Based On MCDM Interval Type-2 Fuzzy Numbers

Fuzzy multi-criteria decision making (MCDM) problems are common in our daily life. In practice, due to the fuzziness in the real world, the criteria values provided by decision makers usually take the form of traditional type-1fuzzy number. However, there are some limitations for type-1fuzzy number to model uncertainty, such as handling linguistics inaccurately. In order to deal with the problems, Zadeh proposed type-2fuzzy number which is characterised by both primary membership and secondary membership. Interval type-2fuzzy number is a special case of type-2fuzzy number where all the secondary membership values are equal to1. Compared with type-1fuzzy number, it can model the uncertainty more effectively and the computation is less complex than type-2fuzzy number. So far, only a few studies are regarding applying interval type-2fuzzy number to multi-criteria decision making problems. Thus, it is significant to study interval type-2fuzzy number in MCDM.In this paper, improvements in some relative theorems regarding trapezoidal interval type-2fuzzy number have been made based on the previous literature. And several decision making methods are proposed with regard to multi-criteria decision making problems where the criteria values are in the form of interval type-2fuzzy number. The main work is as follows:(1) Improved arithmetic operations of trapezoidal interval type-2fuzzy number have been defined. And expected value function is presented to compare trapezoidal interval type-2fuzzy number as well. Based on these, trapezoidal interval type-2fuzzy number weighted arithmetic averaging (TIT2-WAA), trapezoidal interval type-2fuzzy number weighted geometric averaging (TIT2-WGA) are proposed and some properties are proved. For MCDM where the criteria weights are known and taking the form of crisp data, two methods based on TIT2-WAA and TIT2-WGA aggregation operators are presented, separately. First, all the criteria values and criteria weights are aggregated by those two operators, respectively, to obtain the overall value of each alternative, then the expected value function is employed to compare the the computed overall values to rank the alternatives. Besides, those results obtained which are the same based on the two different operators are demonstrated to prove the effectiveness of these aggregation operators. For group MCDM in which the criteria weights are known and in the form of trapezoidal interval type-2fuzzy number, the Hamming distance is defined and a new method is proposed. First, TIT2-WAA is used to aggregate all the criteria values, thus both the positive and negative ideal point are determined. Then the Hamming distance from each alternative to the positive ideal point and negative ideal point are calculated, separately. Finally, the coefficients are computed to get the ranking of all alternatives.(2) Fuzzy MCDM problems are discussed with different preference information taking different forms. With regard to one form of decision information and several forms of decision information in the process of decision making, corresponding methods are proposed, respectively. For MCDM with only one form of preference information in the form of interval type-2fuzzy number, a new way to calculate possibility degree is developed to overcome the drawbacks of the existing one. And some properties are proved subsequently. In this situation, an optimal model based on deviation degree is constructed to obtain the optimal weight coefficients due to the unknown criteria weights. Then a possibility degree matrix is constructed by comparing the overall values of alternatives, thus the ranking vector is calculated to make a ranking to find out the best alternative. For MCDM with two forms of decision information, expected value function is used to convert interval type-2fuzzy number into crisp data to make comparison with other information on the same scale. Given the preference value provided by decision makers, prospect theory is introduced. Above all, the deviations between the criteria value and the preference point are computed. Then the prospect value of each criterion is calculated based on the value function. Moreover, the overall prospect values are obtained by TIT2-WAA operator to rank all the alternatives.(3) Fuzzy MCDM problems based on similarity measure are studied. The similarity of trapezoidal interval type-2fuzzy number is defined above all. For MCDM in which the criteria weights are partly unknown, a new method based on similarity is presented. First, both the positive and the negative ideal alternative are determined by comparing all the expected values. A maximum linear programming model based on the similarity from the alternative to the positive ideal alternative and a minimum linear programming model based on the similarity from the alternative to the negative ideal alternative are constructed, respectively. Combine the two models together to obtain the weight coefficients and then the overall value of each alternative is calculated to sort all alternatives. Besides, another novel approach, to solve MCDM where the criteria weights are known taking the consensus between the individual and expert group into consideration, is proposed. And, trust degree is defined. Above all, according to the criteria weights provided by each expect and the computed relative similarity between the individual and group, the overall criteria weights are calculated. Then, the overall values of alternatives can be computed. Finally, trust degree is obtained, thus a selected sequence is determined to pick out the best alternative.