In our earlier work we have developed the axiomatic theory of the scalar cardinality of interval-valued fuzzy sets following Wygralak’s axiomatic theory of scalar cardinalities of fuzzy sets. The cardinality has been defined as a mapping from the set of interval-valued fuzzy sets with finite support to the set of closed subintervals of [0,+∞). We have shown that each scalar cardinality of inter...

In this paper, we first defined soft intervalvalued neutrosophic rough sets(SIVNrough sets for short) which combines interval valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of soft interval valued intuitionistic fuzzy rough sets( SIVIFrough sets). Finally an illustartive example is given to verfy the developped algorithm and to...

In this paper, associated with dominance relation, lattice theory and intuitionistic fuzzy sets theory, the lattice-valued information systems with interval-valued intuitionistic fuzzy decision are proposed and some of its properties are investigated carefully. And, an approach to knowledge reduction based on discernibility matrix in consistent latticevalued information systems with interval-va...

Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh's Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function. We de...

Bipolarity has not been much exploited in the spatial domain yet, although it has many features to manage imprecise and incomplete information that could be interesting in this domain. This paper is a first step to address this issue, and we propose to define mathematical morphology operations on bipolar fuzzy sets (or equivalently interval valued fuzzy sets or intuitionistic fuzzy sets).

a new approach to define the similarity measure betweeninterval-valued fuzzy sets is presented. the proposed approach isbased on a weighted measure in which the normalized similaritiesbetween lower functions and also between upper functions arecombined by a weight parameter. the properties of this similaritymeasure are investigated. it is shown that, the proposed measurehas some advantages in c...

This paper introduces fuzzy clustering algorithms that can partition objects taking into account simultaneously their relational descriptions given by multiple dissimilarity matrices. The aim is to obtain a collaborative role of the different dissimilarity matrices to get a final consensus partition. These matrices can be obtained using different sets of variables and dissimilarity functions. T...