Multi Attribute Decision Making Based On Two Kinds Of Fuzzy Sets Concerning Probability

Zadeh proposed a fuzzy set,which uses a number(membership degree)between0 and 1 to describe the fuzziness of elements in the set.The proposal of fuzzy sets indicates that the uncertain problems in real life can be handled by mathematical thinking and way.Many scholars refine the uncertainty on the basis of fuzzy sets,and put forward many derived concepts of fuzzy sets according to different actual situations.Among them,the more typical ones are interval fuzzy set,hesitation fuzzy set,intuitionistic fuzzy set,chinese intelligence set and so on.The relevant theories are applied to decision-making,clustering,data mining,image processing,pattern recognition,matrix game,artificial intelligence and so on.Multi attribute decision making is a very important part in the field of decision making.It refers to the process of ranking and selecting the best decision making schemes with multiple attributes.The commonly used decision making methods include analytic hierarchy process,TOPSIS method,regret value decision making method and so on.Its main tools are integration operator and measure theory.The existing integration operators mainly include(weighted)arithmetic average operator,(weighted)geometric average operator,ordered(weighted)average operator,ordered weighted geometric operator,continuous ordered weighted average operator,continuous ordered weighted geometric operator,combined weighted arithmetic average operator,combined weighted geometric average operator,(weighted)Bonferroni average operator,(weighted)geometric Bonferroni average operator,heronian average operator and so on.The existing measurement theories mainly include similarity measure,distance measure,correlation measure and entropy measure,which are used to describe the relationship between fuzzy sets.They are often used in corporate supply chain selection,neural classifier,disease prediction,film review and other issues.Therefore,experts and scholars at home and abroad attach great importance to it.However,with the increasing complexity of the decision environment,the randomness of things in the decision making process inevitably needs to be taken into account.The existing concepts of combining fuzzy sets with probability include probability fuzzy sets,probability hesitation fuzzy sets,probability dual hesitation fuzzy sets,etc.,while fuzzy sets are less combined with the relevant theories of continuous distribution,Therefore,this paper studies the continuous probability distribution and discrete probability distribution according to the derived concepts of two fuzzy sets(interval fuzzy set and q-rung probability dual hesitation fuzzy set).Firstly,in the first part,aiming at the unbalanced value in the membership interval of interval fuzzy set,combined with the continuous random variable of normal distribution,the probability interval fuzzy set of normal distribution is proposed.Through this set,the possibility of probability distribution on the membership interval of interval fuzzy set can be further studied.The second part of the paper considers the probability components on the dual interval hesitation fuzzy set,and puts forward the q-rung probability dual interval hesitation fuzzy set combined with the needs of the decision-making process.In the actual decision making process,it not only considers the probability components of the dual interval hesitation fuzzy set between the membership and non membership regions,but also can well solve the situation that the sum of the maximum value of membership and the maximum value of non membership is greater than 1.The specific research results are as follows:Firstly,the normal distribution probability interval fuzzy set and the normal distribution probability interval fuzzy number are defined.Further,the union,intersection and complement of the normal distribution probability interval fuzzy set and the addition and multiplication of the normal distribution probability interval fuzzy number are given,it is verified that the operation satisfies idempotent law,commutative law,combination law,absorption law,distribution law and restoration law.In order to study decision problems,the similarity measure and distance measure of normal distribution probability interval fuzzy numbers are defined,and their properties are studied.In order to integrate data information,a normal distribution probability interval fuzzy weighted average operator is proposed,and the score function and deviation function are defined to rank the normal distribution probability interval fuzzy numbers.Finally,a decision making method is proposed in the normal distribution probability interval fuzzy environment,and an example is given to verify the feasibility and effectiveness of the method.Secondly,the q-rung probabilistic dual interval hesitant fuzzy sets and q-rung probabilistic dual interval hesitant fuzzy numbers are proposed,furthermore,the addition,multiplication,number multiplication and power operation of q-rung probabilistic dual interval hesitant fuzzy numbers are given.The operation satisfies the exchange law,combination law and distribution law.In order to study the relationship between q-rung probability dual interval hesitant fuzzy sets,the similarity measure and distance measure of q-rung probability dual interval hesitant fuzzy sets are defined.Then,a q-rung probabilistic dual interval hesitant fuzzy weighted average operator is proposed and its properties are studied.The score function and exact function of q-rung probability dual interval hesitation fuzzy set are proposed.Finally,the problem of air cushion selection for different skin types is solved in the q-rung probability dual interval hesitation fuzzy environment.