Guixiang Wang

Using simple fuzzy numbers to approximate general fuzzy numbers is an important research aspect of fuzzy number theory and application. The existing results in this field are basically based on the unweighted metric to establish the best approximation method for solving general fuzzy numbers. In order to obtain more objective and reasonable best approximation, in this paper, we use the weighted distance as the evaluation standard to establish a method to solve the best approximation of general fuzzy numbers. Firstly, the conceptions of I-nearest r-s piecewise linear approximation (in short, PLA) and the II-nearest r-s piecewise linear approximation (in short, PLA) are introduced for a general fuzzy number. Then, most importantly, taking weighted metric as a criterion, we obtain a group of formulas to get the I-nearest r-s PLA and the II-nearest r-s PLA. Finally, we also present specific examples to show the effectiveness and usability of the methods proposed in this paper.

In this article, a new method of option pricing in the form of fuzzy number is established based on fuzzy number binary tree model. Firstly,by using the operation rules of fuzzy number addition and number multiplication in cut set form, the fuzzy number binary tree model is equivalently transformed into two families of classical binary tree models which change with the level value, and some properties of the two binary tree model families are obtained, which are related to solve the problem of fuzzy option pricing. Then, based on the results obtained by us, the concepts of fuzzy set option price and fuzzy number option price are defined, and a sufficient condition is obtained for fuzzy set option price to be fuzzy number option price in the fuzzy number binary tree model. And then, for the convenience of practical application, the concepts of fold line fuzzy set and fuzzy number option price are introduced, a sufficient condition for fold line fuzzy set option price to be fold line fuzzy number option price is obtained, and a specific solution method of the fold line set and the fold line fuzzy number option pricing are set up. At last, two specific examples are given to show how to solve the fold line set and the fold line fuzzy number option price.

In this paper, the problems of basic fuzzy event space and of probability fuzzy space are studied. Firstly, the concepts of basic fuzzy event, fuzzy event and basic fuzzy event space are defined, related properties are investigated, and some results that will be used in the next study of probability fuzzy space are obtained. Then, the definitions of the probability function for fuzzy events and probability fuzzy space are given, some properties of the defined probability function are obtained. In addition, some models of probability distribution of probability fuzzy space based on a known probability space are proposed, and some examples are given to show the usability of the proposed models of probability distribution.

In this paper, the problem of ranking multi-dimensional uncertain information based on fuzzy order is studied. At first, a specific fuzzy order on the fuzzy ellipsoid number space is defined, with which we can set up a dynamic ranking method which changes with the change of the level r for some objects which can be characterized by some multichannel uncertain digital information. Then its properties are investigated, some related results are obtained. And then, we give a practical example to show how to set up a dynamic ranking method which changes with the change of the level r for some objects which can be characterized by some multichannel uncertain digital information by using the fuzzy order proposed by us in the paper.