Weighted pseudometric approximation of 2-dimensional fuzzy numbers by fuzzy 2-cell prismoid numbers preserving the centroid

Abstract

Up to now, there have been many research results about approximations of fuzzy numbers by specific fuzzy numbers under preservation of some operators. However, there are few investigations about approximations of n-dimensional fuzzy numbers. The main reason is that the structure of n-dimensional fuzzy numbers are more complex. This paper devotes to seek an approximation operator that produces a special kind of 2-dimensional fuzzy number which is the nearest one to the given 2-dimensional fuzzy number along the direction k. The concept of four edges approximation for 2-dimensional fuzzy numbers is defined, which is a special kind of 2-dimensional fuzzy numbers. At the same time, the concept of fuzzy 2-cell prismoid numbers is introduced, and the nearest fuzzy 2-cell prismoid numbers of 2-dimensional fuzzy numbers which preserve the centroid of the core for the 2-dimensional fuzzy numbers with respect to the weighted pseudometric are discussed. Finally, with respect to the criteria: scale invariance, identity criterion and nearness criterion, some properties of the approximation operator are presented.