In this paper, (α,β)-interval valued set is studied. The order relation on defined. It shown that complete lattice by giving the definitions of infumum and supremum these sets. Then, negation function sets introduced. 
 With help ,(α,β)-interval intuitionistic fuzzy are fundamental algebraic properties examined. level subsets given. Some propositions examples

organizations need to evaluate project proposals and select the ones that are the most effective in reaching the strategic goals by considering sustainability issue. in order to enhance the effectiveness and the efficiency of project oriented organizations, in this paper a new multi-objective decision making (modm) approach of sustainable project portfolio selection is proposed which applies in...

In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system (FLS). In order to make the type-2 FLS reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and probability type reduce reasoning method for the interval-valued FLS are developed. We have...

A new accuracy function for the theory of interval-valued intuitionistic fuzzy set, which overcomes some difficulties arising in the existing methods for determining rank of interval-valued intuitionistic fuzzy numbers, is proposed by taking into account the hesitancy degree of interval-valued intuitionistic fuzzy sets. By comparing it with several proposed accuracy functions, the necessity and...

seismic hazard assessment like many other issues in seismology is a complicated problem, which is due to variety of parameters affecting the occurrence of earthquake. uncertainty, which is a result of vagueness and incompleteness of the data, should be considered in a rationale way. herein, fuzzy set theory is used to take into account the uncertainty existed in the seismic hazard analysis. the...

Two definitions of fuzzy sets with Boolean-valued membership functions, introduced by Drossos and Markakis and called by them external and internal Boolean fuzzy sets, are compared with a third, classical definition descending more directly from the original Zadeh's and Goguen's ideas. Under some rather general conditions, internal and classical Boolean fuzzy sets are proved to be equivalent in...

We present a procedure for the construction of multi-valued t-norms and t-conorms. Our procedure makes use of a pair of single-valued t-norms and the respective dual t-conorms and produces interval-valued t-norms u and t-conorms t. In this manner we combine desirable characteristics of different t-norms and t-conorms; if we use the t-norm ∧ and t-conorm ∨, then (X,u,t) is a superlattice, i.e. t...

In this paper the notions of bipolar valued fuzzy subsemigroup, bipolar valued fuzzy bi-ideal, bipolar valued fuzzy (1,2)ideal and bipolar valued fuzzy ideal in a Γ-semigroup have been introduced. Some important characterizations are also obtained. Mathematics Subject Classification: 20M12, 03F55, 03E72

In this work, we explain the reasons for which, for some specific problems, interval-valued fuzzy sets must be considered a basic component of Soft Computing.

Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of generalised interval-valued fuzzy soft set are proposed and their basic properties are studied. The lattice structures of generalised interval-valued fuzzy soft set are also discussed. Furthermore, an application o...