Path algebras are additively idempotent semirings and generalize Boolean algebras, fuzzy algebras, distributive lattices and inclines. Thus the Boolean matrices, the fuzzy matrices, the lattice matrices and the incline matrices are prototypical examples of matrices over path algebras. In this paper, generalized fuzzy matrices are considered as matrices over path algebras. Compositions of genera...

—In this paper, we examine and compare de Morgan-, Kleene-, and Boolean-disjunctive and conjunctive normal forms in fuzzy settings. This generalizes papers of Turksen on the subject of Boolean-normal forms.

1. Introduction Cellular Automata have generated much interest [1,2,3] because of their diverse behavior and usefulness as a discrete model for many processes. Wolfram's 1984 paper on universality and complexity in cellular automata [3,4] described four classes of behavior for automata: class 1 for homogeneous stable behavior, class 2 for simple periodic patterns, class 3 for chaotic aperiodic ...

Neuro-fuzzy classi cation systems allow to derive fuzzy classi ers by learning from data. The obtained fuzzy rule bases are sometimes hard to interpret, even if the learning method uses constraints to ensure an appropriate fuzzy partitioning of the input domains. This paper describes an approach to build more expressive rules by performing boolean transformations during and after the learning p...

The conventional fuzzy set model uses the MIN and MAX operators for the evaluation of boolean operators AND and OR, respectively. It has been criticized to generate incorrect ranked output in many cases. This is because the MIN and MAX operators do not well correspond with human behavior for document ranking. There are a variety of fuzzy operators to replace the MIN and MAX operators. In this p...

This paper proposes to cluster any finite data set by optimizing with respect to a cluster score function, assigning a positive real worth to each data subset and thereby dealt with in pseudo-Boolean form, so that the multilinear extension (MLE) allows to evaluate fuzzy data subsets or clusters as well. A fuzzy clustering being a collection of fuzzy clusters over which every data point has to d...

Geomorphological landforms are generally viewed as Boolean objects. However, recent studies have shown that landforms are more suitable to be viewed as fuzzy objects, whereby a landform is defined as a region in the continuum of variation of the surface of the earth. In this paper, the fuzzy classification of physiographic features extracted from multiscale DEMs is performed. First, the lifting...

This paper deals with the problem of searching basic properties for robust implication operators in fuzzy control. We use the word “robust” in the sense of good average behavior in different applications and in combination with different defuzzification methods. We study the behavior of the two main families of implication operators in the fuzzy control inference process. These two families are...

This article gives a tutorial introduction on label semantics framework on reasoning with uncertainty. Modelling real world problems typically involves processing uncertainty of two distinct types. These are uncertainty arising from a lack of knowledge relating to concepts which, in the sense of classical logic, may be well defined and uncertainty due to inherent vagueness in concepts themselve...