Confluence and termination are essential properties connected to the idea of rewriting and substituting which appear in abstract rewriting systems. The aim of the present paper is to investigate confluence, termination, and related properties from the point of view of fuzzy logic leaving the ordinary notions a particular case when the underlying structure of truth degrees is two-valued Boolean ...

This paper explores the use of FPGA technologies to implement fuzzy logic controllers (FLCs). Two different approaches are described. The first option is based on the logic synthesis of the boolean equations describing the controller input-output relations. The second approach uses dedicated hardware to implement the fuzzy algorithm according to a specific architecture based on a VHDL cell libr...

A number of representation schemes have been presented for use within Learning Classifier Systems, ranging from binary encodings to neural networks. This paper presents results from an investigation into using discrete and fuzzy dynamical system representations within the XCSF Learning Classifier System. In particular, asynchronous Random Boolean Networks are used to represent the traditional c...

In this paper we deal with the problem of studying some mathematical aspects regarding the polytope of fuzzy measures when the referential set is finite. More concretely, we study whether two extreme points are adjacent; for general polytopes, this is a NP-hard problem. However, for the case of fuzzy measures, we give a necessary and sufficient condition for two extreme points to be adjacent. T...

In this paper the concept of an $Omega$- Almost Boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $Omega$- Almost Boolean ring over a locally Boolean space.

one of the models that can be used to study the relationship between boolean random sets and explanatory variables is growth regression model which is defined by generalization of boolean model and permitting its grains distribution to be dependent on the values of explanatory variables. this model can be used in the study of behavior of boolean random sets when their coverage regions variation...

I Acknowledgments IV List of Figures X List of Tables XIV List of Abbreviations XV Publications Arising from This Work XVIII Chapter 1: Introduction .................................................................................................. 1 1.1 Aims, Significance, Novelty ........................................................................... 6 1.1.1 Aims .............................

Analogies play an important role in many reasoning tasks. In this paper, we survey a recently proposed modeling for an analogical proportion, i.e. a statement of the form “A is to B as C is to D”, and its diverse applications. The logical representation used for encoding such proportions takes both into account what the four situations have in common and how they differ. Thanks to the use of a ...

For any correct argument in scientific reasoning as well as our everyday reasoning, the premises of the argument must be in some way relevant to the conclusion of that argument, and vice versa. On the other hand, in scientific reasoning as well as our everyday reasoning, many arguments may be correct to some degree, and therefore, a reasoning consisting of such fuzzy arguments is approximate. A...

In this paper we extend the problem of classification using Fuzzy Association Rule Mining and propose the concept of Fuzzy Weighted Associative Classifier (FWAC). Classification based on Association rules is considered to be effective and advantageous in many cases. Associative classifiers are especially fit to applications where the model may assist the domain experts in their decisions. Weigh...