Islamic Azad University, Rasht BranchIranian Journal of Optimization2588-572306220140701A NEW APPROACH OF FUZZY NUMBERS WITH DIFFERENT SHAPES AND DEVIATION730736526829ENA. GhanizadehDepartment of Statistics, Islamic Azad University of Kermanshah Branch,
Kermanshah, IranN. ParandinDepartment of Mathematics, Islamic Azad University of Kermanshah Branch, Kermanshah, IranJournal Article20140120In this paper, we propose a new method for fuzzy numbers. In this method, we assume that A<sub>i</sub>= (a<sub>i1</sub>, a<sub>i2</sub>, a<sub>i3</sub>, a<sub>i4</sub>) is to be a fuzzy number. So, the convex combination of a<sub>i1</sub> and a<sub>i2 </sub>and also the convex combination of a<sub>i3</sub> and a<sub>i4</sub> are obtained separately. Then, M<sub>ic</sub> and M<sub>is</sub> that are to be the convex combinations and the standard deviation respectively we acquire them from these components. Finally, we can obtain ranking index (M<sub>i)</sub> that is the convex combination of, M<sub>ic</sub> and M<sub>is</sub>. At the end of paper, in one example, the proposed method is compared with other methods.http://ijo.iaurasht.ac.ir/article_526829_4387ae04443c3fe52b0c60ad9beeaa47.pdf