A new attitude coupled with the basic fuzzy thinking to distance between two fuzzy numbers

Document Type : Research Paper


1 Department of Mathematics Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran


Fuzzy measures are suitable in analyzing human subjective evaluation processes. Several different strategies have been proposed for distance of fuzzy numbers. The distances introduced for fuzzy numbers can be categorized in two groups:\\
1. The crisp distances which explain crisp values for the distance between two fuzzy numbers.\\
2. The fuzzy distance which introduce a fuzzy distance for normal fuzzy numbers. It was introduced by Voxman \cite{33} for the first time through using  $\alpha$-cut.\\
However, both mentioned concepts can lead to unsatisfactory results from the applications point of view, but there is no method, which gives a satisfactory result to all situations. In this paper,  a new attitude coupled with fuzzy thinking to the fuzzy distance function on the set of fuzzy numbers is proposed. In this new fuzzy distance, we considered both mentioned attitudes,  then we introduced new fuzzy distance based on a combination (hybrid) of those two. Some properties of the proposed fuzzy distance have been discussed. Finally, several examples have been provided to explain the application of the proposed method and compare this methods with others.


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