Consider sets X and Y each with associated membership functions. Further suppose that there is a map f : X → Y . A membership may be induced onY from the membership ofX calculated using the extension principle, and the two memberships on Y may be combined to give an overall membership. The point with the highest membership in X can be determined directly or by back mapping the value with the hi...

Using mid-infrared and radio criteria, we select a sample of candidate z ∼ 2 obscured quasars. Optical spectroscopy confirms about half of these as type-2 quasars, and modelling the population suggests 50-80% of the quasars are obscured. We find some flat radio spectrum type-2 quasars, and tentative evidence for obscuration unrelated to the torus. Using a similar sample, we also find evidence f...

The concepts of fuzzy e-open sets and fuzzy e-continuous are introduced and studied in fuzzifying topology and by making use of these concepts, we introduce and study T e 0 -, R e 0-, T e 1 -, R e 1-, T e 2 -, T e 3 -, T e 4 -, strong T e 3 and strong T e 4 separation axioms in fuzzifying topology and give some of their characterizations as well as the relations of these axioms and other separa...

in this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. thena relation between totally fuzzy bounded sets and n-compactness is discussed.finally, a geometric characterization for fuzzy totally bounded sets in i- topologicalvector spaces is derived.

Welcome to the Journal of Intelligent and Fuzzy Systems’s special issue for “FUZZYSS’2009: 1st International Fuzzy Systems Symposium”. Since its introduction by Prof. Lotfi A. Zadeh fuzzy logic has found numerous applications in many diverse areas. Scientific research related to fuzzy logic and its extensions is still an open and promising active research area. There is still a very long way to...

The present paper studies fuzzy matroids in view of degree. First wegeneralize the notion of $(L,M)$-fuzzy independent structure byintroducing the degree of $M$-fuzzy family of independent $L$-fuzzysets with respect to a mapping from $L^X$ to $M$. Such kind ofdegrees is proved to satisfy some axioms similar to those satisfiedby $(L,M)$-fuzzy independent structure. ...

Fuzzy relations are able to model vagueness, in the sense that they provide the degree to which two objects are related to each other. However, they cannot model uncertainty: there is no means to attribute reliability information to the membership degrees. Intuitionistic fuzzy sets, as de1ned by Atanassov (Instuitionistic Fuzzy Sets, Physica-Verlag, Heidelberg, New York, 1999), give us a way to...

Fuzziness is not a priori an obvious concept and demands some explanation. “Fuzziness” is what Black (NF 1937) calls “vagueness” when he distinguishes it from “generality” and from “ambiguity.” Generalizing refers to the application of a symbol to a multiplicity of objects in the field of reference, ambiguity to the association of a finite number of alternative meanings having the same phonetic...

In many applications, multiple correlation and partial correlation for three or more fuzzy sets are very important, but Chiang and Lin (1999, Fuzzy Sets and Systems 102: 221–226) do not solve this problem. Here, we propose a method to calculate the multiple correlation and partial correlation for fuzzy data, by adopting the concepts from the multivariate correlation model. In order to fit into ...

Since its original formulation, the theory of fuzzy sets has spawned a number of extensions where the role of membership values in the real unit interval $[0, 1]$ is handed over to more complex mathematical entities. Amongst the many existing extensions, two similar ones, the fuzzy multisets and the hesitant fuzzy sets, rely on collections of several distinct values to represent fuzzy membershi...