|||||||||||||||||||||||||||||||Abstract In this paper, the researcher proposes a modi ed new method to rank L-R fuzzy numbers. The modi ed method uses a defuzzi cation of parametrically represented fuzzy numbers that have been studied in [20]. This parameterized defuzzi cation can be used as a crisp approximation with respect to a fuzzy quantity. In this article, the researcher uses this defuzz...

We examine gauge theories on Minkowski space-time times fuzzy coset spaces. This means that the extra space dimensions instead of being a continuous coset space S/R are a corresponding finite matrix approximation. The gauge theory defined on this non-commutative setup is reduced to four dimensions and the rules of the corresponding dimensional reduction are established. We investigate in partic...

Abslracl: The Fuzzy Medial Axis Transformation (FMAT) of a fuzzy set f is a set of fuzzy disks whose sup is f. Unforlunately, specifying the FMAT sometimes requires more storage space than specifying.f itself. The present paper describes some techniques Lo improve the compact representatiou of FMAT; thereby making it practically feasible and useful. The algorithms involve reduction of redundanc...

This paper presents a general framework for the study of rough set approximation operators in fuzzy environment in which both constructive and axiomatic approaches are used. In constructive approach, a pair of lower and upper generalized fuzzy rough (and rough fuzzy, respectively) approximation operators is first defined. The representations of both fuzzy rough approximation operators and rough...

This paper aims to fuzzify the width problem of classical approximation theory. New concepts fuzzy Kolmogorov n-width and linear are introduced on basis α-fuzzy distance which is induced by norm. Furthermore, relationship between widths in normed space discussed. Finally, exact asymptotic orders corresponding a given norm finite-dimensional Sobolev estimated.

we prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of aliouche, et al. [2], rao et al. [14] and [15].

The fuzzy K-means problem is a generalization of the classical K-means problem to soft clusterings, i.e. clusterings where each points belongs to each cluster to some degree. Although popular in practice, prior to this work the fuzzy K-means problem has not been studied from a complexity theoretic or algorithmic perspective. We show that optimal solutions for fuzzy K-means cannot, in general, b...

Fuzzy rough set theory is a candidate framework for query refinement. Indeed, a thesaurus defines an approximation space in which the query, which is a set of terms, can be approximated from the upper and the lower side. The upper approximation turns out to be too flexible however, resulting in query explosion, while the lower approximation is too strict, resulting in the empty query. Therefore...

It is well known that lattice-valued rough sets are important branches of fuzzy sets. The axiomatic characterization and related topology the main research directions For L=(L,⊛), a complete co-residuated lattice (CCRL), Qiao recently defined an L-fuzzy lower approximation operator (LFLAO) on basis relation. In this article, we give further study Qiao’s LFLAO around induced L-topology. Firstly,...

7 In this paper, we show that weakly null-additive fuzzy measures on metric spaces possess regularity. Lusin’s theorem, which is well-known in classical measure theory, is generalized to fuzzy measure space by using the 9 regularity and weakly null-additivity. A version of Egoro2’s theorem for the fuzzy measure de3ned on metric spaces is given. An application of Lusin’s theorem to approximation...