Multiple Attribute Group Decision Making Method Based On Correlation Coefficient And Entropy For Hesitant Fuzzy Information

Fuzzy theory is an important part of uncertain theory. The correlation coefficient and entropy measures have important theoretical value and practical meaning, they have become one of hot topics for domestic and foreign scholars. On the basis of the existing literature, we construct correlation coefficient formulae and entropy measures for hesitant information environment. When the attribute weights are completely unknown, we constructe a model based on the entropy measures to determine the weight vector. When the attribute weights are partially unknown, we establish a linear programming model to determine the weight vector. Finally, the correlation coefficient formulae and entropy measures are applied to solve the multiple attribute group decision-making problem. The specific work is as follows:1. In Hesitant fuzzy sets, two kinds of entropy formulae and correlation coefficient formulae are proposed. We establish the entropy weight model when the attribute weights are completely unknown. A new method for multi-attribute group decision making problem with correlation coefficient and entropy formulae is proposed.2. In the interval hesitant fuzzy sets, two kinds of distance measures and correlation coefficient formulae are proposed. Based on the distance measure, we present the definition of close degree. When the attribute weights are completely known, we apply the correlation coefficient and the close degree to rank alternatives and verify if the results are the same through an example.3. The definition of the dual hesitant fuzzy correlation coefficient is proposed. Two kinds of entropy for dual hesitant fuzzy sets are put forward, based on which, we present the method of determining weight for fuzzy multiple attribute group decision making. On the basis of the correlation coefficient and entropy, a new method for dual hesitant fuzzy multi-attribute group decision making problem with completely unknown attribute weight information is proposed.4. The definition of the Interval-valued dual hesitant fuzzy sets is proposed on the basis of the definition of the dual hesitant fuzzy sets, then we discuss some basic operation laws of it. We present the definition of the Interval-valued dual hesitant fuzzy correlation coefficient and construct the optimal modle for determining weight vector. A new method for Interval-valued dual hesitant fuzzy multi-attribute group decision making problem with incompletely known attribute weight information is proposed and we demonstrate that the method is practically and effective through an analysis of a case.5. In the intuitionistic dual hesitant fuzzy sets, the definition and the basic operation laws of the intuitionistic dual hesitant fuzzy set are proposed. We constucte the weighted arithmetic averaging operator and the weighted geometric averaging operator of intuitionistic dual hesitant fuzzy sets, then we consider the order and general situation. At the same time, for some special properties of the operators, we present the detailed description and proof. We demonstrate that the operators are practical and effective in solving multi-attribute group decision making problems.