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...

It is believed that multi attribute decision making problem is an ill-defined and unstructured problem. This difficulty intensifies while considering the uncertainty of decision makers’ information about the problem. In recent years, interval valued intuitionistic fuzzy sets (hereafter IVIFs) as a generalization of ordinal fuzzy sets, became a well-known and widely applied framework for dealing...

In the interval-valued intuitionistic fuzzy environment unconscientious opinions may cause problems in data processing. The problem is similar to those arising case of sets. this paper previous ways correction experts’ evaluations sets are presented and some new algorithms proposed.

The aim of this paper is further to develop the filter theory on residuated lattices. The concept of interval valued intuitionistic (T, S)-fuzzy filters on residuated lattices is introduced by linking the intuitionistic fuzzy set, t-norm, s-norm and filter theory of residuated lattices; The properties and equivalent characterizations of Interval valued intuitionistic (T, S)-fuzzy filters are in...

The linear programming technique for multidimensional analysis of preference (LINMAP) is one of the well-known methods for multiple attribute group decision making (MAGDM). In this paper, we extend the LINMAP method to solve MAGDM problems in interval-valued intuitionistic fuzzy environment in which all the preference information provided by the decisionmakers is presented as interval-valued in...

As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number. However, there are fewer relia...

Based on the Choquet integral and the generalized Shapley function, two new induced Atanassov’s interval-valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley Atanassov’s interval-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley Atanassov’s interval-val...

Various attempts have been made by researchers on the study of vagueness of data through intuitionistic fuzzy sets and vague sets, and also it was shown that vague sets are intuitionistic fuzzy sets. But there are algebraic and graphical differences between vague sets and intuitionistic fuzzy sets. In this paper an attempt is made to define the correlation coefficient of interval vague sets lyi...