The concept of quasi-coincidence of interval valued fuzzy point with an interval valued fuzzy subset has considered. By using this idea, the notion of interval valued (α, β)-fuzzy hyperideal in a semihyperring introduced and consequently, a generalization of interval valued fuzzy hyperideals and interval valued fuzzy hyperideals have defined. In this paper, we study the related properties of th...

In this paper, we show that bilattices are robust mathematical structures that provide a natural accommodation to, and bridge between, intuitionistic fuzzy sets and interval-valued fuzzy sets. In this way, we resolve the controversy surrounding the formal equivalence of these two models, and open up the path for a new tradition for representing positive and negative information in fuzzy set the...

This study suggested a new similarity measured method that based on the map distance operator to solve before similarity measurement between interval-valued fuzzy numbers. In addition, some properties of the proposed similarity measure have been demonstrated, and 19 sets of interval-valued fuzzy numbers are adopted to compare the proposed method with existing similarity measures. The results of...

One of the extensions of binary morphology to greyscale images is given by the classical fuzzy mathematical morphology. Interval-valued fuzzy mathematical morphology further extends the latter theory by now also allowing uncertainty in the grey values of the image. In this paper, the decomposition of the intervalvalued fuzzy morphological operations into their binary counterparts is studied bot...

Fuzzy relations on the same domain are classified according to the equality of families of cut sets. This equality of fuzzy relations is completely characterized, not only for unit interval valued fuzzy relations, but more generally, for fuzzy relations whose domain is a (complete) lattice. Similar results for fuzzy sets in general are considered in [12]. Applications of the results for fuzzy c...