Distance Measure Of Complex Hesitant Fuzzy Information And Its Application In Decision-making

As the decision-making environment becomes more and more complicated,decision-making theories and methods that only consider precise numbers can no longer meet practical requirements.Hesitant fuzzy sets,probabilistic hesitant fuzzy sets and probabilistic linguistic term sets contain multiple possible evaluation values and their corresponding weights.These different types of complex hesitant fuzzy information can more comprehensively describe the hesitation and preference of decision makers and hence,they are main types of data used in multi-attribute decision-making issues.The present paper focuses on complex hesitant fuzzy distance measures and their applications in multi-attribute decision-making problems.The main research contents are as follows:(1)Propose a new method by a way of fitting hesitant fuzzy elements with normal distribution functions,and define a new hesitant fuzzy distance measure according to characteristics of normal distribution curves of two hesitant fuzzy elements.The measure can give differences of two probabilistic hesitant fuzzy elements by calculating the ratio of the difference in the area covered by two curves and their total area.Using the new measure,we establish a model that can maximize satisfaction of a scheme aiming at obtaining attribute weights.In addition,based on the prospect theory we propose a multi-stage and dynamic decision-making method under hesitant fuzzy environment.Applications to emergency decision-making problems,for instance,debris flow disaster,demonstrates the validity of the new method.(2)Propose new distance measures that can characterize the difference of probabilistic hesitant fuzzy information.It employs not only the difference in area covered by two curves to show the difference in possible values of probabilistic hesitant fuzzy elements but also the difference in the position of centers of two curves to reflect their overall difference,which can increase the discrimination of differences among different probabilistic hesitant fuzzy elements.On the basis of the new measure formula,by getting attribute weights with entropy weight methods and deviation maximization methods,the TODIM decision-making method that is suited for the probabilistic hesitant fuzzy environment is proposed.It is applied to handle emergency decisionmaking for subway waterlogging disasters as well as the decision-making problem of online conference software evaluation.(3)Probabilistic linguistic term sets can effectively express uncertain decisionmaking information.Using conversion functions to give expectation and standard deviations of probabilistic linguistic elements and the idea of fitting data by distribution functions,we put forward a new probabilistic linguistic distance measure formula.To better deal with complexity and uncertainty of decision-making problems,with the new distance measure we can take into account both quantitative hesitant fuzzy information and qualitative probabilistic linguistic information as evaluation values.We further suggest ELECTRE III methods that can tackle decision-making problems under complex hesitant fuzzy environments.College students’ employment is used as a case to illustrate the validity of the new decision-making method.