The Study Of Uncertain Information Processing Based On Z-number

Plenty of uncertain information has been taken into consideration in the scientific research and real applications.According to the originality of the uncertainty of the information,uncertain information can be divided into two categories: stochastic uncertain information and fuzzy uncertain information.Stochastic uncertainty causes from the uncertain results of the related event(or proposition),which belongs to the field of probability theory and statistic theory.Fuzzy uncertainty causes from the uncertain definition of the object,which belongs to the field of fuzzy theory and possibility theory.The fuzzy phenomenon,which is deriving from the imprecise and unreliable knowledge of the humans,especially in the research of intelligent expert system,drives the study of uncertain information processing into an increasingly hot topic since the founder of fuzzy theory Zadeh presents the concept of fuzzy set in 1960.Kinds of the extended fuzzy sets,e.g.intuitionistic fuzzy sets,Type-2fuzzy sets,and Z-numbers become the research focus in the artificial intelligence gradually.Znumber proposed by Zadeh in 2011,is a new framework of the fuzzy sets to deal with uncertain information,which is combined with stochastic uncertain and fuzzy uncertain information.Comparing with the previous fuzzy set,e.g.Type-2 fuzzy set,Z-numbers explicitly add the information of reliability for the fuzzy constraint.Zadeh noted that the additive reliability of fuzzy constraint can better simulate the thinking of human.From this perspective,Znumber is a more flexible framework to express the human knowledge.In the past six years,some scholars have investigated the development of the theory of Z-number and applications based on Z-number.The study of the theory of Z-number mainly includes the arithmetic of Z-numbers,approximate reasoning based on Z-numbers,and ranking of Z-numbers,etc.The research of the application of Z-number mainly includes control systems based on Z-number,and multiple attribute decision-making using Z-numbers,etc.Generally speaking,the study of Z-number still stands its initialization.Some of the shortcomings of the previous work of Z-numbers are heavy time costing of the procedure,hard understanding of the process,and not available to the real application,especially in the management of the emergent event.For the shortcomings of the previous work of Z-numbers,we mainly focus the issues of Z-number as follows,1)How to generate Z-number according to the least information automatically.Decision process depends not only the membership function but also the decision-maker's attitude or preference.We proposed a method of generating Z-number based on the OWA weights using maximum entropy considering the attitude(preference)of the decision-maker.Some numerical examples are used to illustrate the effectiveness of the proposed method.Results show that the attitude(preference)of the decision-maker can give an optimal possibility distribution of the reliability for Z-number using maximum entropy.2)How to manage the uncertainty for Z-number.We developed a modifed uncertainty measure of fuzzy set considering the influence of fuzziness measure and the range(or cardinality)of the fuzzy set.Some properties of the developed uncertainty measure of the fuzzy set are presented.We propose a method of measuring the uncertainty of Z-number,of which the properties are discussed.Some examples are used to illustrate the effectiveness of the proposed methodologies.Results show that the developed uncertainty measure for the fuzzy set can overcome the shortcoming of the original measure only considering fuzziness measure.In addition,the proposed uncertainty measure for Z-number can effectively represent the uncertainty of the Z-number.3)How to simplify the information process of Z-number.To some extent,how to convert Z-number to classical fuzzy number is rather significant for the application.In this paper,a method of transforming Z-number to classical fuzzy number is proposed according to the Fuzzy Expectation of fuzzy number.The proposed methodology is easy,less time costing and available to the real applications.In addition,a methodology for supplier selection using Z-numbers is proposed.It includes two parts: one solves the issue how to convert Z-number to the classic fuzzy number according to the fuzzy expectation;the other solves the problem how to get the optimal priority weight for supplier selection with genetic algorithm(GA),which is a more efficient method for calculating the priority weight of the judgment matrix.Finally,an example for supplier selection is used to illustrate the proposed methodology.4)To handle the utility of Z-number,we developed a new notion,i.e.the total utility of Z-number to measure the comprehensive effects of a Z-number,which is potentially useful in simplifying the Z-number based applications in fuzzy decision making.The function of the total utility of Z-numbers is absolutely derived from the format of Z-numbers without subjective judgment.The proposed total utility of Z-numbers is a general framework to deal with arbitrary kinds of Z-numbers(e.g.,triangular fuzzy number-based,Gaussian fuzzy number-based,trapezoidal fuzzy number-based,mixed types-based,etc.).The analytical solutions of the common cases of Z-numbers based on triangular fuzzy numbers and Gaussian fuzzy numbers are obtained using the proposed method in this paper.The mathematical properties of the total utility of Z-numbers are also specifically discussed.The results of the proposed method were compared with the results of previous work,and the effectiveness of the total utility of Z-number was verified.Finally,a real-world application of the total utility of Z-number in the failure modes risk assessment of a geothermal power plant(a case study)were used to illustrate the procedure of application of the total utility of Z-numbers.From the results of the application in the failure modes risk assessment of the geothermal power plant,the proposed method was deemed useful to identify the top potential failure modes.The results of the proposed method are of great significance for dealing with emergency scenarios.5)The method to determine the basic probability assignment of Z-numbers is a significant and open issue in the Dempster-Shafer framework since the aggregation of the Z-information is a pervasive phenomenon in the real application,especially in the multi-sources information scenarios.In this paper,we generalize the formulation of total utility of Z-number into Znumber with generalized fuzzy numbers based.In addition,a method to determine the basic probability assignment(BPA)based on the generalized total utility of Z-number is proposed.We illustrate the effectiveness of the generalized total utility of Z-number by the classical testing database of the fuzzy number.The method of generating BPA using the generalized total utility of Z-number is applied to estimate the risk of contaminant intrusion in a water distribution network to illustrate the effectiveness of the method.The proposed method is simple and practical in decision-making with multi-sources information.6)Evolutionary games with the fuzzy set are attractively growing.Among previous studies,the role of the reliability of knowledge is still virgin and may become a fascinating issue.In this paper,the stable strategy analysis based on the utility of Z-number in the evolutionary games is proposed,which can simulate the procedure of human's competition and cooperation more authentically and more flexibly.Some numerical examples have been used to illustrate the effectiveness of the proposed methodology.It is concluded that the proposed method can degenerate into the classical ESS when the information is extremely reliable.Another interesting conclusion can be made that the profit decreases with the increasing uncertainty of the information in spite of unchangeable ESS.