Interval-valued Intuitionistic Fuzzy Matrix Research Articles

Interval-valued intuitionistic fuzzy multi-attribute group decision-making method considering risk preference of decision-makers and its application

An improved interval-valued intuitionistic fuzzy multi-attribute group decision-making method considering the risk preference of decision-makers is proposed to solve the multi-attribute group decision-making problem with interval-valued intuitionistic fuzzy numbers and the condition that the attribute weight information is completely unknown. Firstly, the decision-maker weight of each attribute is determined by combining similarity and proximity. In order to consider the influence of the decision-maker's risk preference on the decision result and avoid the asymptotic behavior of interval-valued intuitionistic fuzzy matrix, the risk aversion coefficient of the decision-maker is introduced and combined with the determined decision-maker's weight aggregation to form a group decision matrix. Then, the information of group decision matrix is mined, and the interval-valued intuitionistic fuzzy entropy is used to determine the attribute weight and relative weight. Based on the interval-valued intuitionistic fuzzy distance measure formula and the TODIM method, the overall superiority of each scheme relative to other schemes is obtained by calculating the superiority between schemes, and the optimal scheme is determined by comparing and sequencing. Finally, the rationality and effectiveness of the proposed method are verified by an example of mechanical assembly supplier selection decision.

English

Inequality, also known as inequation, but unlike equation does not have rich history. After the introduction of equation, inequation captures its popularity in different fields namely algebra, geometry, trigonometry, probability, set theory, fuzzy set theory, logic, calculus etc. Whereas inequalities used in algebra are called algebraic inequalities, the ones used in geometry are called geometric inequalities etc. However, if the same techniques used in solving an equation are used for an inequation, wrong results may be obtained. Unlike equation, it has limited applications. When two quantities or expressions are not the same, then we use inequality and it is written by cross-out equal sign ( ) or . From a logical point of view, there is a difference between and . Sometimes we explain inequalities in linguistic form to describe the social values. All the above discussions on inequalities have been done according to the classical sense. In view of the present situation, it is necessary to extend this concept to fuzzy sense. Many researchers and mathematicians have shown the use of inequalities in fuzzy set, intuitionistic fuzzy set, soft set, rough set etc to describe the imprecise data. In this paper, some results related to inequalities of interval-valued intuitionistic fuzzy matrices with respect to algebraic sum and algebraic product were studied and proven. Key words: Fuzzy matrix, Interval-valued intuitionistic fuzzy matrix, algebraic sum, algebraic product.

Interval-valued intuitionistic fuzzy matrix games based on Archimedean t-conorm and t-norm

Fuzzy game theory has been applied in many decision-making problems. The matrix game with interval-valued intuitionistic fuzzy numbers (IVIFNs) is investigated based on Archimedean t-conorm and t-norm. The existing matrix games with IVIFNs are all based on Algebraic t-conorm and t-norm, which are special cases of Archimedean t-conorm and t-norm. In this paper, the intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm are employed to aggregate the payoffs of players. To derive the solution of the matrix game with IVIFNs, several mathematical programming models are developed based on Archimedean t-conorm and t-norm. The proposed models can be transformed into a pair of primal–dual linear programming models, based on which, the solution of the matrix game with IVIFNs is obtained. It is proved that the theorems being valid in the exiting matrix game with IVIFNs are still true when the general aggregation operator is used in the proposed matrix game with IVIFNs. The proposed method is an extension of the existing ones and can provide more choices for players. An example is given to illustrate the validity and the applicability of the proposed method.

A method based on distance measure for interval-valued intuitionistic fuzzy group decision making

In this paper we introduce some relations and operations of interval-valued intuitionistic fuzzy numbers and define some types of matrices, including interval-valued intuitionistic fuzzy matrix, interval-valued intuitionistic fuzzy similarity matrix and interval-valued intuitionistic fuzzy equivalence matrix. We study their properties, develop a method based on distance measure for group decision making with interval-valued intuitionistic fuzzy matrices and, finally, provide an illustrative example.