Type-2 fuzzy sets and complex fuzzy sets are both three dimensional extensions of type-1 fuzzy sets. Complex fuzzy sets come in two forms, the standard form, postulated in 2002 by Ramot et al., and the 2011 innovation of pure complex fuzzy sets, proposed by Tamir et al.. In this paper we compare and contrast both forms of complex fuzzy set with type-2 fuzzy sets, as regards their rationales, ap...

The paper focuses on the fuzzy extensions of two data analysis methods, namely the fuzzy cluster analysis and the fuzzy interpolation of spatial data (the so-called fuzzy kriging) and their suitability for ecological applications. Both extensions utilize exact (crisp) measurement data as well as imprecise data defined as fuzzy numbers or fuzzy vectors. Fuzzy clustering of fuzzy data (conical fu...

in this paper, we deal with molaei’s generalized groups. we definethe notion of a fuzzy generalized subgroup with respect to a t-norm (ort-fuzzy generalized subgroup) and give some related properties. especially,we state and prove the representation theorem for these fuzzy generalizedsubgroups. next, using the concept of continuity of t-norms we obtain a correspondencebetween tf(g), the set of ...

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 aim of this paper is to introduce and study the fuzzy neighborhood, the limit fuzzy number, the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence on the base which is adopted by Abdul Hameed every real number r is replaced by a fuzzy number r either triangular fuzzy number or singleton fuzzy set fuzzy point . And then, we will consider that some results re...

We characterize a fuzzy partial order relation using its level set, find sufficient conditions for the image of a fuzzy partial order relation to be a fuzzy partial order relation, and find sufficient conditions for the inverse image of a fuzzy partial order relation to be a fuzzy partial order relation. Also we define a fuzzy lattice as fuzzy relations, characterize a fuzzy lattice using its l...

We introduce a new notion of fuzzy r -interior which is an extension of Chang’s fuzzy interior. Using fuzzy r -interior, we define fuzzy r -semiopen sets and fuzzy r semicontinuous maps which are generalizations of fuzzy semiopen sets and fuzzy semicontinuous maps in Chang’s fuzzy topology, respectively. Some basic properties of fuzzy r -semiopen sets and fuzzy r -semicontinuous maps are invest...

Fuzzy decision tree induction algorithms require the fuzzy quantization of the input variables. This paper demonstrates that supervised fuzzy clustering combined with similarity-based rule-simplification algorithms is an effective tool to obtain the fuzzy quantization of the input variables, so the synergistic combination of supervised fuzzy clustering and fuzzy decision tree induction can be e...

The success and proliferation of the Semantic Web depends heavily on construction of Web ontologies. However, classical ontology construction approaches are not sufficient for handling imprecise and uncertain information that is commonly found in many application domains. Therefore, great efforts on construction of fuzzy ontologies have been made in recent years. In this paper, we propose a for...

The aim of this paper is to study monadic L-fuzzy quantifiers of the type 〈1〉 determined by fuzzy measures. These fuzzy quantifiers are defined using a novel notion of ⊗-fuzzy integral. Several semantic properties of these L-fuzzy quantifiers are studied. Keywords— fuzzy integral, fuzzy logic, fuzzy measure, fuzzy quantifier, generalized quantifier