In this work, the axiomatical definition of similarity measure, distance measure and inclusion measure for interval-valued intuitionistic fuzzy soft set (IV IFSSs) are given. An axiomatical definition of entropy measure for IV IFSSs based on distance is firstly proposed, which is consistent with the axiomatical definition of fuzzy entropy of fuzzy sets introduced by De Luca and Termini. By diff...

In this paper, we investigate the multiple attribute decision making (MADM) problems for for evaluating the computer network security with interval-valued intuitionistic fuzzy information. To determine the attribute weights, a model based on the information entropy, by which the attribute weights can be determined, is established. We utilize the interval-valued intuitionistic fuzzy weighted ave...

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...

In this paper, an algorithm for VLSI standard cell placement for low power and high performance design is presented. This is a hard multiobjective combinatorial optimization problem with no known exact and efficient algorithm that can guarantee finding a solution of specific or desirable quality. Approximation iterative heuristics such as Simulated Evolution (SE) are best suited to perform an i...

the paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. motivated by an open question of s. e. rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of l. a. zadeh. on the next step, w...

For general type-2 fuzzy sets, the defuzzification process is very complex, and the exhaustive direct method of implementing type-reduction is computationally expensive and turns out to be impractical. This has inevitably hindered the development of type-2 fuzzy inferencing systems in real world applications. The present situation will not be expected to change, unless an efficient and fast met...

With respect to multiple attribute decision making problems with intuitionistic fuzzy information, some operational laws of intuitionistic fuzzy numbers, score function and accuracy function of intuitionistic fuzzy numbers are introduced. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established. For the special situations w...

In this paper the substantiation of the method of full averaging for fuzzy differential inclusions is considered. These results generalize the results of [17, 20] for differential inclusions with Hukuhara derivative and of [18] for fuzzy differential equations.

Cubic intuitionistic fuzzy (CIF) set is the hybrid set which can contain much more information to express an interval-valued intuitionistic fuzzy set and an intuitionistic fuzzy set simultaneously for handling the uncertainties in the data. Unfortunately, there has been no research on the aggregation operators on CIF sets so far. Since an aggregation operator is an important mathematical tool i...

This paper establishes the network marketing performance evaluation index system followed the principles of "scientific, objective, systematic, feasibility and stability". Then use interval-valued intuitionistic fuzzy sets OWA (Ordered Weighted Averaging) operator to calculate the evaluation value. The reason of this paper use interval-valued intuitionistic fuzzy sets is some index value is not...