The Research Of Approximate Equal Or Greater Than Relation On Fuzzy Numbers

Uncertain information exists widely in real life.For instance,weather conditions and global economic situations are uncertain.Fuzzy numbers are used to describe uncertain information.The theory of fuzzy number plays an important role in fuzzy decision making,fuzzy control and fuzzy data analysis.In fuzzy multi-attribute decision making,the ordering of fuzzy numbers is an important part.For example,when the decision problems are solved in the fuzzy environment,the factor indicators related to the alternatives are usually described by fuzzy numbers.Thus the comparison between alternatives can be transformed into the comparison between fuzzy numbers.The main contents of this paper are as follows:(1)We introduce the approximately greater than or equal relation on fuzzy n-cell numbers and study elaborately its properties.The discussions focus on the variation of this relationship under addition,subtraction,multiplication,division and scalar-multiplication;(2)We discuss the transformation of approximate equal or greater than relation and approximate greater than relation under the level convergence on fuzzy n-cell number space.Similar to the case of real numbers,on fuzzy n-cell numbers,the approximate equal or greater than relation is maintained and the approximate greater than relation may not under the level convergence.Being different from the case of real numbers,sign-preserving theorem of the sequence of fuzzy n-cell numbers may not hold under the level convergence;(3)We propose a new weighted ordering method for fuzzy n-cell numbers based on the possibility theory,and use two indexes: possibilistic mean value and possibilistic variance.We also illustrate the rationality of this method by some examples.