New defuzzification method based on weighted intervals

A new method for the defuzzification of fuzzy numbers is developed in this paper. As is well-known, defuzzification methods allow to find aggregative crisp numbers for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number. In this case loss of essential information is possible. It may result in inadequate final conclusions, for example, in expert estimation problems, prediction problems, etc. In connection with this, the necessity to develop a method for the defuzzification of fuzzy numbers, that will allow us to save their informative properties has occurred. The purpose of this paper is to develop such a method. The method allows to find aggregative intervals for fuzzy numbers. These intervals are called the weighted intervals. We start with the definition of weighted points for unimodal (L - R) numbers. The weighted interval for (L - R) fuzzy number is defined as the set of weighted points of all unimodal (L - R) numbers, that belong to this number. Three propositions about weighted intervals properties are proved. A numerical example is used to demonstrate the proposed method.