The paper presents an evolutionary approach for generating fuzzy rule based classifier. First, a classification problem is divided into several two-class problems following a fuzzy unordered class binarization scheme; next, a fuzzy rule is evolved (not only the condition but the fuzzy sets are evolved (tuned) too) for each two-class problem using a Michigan iterative learning approach; finally,...

This paper studies fuzzy relations in the graded framework of Fuzzy Class Theory (FCT). This includes (i) rephrasing existing work on graded properties of binary fuzzy relations in the framework of Fuzzy Class Theory and (ii) generalizing existing crisp results on fuzzy relations to the graded framework. Our particular aim is to demonstrate that Fuzzy Class Theory is a powerful and easy-to-use ...

This paper presents a framework for genetic fuzzy rule based classifier. First, a classification problem is divided into several two-class problems following a fuzzy class binarization scheme; next, a fuzzy rule is evolved for each two-class problem using a Michigan iterative learning approach; finally, the evolved fuzzy rules are integrated using the fuzzy class binarization scheme. In particu...

In this manuscript, we introduce  a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and   propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between  the fuzzy solution set of a  fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtain...

A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets. Alongwith the study of fundamental results of such closed sets, we define and characterize fuzzy weakly compact space and fuzzy weakly closed space.

Modules and linking are usually formalized by encodings which use the-calculus, records (possibly dependent), and possibly some construct for recursion. In contrast, we introduce the m-calculus, a calculus where the primitive constructs are modules, linking, and the selection and hiding of module components. The m-calculus supports smooth encodings of software structuring tools such as function...

In the early 80's, there was a number of papers on what should be called proofs by consistency. They describe how to perform inductive proofs, without using an explicit induction scheme, in the context of equational speciications and ground-convergent rewrite systems. The method was explicitly stated as a rst-order consistency proof in case of pure equational, constructor based, speciications. ...

In this paper, we present triangle algebras: residuated lattices equipped with two modal, or approximation, operators and with a third angular point u, different from 0 (false) and 1 (true), intuitively denoting ignorance about a formula’s truth value. We prove that these constructs, which bear a close relationship to several other algebraic structures including rough approximation spaces, prov...