DEFUZZIFICATION METHOD FOR RANKING FUZZY NUMBERS BASED ON CENTER OF GRAVITY

Ranking fuzzy numbers plays a very important role in decision making and some other fuzzy application systems. Many different methods have been proposed to deal with ranking fuzzy numbers. Constructing ranking indexes based on the centroid of fuzzy numbers is an important case. But some weaknesses are found in these indexes. The purpose of this paper is to give a new ranking index to rank various fuzzy numbers effectively. Finally, several numerical examples following the procedure indicate the ranking results to be valid. A pervasive and controversial issue in the field of theoretical and applied research has been devoted to the role of fuzzy system theory in decision making process and other fuzzy application systems. It is acknowledged that fuzzy system theory has been improved steadily and has essential consequence for decision making process in engineering, economics, and social systems, to name a few (Zadeh, 1965). A growing body of research has concerned with fuzzy multi-attribute decision making problem especially in regard to show how ranking fuzzy numbers are not the total order relations under the ordinary meaning, but the partial order under the lattice structure. This implies that one significant aspect of fuzzy decision problems is the significance of ranking theories of fuzzy numbers. To date, substantial body of research on fuzzy system theory has examined different methods of ranking fuzzy numbers in different contexts. However, which types of methods are more influential is still substantiated. Among the existing ranking methods, centroid-index methods are considered as an important part of decision making problems. In that way the main concern of the present study is to investigate some drawbacks of the existing centroid ranking methods. As a result, conducting investigation on the possible drawbacks of the existing centroid ranking method (i.e., they cannot correctly rank fuzzy numbers in some situations), seems a fruitful area. Accordingly the present study aims to explore a novel technique for ordering fuzzy numbers (normal/non- normal/trapezoidal/general) to deal. The present paper also uses some examples to compare the proposed method with other ranking techniques.