Multi-attribute Group Decision Making For Hesitant Fuzzy Based On Probabilistic Information

Uncertainty and fuzziness exist extensively in the decision-making problems,which make big challenge for decision makers.Probabilistic hesitation fuzzy sets not only include memberships,but also include their corresponding probability information of memberships,which makes the description of fuzzy and uncertain information more accurate and more suitable to more complex multi-attribute decision-making problems.In this paper,several multiple attribute decision-making methods are studied including score functions,accuracy functions,distance measures,and matrix games based on the Pythagorean probabilistic hesitant fuzzy sets and probabilistic hesitant fuzzy language term set.The main work of this article is as follows:Pythagorean probabilistic hesitant fuzzy MABAC method is proposed based on TODIM method.First,Pythagorean probability hesitant fuzzy score function and accuracy function are developed considering mean,hesitancy of membership and nonmembership and herd psychology of decision makers.Second,attribute weights are calculated based on the theory of water-filling.Then incorporate dominant functions into MABAC method to give a new Pythagorean probabilistic hesitant fuzzy MABAC method based on TODIM method considering the decision makers’ psychology behavior.Finally,selection of invest alternatives has been used to illustrate its feasibility and effectiveness.A Pythagorean probabilistic hesitant fuzzy ELECTRE-II method is proposed based on combination weighting and a new distance measure.Firstly,a new distance measure is proposed for Pythagorean probability hesitant fuzzy environment considering the fuzziness and fluctuation of Pythagorean probability hesitant fuzzy sets and its four axioms,namely non-negativity,symmetry,reflexivity,and triangle inequality,are proved.Secondly,a maximum entropy model is constructed based on grey correlation to calculate the objective weights of attributes.Based on game theory,a combination weighting method is used to aggregate subjective and objective weights.Furthermore,the ELECTRE-II method is extended to the Pythagorean probability hesitant fuzzy environment,and alternatives are ranked obtained based on the positive and negative dominance graphs of alternatives.Finally,the feasibility and effectiveness of the proposed method are verified through a case study of selecting a medical health system.A new multiple attribute decision making method is proposed based on probabilistic hesitant fuzzy linguistic term information and matrix games.First of all,improve the value function of existing prospect theory by calculating the average values of decisionmaker evaluation information for each attribute as a reference point for the new value function of prospect theory in the probabilistic hesitant fuzzy linguistic environment.Secondly,construct double-objective optimization model based on min-max strategy to calculate expected returns to get the optimal solution of both sides of the game.A multi attribute decision making method is developed based on probabilistic hesitant fuzzy language terms by combing the prospect theory value function and matrix game.Finally,this method is verified through a case study of building a low-carbon economy to illustrate the feasibility and effectiveness.