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...

Multi-criteria decision-making (MCDM) problem is the process of finding the best option from all of the feasible alternatives where all the alternatives can be evaluated according to a number of criteria or attribute. Since human judgments including preferences are often vague and cannot estimate his preference with an exact numerical value. Multi-criteria decision-making problems usually consi...

Recently, the rough set and fuzzy set theory have generated a great deal of interest among more and more researchers. Granular computing (GrC) is an emerging computing paradigm of information processing and an approach for knowledge representation and data mining. The purpose of granular computing is to seek for an approximation scheme which can effectively solve a complex problem at a certain ...

In the present paper, a new entropy of order and type on Interval-Valued Intutionistic Fuzzy Sets (IVIFSs) along with their proofs of validity is proposed. It has been proved that the proposed entropy has monotonic decreasing behavior with respect to and . Further, a new algorithm for multiple attribute decision making method (MADM) has been provided using the benefit attributes and cost attrib...

We introduce the notions of interval-valued fuzzy prime ideals, interval-valued fuzzy completely prime ideals and intervalvalued fuzzy weakly completely prime ideals. And we give a characterization of interval-valued fuzzy ideals and establish relationships between interval-valued fuzzy completely prime ideals and interval-valued fuzzy weakly completely prime ideals.