The Study Of Intuitionistic Hesitant Fuzzy Multi-criteria Group Decision-making Methods

Abstract:With the increasing complexities of environment, more and more factors should be taken into consideration in the decision making process and the multi-criteria group decision making problem is becoming a hot spot of research. As the environment of natural disasters is of great complexities which resulted from the pressure of time and the block of information and transportation, the emergency logistics decision-making of natural disaster background has a great deal of uncertainties. Regarding to the uncertain multi-criteria decision-making problems in complex environment, the uncertainties includes fuzziness, randomness, grayness, generic grayness and multi-uncertainty etc., where the fuzziness is the kernel of this paper. On the basis of predecessors’ research achievements, this paper provides a solution to the emergency logistics evaluation problems of natural disaster background, the main research achievements are listed as follows:(1) The definition of intuitionistic hesitant fuzzy set (number) together with corresponding properties and arithmetic operations are introduced. Score function and uncertain function are defined to compare the intuitionistic hesitant fuzzy numbers. The intuitionistic hesitant fuzzy number (IHFN) proposed in this paper is an improvement of dual hesitant fuzzy number, of which operational rules are on the basis of t-norm and t-conorm theories.(2) Two kinds of multi-criteria decision-making methods which on the basis of the intuitionistic hesitant fuzzy aggregation operators are proposed, where one kind of the aggregation operators is the intuitionistic hesitant fuzzy traditional operators, including intuitionistic hesitant fuzzy weighted arithmetic averaging (IHFWAA) operator and intuitionistic hesitant fuzzy weighted geometric average (IHFWGA) operator, another kind of aggregation operators is the intuitionistic hesitant fuzzy prioritized operators, including intuitionistic hesitant fuzzy PRI-AND (IHFPRI-AND) operator and intuitionistic hesitant fuzzy PRI-OR (IHFPRI-AND) operator. A hypothesis of "completely compensability between criteria" is a precondition to the above two methods.(3) Two kinds of outranking methods with intuitionistic hesitant fuzzy information are proposed, they are intuitionistic hesitant fuzzy ELECTRE I method and intuitionistic hesitant fuzzy PROMETHEE II method, respectively. For these two methods, a hypothesis of "incompletely compensability between criteria" is a precondition.(4) Applying the above methods in evaluating the emergency logistics alternatives of natural disaster background, it turns out that the results of the four methods are of great consistency. The proposed four methods can effectively depict the fuzziness inherent in the evaluation of emergency logistics alternatives and make the evaluation closer to the practical situation. Hence, the research of this paper can provide a good reference to the multi-criteria decision-making problems similar to the emergency logistics alternatives evaluation in natural disaster circumstance.