Using the concept of m-open sets, M-regularity and M-normality are introduced investigated. Both these notions closed under arbitrary product. M-normal spaces found to satisfy a result similar Urysohn lemma. It is shown that sets can be separated by m-continuous functions in regular space.

We reformulate Mesiar’s hypothesis [Possibility measures, integration and fuzzy possibility measures, Fuzzy Sets and Systems 92 (1997) 191196], which as such was shown to be untrue by Murofushi [Two-valued possibility measures induced by σ-finite σ-additive measures, Fuzzy Sets and Systems 126 (2002) 265268]. We prove that a two-valued σ-maxitive measure can be induced by a σ-additive measure u...

It is shown that, for any spatial frame L (i.e., L is a complete lattice generated by the set of all prime elements), both the specialization L-preorder of L-topological spaces introduced by Lai and Zhang [Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006) 1865–1885] and that of L-fuzzifying topological spaces introduced by Fang and Qiu [Fuzzy orders and fuzzifying topologies,...

In fuzzy data analysis, a simple correlation coefficient provides us with a good sense of linear relationship between two fuzzy attributes, while a partial correlation coefficient shows the relationship between two fuzzy attributes when the influences of other fuzzy attributes are partialed out from both of the two attributes. But, in some practical applications, we need to use the correlation ...

In this paper, a new class of fuzzy sets called fuzzy strongly g∗-closed sets is introduced and its properties are investigated. Moreover, we study some more properties of this type of closed spaces.

In this paper, we have dealt with the concept of fuzzy b-closed and fuzzy bcompact set, and we study the characterization of fuzzy b-compact set by using fuzzy filterbases. We consider some relations between the fuzzy b-compact space and fuzzy b-closed space. Finally, the concept of bounded and semi bounded operators between fuzzy normed space are studied and some immediate results are also pro...

semi-regular locales are extensions of the classical semiregularspaces. we investigate the conditions such that semi-regularizationis a functor. we also investigate the conditions such that semi-regularizationis a reflection or coreflection.

This derivation of (2) is not valid, because this duality applies to inferences and theorems only, not to definitions. In fact, (1) should be treated as an axiom. Accordingly, the duality of Lemma 3.3.1 would not be valid until the dual (2) of (1) is proved independently, as we do below. Our new proof will make use of Proposition 3.3.3, the original proof of which is based on duality. So, we mu...

Answering a recent question posed by Gregori, Morillas and Sapena (“On a class of completable fuzzy metric spaces”, Fuzzy Sets and Systems, 161 (2010), 2193–2205) we present two examples of non strong fuzzy metrics (in the sense of George and Veeramani).