusion grade operators, including as particular case, other ones existing in related literature In the definition of fuzzy erosio...

The aim of this work is to analyze the interval canonical representation for fuzzy QL-implications and automorphisms. Intervals have been used to model the uncertainty of a specialist’s information related to truth values in the fuzzy propositional calculus: the basic systems are based on interval fuzzy connectives. Thus, using subsets of the real unit interval as the standard sets of truth deg...

This chapter deals with the construction of distance and similarity measures by utilizing the theoretical advantages of the fuzzy implications. To this end the basic definitions of fuzzy implications are initially discussed and the conditions of typical distance and similarity measures that need to be satisfied are defined next. On the basis of this theory a straightforward methodology for buil...

A new family of implication operators, called probabilistic implications, is introduced. The suggested implications are based on conditional copulas and make a bridge between probability theory and fuzzy logic. It is shown that some well-known fuzzy implications appear as a particular probabilistic implications. Therefore, it seems that this new family of implication operators might be a useful...

In this paper, a new construction method of a fuzzy implication from two given ones, called e-generation method, is introduced. This method allows to control, up to a certain level, the increasingness on the second variable of the fuzzy implication through an adequate scaling on that variable of the two given implications. The natural propagation of the most usual properties of fuzzy implicatio...

Properties valid on the classical theory (Boolean laws) have been extended to fuzzy set theory and so-called Boolean-like laws. The fact that they are not always valid in any standard fuzzy set theory induced a wide investigation. In this paper we show the sufficient and necessary conditions that the Boolean-like law y ≤ I(x, y) holds in fuzzy logic. We focus the investigation on the following ...

We present a new approach for handling fuzzy triadic data in the setting of Formal Concept Analysis. The starting point is a fuzzyvalued triadic context (K1,K2,K3, Y ), where K1,K2 and K3 are sets and Y is a ternary fuzzy relation between these sets. First, we generalise the methods of Triadic Concept Analysis to our setting and show how they fit other approaches to Fuzzy Triadic Concept Analys...

This paper deals with propositional fuzzy modal logic with evaluated syntax based on MV-algebras. We focus on its semantical theory from the viewpoint of Pavelka’s graded semantics of propositional fuzzy logic, investigate the L-tautologies based on different Kripke frames. We also define the notion of Lsemantical consequence operation, its some basic properties are obtained. Finally, this pape...