Researches On Decision-making Methods And Applications Based On Probabilistic And Dual Hesitant Fuzzy Information

With the continuous development of science and technology,human beings are faced with more and more complex social problems.In the face of a large number of uncertain information,how to make necessary decisions more reasonably and effectively has become more and more important.Decision makers can effectively express their uncertain evaluations by using hesitant fuzzy information and its extended forms.Based on probabilistic and dual hesitation fuzzy information,this paper studies its multi-criteria decision-making methods and applies them to solve practical decisionmaking problems.The research work of this paper mainly includes the following aspects:(1)Based on dual hesitation fuzzy information,we study the multi-criteria decision-making method,which could deal with the interactive relationships among criteria.First of all,fuzzy measure is used to describe the interactive relationships between decision criteria so that the obtained weights of criteria could express the correlation between attributes more accurately.Then based on the prospect theory and the idea of the score function of the intuitionistic fuzzy number,a new score function and the corresponding comparison method of the dual hesitation fuzzy elements are proposed.In addition,combining the characteristics of the new score function and the traditional distance measure,we propose a new distance measure of dual hesitant fuzzy information.Finally,based on the new score function and the new distance measure,an extended VIKOR method is proposed under dual hesitant fuzzy environment and applied in the smartphone accessories supplier selection problem.(2)We propose a dual hesitant fuzzy multi-criteria group decision-making method based on the priority degree and decision makers' professional degree of dual hesitant fuzzy sets.Firstly,based on the priority degree of hesitant fuzzy information,we propose the priority of dual hesitant fuzzy sets based on pairwise comparisons.Then,based on the uniformity and stability of dual hesitant fuzzy information,the membership professional measure and the non-membership professional degree measure of decision expert are proposed.For determining the stability of dual hesitant fuzzy information,we propose a new entropy measure of dual hesitant fuzzy information.With the new entropy measure,we propose the decision professional measure of decision expert by combining the membership professional measure and the non-membership professional degree measure.The weight information of decision experts is analyzed from three expert professional degrees.Finally,a multi-criteria group decision-making method is proposed based on the priority degree and the professional degrees of decision expert,which could consider the ranking of alternatives from three aspects so as to obtain more reasonable decision-making results.The proposed multi-criteria group decisionmaking method is then applied to the policy promotion of rural land transfer in China.(3)Studying how to mine the deep hesitant or uncertain information of decision experts' hesitant fuzzy information,we propose the normal wiggly hesitant fuzzy set and apply it to practical decisionmaking problem.Considering that the hesitant fuzzy set could not fully express all the uncertain information of decision makers,we propose the real preference degree of hesitant fuzzy elements based on orness measure.The real preference degree could reflect the overall data preference of decision makers to hesitant fuzzy elements.By using the characteristics of normal distribution,the normal wiggly uncertainty range of every value in the hesitant fuzzy element could be determined,and then,we propose the normal wiggly range based on hesitant fuzzy element.Imitating the idea of interval-valued hesitant fuzzy set and triangular hesitant fuzzy set,based on the real preference degree and the normal wiggly range,we construct the normal wiggly hesitant fuzzy set.In addition,we study some necessary properties of normal wiggly hesitant fuzzy set and propose its basic operational laws,score function and aggregation operators.Finally,based on the aggregation operators of normal wiggly hesitant fuzzy set,we propose a multi-criteria group decision-making method and use it to solve the problem involving environmental quality evaluation.(4)Based on the probabilistic dual fuzzy information,an extended TODIM method is proposed and applied to enterprise strategy evaluation.Firstly,the modified score function of the probabilistic dual hesitant fuzzy element is proposed,which not only makes up for the deficiency of the existing comparison method that may ignore the deviation degree,but also corrects the calculation of the standard deviation of the deviation degree.Then,by analyzing the characteristics of probabilistic dual hesitant fuzzy information,the equiprobabilistic distance measure of probabilistic dual hesitant fuzzy set is proposed,which makes the calculation of distance measure more convenient and accords with people's cognition.Finally,based on the modified score function and the equiprobabilistic distance measure,we extend the TODIM method to the probabilistic dual hesitant fuzzy situations and use it to solve the problem of enterprise strategic assessment.(5)Based on probabilistic dual hesitant fuzzy information,we propose an integrated VIKOR-AHP multi-criteria group decision-making method and apply it to solve the problem of artificial intelligence strategy selection of enterprise.On the basis of the modified score function of probabilistic dual hesitant fuzzy element,considering that decision makers are more sensitive to negative evaluation(non-membership degree),we propose a comprehensive score function of probabilistic dual hesitant fuzzy element.Combined with the equiprobabilistic distance measure of probabilistic dual hesitant fuzzy set and the comprehensive score function,the general distance measure of probabilistic dual hesitant fuzzy information is proposed,which could consider the distance between different types of information from two different aspects.In addition,the concept of probabilistic dual hesitant fuzzy judgment matrix is proposed for the first time,and its consistency index detection and promotion method are studied to determine the weights of decision makers and decision criteria in multi-criteria group decision-making.Finally,based on the comprehensive score function,general distance measure and probability dual hesitant fuzzy judgment matrix,an integrated VIKOR-AHP multi-criteria group decision-making method is proposed and applied to the problem of artificial intelligence strategy selection of enterprise.