Abstract
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.
Highlights
Due to the complexity of the environment and the limitations of human inherent cognition, daily life is full of uncertain information
A fuzzy number, which the notion was proposed by Zadeh in [5,6,7], has a good application in dealing with uncertain information
In [11], with the aid of fuzzy soft β−neighborhoods, Atef, Ali and Al-shami introduced fuzzy soft covering-based multi-granulation fuzzy rough set models, which have a good application in solving multiattribute group decision making (MAGDM) problems
Summary
Due to the complexity of the environment and the limitations of human inherent cognition, daily life is full of uncertain information. In order to establish a method to obtain a more objective and reasonable approximation solution, in this paper, we are going to use the weighted metric as the evaluation standard to explore the problem of using simple fuzzy numbers to approximate general fuzzy numbers. From the structure of the two metrics, the establishing of a method of solving the best approximation fuzzy numbers based on weighted metric is much more complex to calculate than that based on unweighted metric. This will bring some difficulties to the work we will do.
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