Fuzzy Projection Over a Crisp Set and Applications

Abstract

This paper presents a new approach for projecting a fuzzy number over a crisp closed convex set. Based on this approach, a kind of fuzzy linear projection equation is introduced and also it is used to solve a fuzzy system of linear equations with crisp variables, fuzzy right-hand side, and fuzzy coefficients. The proposed definition for fuzzy projection is based on $$\alpha-$$ cut approach. Numerical examples illustrate the applicability of new approach for solving fuzzy system of linear equations with crisp variables. However, the applications of fuzzy projection cannot be limited just to solving a fuzzy system of linear equations.