A novel approach to interval-valued intuitionistic fuzzy soft set based decision making

Uncertain linguistic fuzzy soft sets and their applications in group decision making

“…The advantage of soft set is that it is free from the inadequacy of the parameterization tools, such as the probability theory, fuzzy sets and rough sets [1,4]. Recently, with these developments of soft set theory, kinds of applications have been studied, such as decision making [4][5][6][33][34][35][36], engineering [7], economics [8] and medical science [9], and so on. The meanings of kinds of soft sets are dealing with different practical issues based on vagueness and uncertainties.…”

Neutrosophic soft matrices and NSM-decision making

“…Later on, many interesting results of soft set theory have been obtained by embedding the idea of fuzzy set, intuituionstic fuzzy set, vague set, rough set, interval intuitionistic fuzzy set, intuitionistic neutrosophic set, interval neutrosophic set, neutrosophic set and so on. For example, fuzzy soft set [34], intuitionistic fuzzy soft set [17,31], rough soft set [24,25], interval valued intuitionistic fuzzy soft set [27,53,55], neutrosophic soft set [32,33], generalized neutrosophic soft set [7], intuitionstic neutrosophic soft set [8], interval valued neutrosophic soft set [20]. The theories has developed in many directions and applied to wide variety of fields such as on soft decision making [12,56], fuzzy soft decision making [18,19,30,45] ,on relation of fuzzy soft set [50,51], on relation on intuiotionstic fuzzy soft set [22,40], on relation on neutrosophic soft set [21], on relation on interval neutrosophic soft set [20] and so on.…”

Interval-valued neutrosophic soft sets and its decision making

“…Example 4.2 Consider the above Example 3.7, then, r ΥK (x, u) = υ K(x) (u) can be given as follows Zhang et al [40] introduced level-soft set and different thresholds on different parameters in interval-valued intuitionistic fuzzy soft sets. Taking inspiration these definitions we give level-soft set and different thresholds on different parameters in ivn−soft sets.…”

“…Obviously, the definition is an extension of level soft sets of interval-valued intuitionistic fuzzy soft sets [40]. can be viewed as a given greatest threshold on degrees of falsity-membership.…”

“…Obviously, the definition is an extension of level soft sets of interval-valued intuitionistic fuzzy soft sets [40]. If < α, β, γ > ΥK (x i ) ≤υ K(xi) (u) it shows that the degree of the truth-membership of u with respect to the parameter x is not less than α, the degree of the indeterminacy-membership of u with respect to the parameter x is not more than γ and the degree of the falsity-membership of u with respect to the parameter x is not more than β.…”