Intuitionistic fuzzy information aggregation plays an important part in intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. In this paper, we investigate the multiple attribute decision making (MADM) problems with intuitionistic fuzzy numbers. Then, we first introduce some operations on intuitionistic fuzzy sets, such as Einstein sum, Einstein product, and Einstein exponentiation, and further develop some new Einstein hybrid aggregation operators, such as the intuitionistic fuzzy Einstein hybrid averaging (IFEHA) operator and intuitionistic fuzzy Einstein hybrid geometric (IFEHG) operator, which extend the hybrid averaging (HA) operator and the hybrid geometric (HG) operator to accommodate the environment in which the given arguments are intuitionistic fuzzy values. Then, we apply the intuitionistic fuzzy Einstein hybrid averaging (IFEHA) operator and intuitionistic fuzzy Einstein hybrid geometric (IFEHG) operator to deal with multiple attribute decision making under intuitionistic fuzzy environments. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness.

Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making

In this paper, a decision-making method based on a cloud model is proposed in order to solve multi-criteria group decision-making problems in the situations where the criteria weights are known completely, but the decision-makers’ weights are unknown and the criteria values are interval linguistic variables. In the proposed method, the interval linguistic values are firstly converted into interval integrated clouds, and the preference aggregation is executed by means of generating floating clouds. Then the decision-makers’ weights are obtained by calculating the ‘uncertainty’ and ‘deviation’ degrees of the decision-makers, and the distances between alternatives are assessed by using the Hamming distance. Finally the ranking of all alternatives is determined by the corresponding distances. An example to illustrate the applicability of the proposed method is provided together with a comparison with some existing methods.

An Uncertain Linguistic Multi-criteria Group Decision-Making Method Based on a Cloud Model

Uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making

Many multi-criteria decision making (MCDM) methods have been proposed to handle uncertain decision making problems. Most of them are based on fuzzy numbers and they are not able to cope with risk in decision making. In recent years, some MCDM methods based on prospect theory to handle risk MCDM problems have been developed. In this paper, we propose a hybrid approach combining prospect theory and fuzzy numbers to handle risk and uncertainty in MCDM problems. So, it is possible to tackle more challenging MCDM problems. A case study involving oil spill in the sea illustrates the application of the novel method.

Combining prospect theory and fuzzy numbers to multi-criteria decision making

Evaluation based on Distance from Average Solution (EDAS) is a new multicriteria decision making (MCDM) method, which is based on the distances of alternatives from the average scores of attributes...

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Intuitionistic fuzzy edas method: an application to solid waste disposal site selection

With respect to risk decision making problems with interval probability in which the attribute values take the form of the uncertain linguistic variables, a multi-attribute decision making method based on prospect theory is proposed To begin with, the uncertain linguistic variables can be transformed into the trapezoidal fuzzy number, and the prospect value function of the trapezoidal fuzzy number based on the decision-making reference point of each attribute and the weight function of interval probability can be constructed; then the prospect value of attribute for every alternative is calculated through prospect value function of the trapezoidal fuzzy number and the weight function of interval probability, and the weighted prospect value of alternative is acquired by using weighted average method according to attribute weights, and all the alternatives are sorted according to the expected values of the weighted prospect values; Finally, an illustrate example is given to show the decision-making steps, the influence on decision making for different parameters of value function and different decision-making reference point, and the feasibility of the method

Minghe Wang

Papers

Research on the multi-attribute decision-making under risk with interval probability based on prospect theory and the uncertain linguistic variables