In recent years, many nearest neighbor algorithms based on fuzzy sets theory have been developed. These methods form a field, known as fuzzy nearest neighbor classification, which is the source of many proposals for the enhancement of the k nearest neighbor classifier. Fuzzy sets theory and several extensions, including fuzzy rough sets, intuitionistic fuzzy sets, type-2 fuzzy sets and possibil...

This paper presents a general framework for the study of rough fuzzy sets in which fuzzy sets are approximated in a crisp approximation space. By the constructive approach, a pair of lower and upper generalized rough fuzzy approximation operators is first defined. The rough fuzzy approximation operators are represented by a class of generalized crisp approximation operators. Properties of rough...

In the formal and fully graded setting of Fuzzy Class Theory (or higher-order fuzzy logic) we make an initial investigation into basic notions of fuzzy topology. In particular we study graded notions of fuzzy topology regarded as a fuzzy system of open or closed fuzzy sets and as a fuzzy system of fuzzy neighborhoods. We show their basic graded properties and mutual relationships provable in Fu...

The concept of intuitionistic fuzzy sets is the generalization of the concept of fuzzy sets. The theory of intuitionistic fuzzy sets is well suited to dealing with vagueness. Recently, intuitionistic fuzzy sets have been used to build soft decision making models that can accommodate imprecise information, and two solution concepts about the intuitionistic fuzzy core and the consensus winner for...

(This paper is an extended abstract for an invited talk at 29th Linz Seminar on Fuzzy Set Theory, February 2008.) Höhle has shown that fuzzy sets, valued in a frame (complete Heyting algebra) Ω, can be identified with certain sheaves over Ω: they are the subsheaves of constant sheaves, and more general sheaves can be got as quotients of the fuzzy sets. The technical development is complicated b...

This paper demonstrates twometa-mathematical propositions concerning the increasingly popular “intuitionistic” (= vague) approaches to fuzzy sets and fuzzy topology, as well as the closely related interval-valued (= grey) sets and interval-valued “intuitionistic” sets: (1) the term “intuitionistic” in these contexts is historically inappropriate given the standard mathematical usage of “intuiti...

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Fuzzy sets theory has several applications in biomedicine. The dissimilarity of fuzzy sets is used for this purpose. In this paper, we present the generalized equation of the dissimilarity of fuzzy sets. This relation is based on the set theoretic point of view. The parameter of this generalized equation and also its relation to a recently introduced metric defined in fuzzy hypercube are discus...

A voting model semantics for fuzzy sets is assumed with the corresponding ideas of mass assignment theory. The use of fuzzy sets in this way will provide better interpolation, greater knowledge compression, less dependence on the effects of noisy data than if only crisp sets were used. We will see how easy and useful it is to use successful inference methods such as decision trees, probabilisti...

The publication opportunities in science require knowing the existing gaps academic debate. In recent decades, scholars specializing fuzzy theory and applied methodologies have experienced an unprecedented evolution of field. Sustainable Development Goals (SDGs) shaped way socio-technical transitions use to solve environmental problems. This study conducts a systematic literature review article...