interval-valued intuitionistic fuzzy sets (ivifss) are widely used to handle uncertainty and imprecision in decision making. however, in more complicated environment, it is difficult to express the uncertain information by an ivifs with considering the decision-making preference. hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (g-givifss) which conta...

The purpose of this paper is to introduce and study the concepts of intuitionistic fuzzy weakly generalized closed set and intuitionistic fuzzy weakly generalized open set in intuitionistic fuzzy topological space. We investigate some of their properties. Also we study the application of intuitionistic fuzzy weakly generalized closed set namely intuitionistic fuzzy wT1/2 space and intuitionisti...

This paper is devoted to the study of intuitionistic fuzzy topological spaces. In this paper an intuitionistic fuzzy regular weakly generalized closed set and intuitionistic fuzzy regular weakly generalized open set are introduced. Some of its properties are studied. Also we have provided some applications of intuitionistic fuzzy weakly generalized closed set namely intuitionistic fuzzy rwT1/2 ...

Traditional fuzzy logic uses real numbers as truth values. This description is not always adequate, so in intuitionistic fuzzy logic, we use pairs of real numbers to describe a truth value. Such pairs can be described either as pairs (t; f) for which t + f 1, or, alternatively, as pairs (t; 1 ? f) for which t 1 ?f. To make this description even more adequate, instead of using real numbers to de...

Using a system of axioms among with a modified definition of boundary on the basis of the intuitionistic fuzzy sets, we formulate an inductive structure for the dimension of fuzzy spaces which has been defined by Coker. This new definition of boundary allows to characterize an intuitionistic fuzzy clopen set as a set with zero boundary. Also, some critical properties and applications are establ...

in some multi-attribute decision making (madm) problems, various relationships among the decision attributes should be considered. this paper investigates the prioritization relationship of attributes in madm with trapezoidal intuitionistic fuzzy numbers (trifns). trifns are a special intuitionistic fuzzy set on a real number set and have the better capability to model ill-known quantities. fir...

Intuitionistic fuzzy linguistic numbers (IFLNs) are an extension of the linguistic variables and the intuitionistic fuzzy sets, which are proposed by Wang and Li (Wang J.Q., Li J.J. (2009) The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Science & Technology Information (33), 8-9.). In this paper, we introduced some operational laws of IFL...

The problem of evaluating the building engineering quality with intuitionistic fuzzy information is the multiple attribute group decision making (MAGDM) problems. In this paper, we investigate the multiple attribute group decision making (MAGDM) problems for evaluating the building engineering quality with intuitionistic fuzzy information. We utilize the induced intuitionistic fuzzy ordered wei...

As a further extension of the fuzzy set and intuitive set, interval-valued (IIFS) is more effective tool to deal with uncertain problems. However, classical rough based on equivalence relation, which do not apply IIFS. In this paper, we combine IIFS ordered information system obtain (IIFOIS). On basis, three types multiple granulation models dominance relation are established effectively overco...

in this paper, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...