Another Method for Defuzzification Based on Regular Weighted Point
Subject Areas : International Journal of Industrial Mathematics
Rasoul Saneifard
1
,
Rahim Saneifard
2
1 - Department of Engineering Technology, Texas Southern University, Houston, Texas, USA.
2 - Department of Applied Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran.
Keywords: Ranking, Fuzzy number, L-R type, Defuzzification, Regular weighted point,
Abstract :
A new method for the defuzzification of fuzzy numbers is developed in this paper. It is well-known, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number. In this case the loss of essential information is possible. It may result in inadequate final conclusions, for example, expert estimation problems, prediction problems, etc. Accordingly, the necessity to develop a method for the defuzzification of fuzzy numbers, allowing us to save their informative properties has arisen. The purpose of this paper is to develop such a method. The method allows us to find aggregative intervals for fuzzy numbers. These intervals are called the Regular weighted intervals. We start with the definition of regular weighted points for fuzzy numbers. The regular weighted interval for fuzzy number is defined as the set of regular weighted points of all unimodal numbers, that belong to this number. Some propositions and examples about regular weighted point and regular weighted intervals properties are offered.