Trapezoidal Interval Type-2 Fuzzy Sets Research Articles

Fuzzy Multiple Attributes Group Decision-Making Based on Ranking Interval Type-2 Fuzzy Sets and the TOPSIS Method

In this paper, we present a new method for fuzzy multiple attributes group decision-making based on the proposed ranking method of trapezoidal interval type-2 fuzzy sets and the TOPSIS method. Firstly, we present a new method for ranking trapezoidal interval type-2 fuzzy sets. Secondly, we construct the decision matrix and the average decision matrix, respectively. Thirdly, we construct the weighting decision matrix and average weighting decision matrix, respectively. Fourthly, we construct the ranking decision matrix by calculating the ranking values of trapezoidal interval type-2 fuzzy sets in the average decision matrix. Then, we get the absolute positive ideal solution and the absolute negative ideal solution with respect to the attributes based on the ranking decision matrix. Then, we calculate the distance between each alternative and the absolute positive ideal solution and calculate the distance between each alternative and the negative ideal solution, respectively. Finally, we calculate the relative degree of closeness of each alternative. The larger the value of the relative degree of closeness of an alternative, the better the preference order of the alternative. The proposed fuzzy multiple attributes group decision-making method can overcome the drawbacks of the existing method.

An Approach to Multi-attribute Group Decision Making with Trapezoidal Interval Type-2 Fuzzy Sets and Application to Teaching Quality Assessment

AbstractTrapezoidal interval type-2 fuzzy sets (TIT2FSs) are a special kind of type-2 fuzzy sets. TIT2FSs are useful in dealing with fuzziness inherent in decision data and the decision-making process. For multi-attribute group decision-making problems in which the attribute values and attribute weights are TIT2FSs, a new decision-making approach is proposed. On the basis of the concept of barycenters, a new approach to ranking TIT2FSs is given. Four kinds of geometric aggregation operators for TIT2FSs are developed, including the TIT2FS weighted geometric average operator, TIT2FS ordered weighted geometric average operator, TIT2FS hybrid weighted geometric average operator, and extended TIT2FS hybrid weighted geometric average operator. The individual comprehensive values of alternatives are derived through the extended TIT2FS weighted geometric average operators. Using the TIT2FS hybrid weighted geometric average operator and the expert weights, the individual comprehensive values of alternatives are integrated into the collective ones, which are used to rank the alternatives. The practicability and effectiveness of the developed method are illustrated with a teaching quality assessment example.

A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets

Soft set theory, originally proposed by Molodtsov, has become an effective mathematical tool to deal with uncertainty. A type-2 fuzzy set, which is characterized by a fuzzy membership function, can provide us with more degrees of freedom to represent the uncertainty and the vagueness of the real world. Interval type-2 fuzzy sets are the most widely used type-2 fuzzy sets. In this paper, we first introduce the concept of trapezoidal interval type-2 fuzzy numbers and present some arithmetic operations between them. As a special case of interval type-2 fuzzy sets, trapezoidal interval type-2 fuzzy numbers can express linguistic assessments by transforming them into numerical variables objectively. Then, by combining trapezoidal interval type-2 fuzzy sets with soft sets, we propose the notion of trapezoidal interval type-2 fuzzy soft sets. Furthermore, some operations on trapezoidal interval type-2 fuzzy soft sets are defined and their properties are investigated. Finally, by using trapezoidal interval type-2 fuzzy soft sets, we propose a novel approach to multi attribute group decision making under interval type-2 fuzzy environment. A numerical example is given to illustrate the feasibility and effectiveness of the proposed method.