An important line of research within the field of fuzzy DLs is the computation of an equivalent crisp representation of a fuzzy ontology. In this short paper, we discuss the relation between tractable fuzzy DLs and tractable crisp representations. This relation heavily depends on the family of fuzzy operators considered. Introduction. Despite the undisputed success of ontologies, classical onto...

We consider linguistic data(base) summaries in the sense of Yager [Information Sciences 28 (1982) 69–86], exemplified by ‘‘most employees are young and well paid’’ (with some degree of truth added), for a personnel database, as an intuitive, human consistent and natural language based knowledge discovery tool. We present first an extension of the classic Yager s approach to involve more sophist...

The concepts of Soft Computing introduced by Lotfi A. Zadeh in 1991 has integrated different methodologies and approaches, as: fuzzy set theory, fuzzy logic, approximate reasoning, linguistic expression of knowledge, probabilistic reasoning, and others for solving problems of complex systems in the way similar to human perception, recognition and solving problem methods. Linguistic fuzzy modell...

Abstract In the Internet era, soccer teaching has gotten rid of previous theoretical mode and paid more attention to use video multimedia for network teaching. this paper, from perspective a fuzzy mathematical algorithm, set algorithm is used construct matrix through mapping, calculate NMI value equivalent comprehensive rating weights U1-U10 in evaluation elements teaching, derive transformatio...

The existing approaches to supporting the tasks of managing urban areas development are aimed at choosing an alternative from a set ready-made solutions. Little attention is paid procedure for formation and analysis acceptable options use territories. study's purpose understand how various factors affect efficiency using city’s territory. In addition, we trying this understanding assess possibl...

OBJECTIVE A theory of fuzzy polynucleotides, including an n-dimensional metric fuzzy polynucleotide space, has been previously introduced by the present author for fuzzy-theoretical analysis of nucleic acids [Sadegh-Zadeh K. Fuzzy genomes. Artif Intell Med 2000;18:1-28; Sadegh-Zadeh K. Ein Verfahren zur Fuzzydecodierung und Fuzzydechiffrierung von Informationen. Offenlegungsschrift DE 199 36 92...

Mathematical Fuzzy Logics [51,60] have a long tradition with roots going back to the many-valued logics of Łukasiewicz, Gödel, and Kleene [57, 68, 73] and the Fuzzy Set Theory of Zadeh [111]. Their purpose is to model vagueness or imprecision in the real world, by introducing new degrees of truth as additional shades of gray between the Boolean true and false. For example, one can express the d...

It is well known that the notions of a "decidable subset" and "recursively enumerable subset" are basic one for classical logic. In particular, they are basic tools for the proof of the famous limitative theorems about the undecidability and incompleteness of first order logic. Then, the question of a suitable extension of such concepts to fuzzy set theory arises. A first proposal in such a dir...

To make a fuzzy value more reliable, Zadeh presented the notion of Z-number, which reflects related to its reliability measure. Since linguistic expression conforms human thinking habits, neutrosophic decision-making is one key research topics in indeterminate and inconsistent setting. In order ensure multiattribute group (MAGDM) problems environment truth, falsehood, indeterminacy, we require ...

What is granular computing(GrC)? It is a shifting paradigm. Let us start with a few words about how the term was coined. In the academic year 1996-97, when Lin (this section editor) took his sabbatical leave at UC-Berkeley, Zadeh suggested granular mathematics (GrM) to be his research area. To limit the scope, Lin proposed the term granular computing [14]. What was GrC then? Zadeh had outlined ...