Method for solving quasi-concave and non-concave fuzzy multi-objective programming problems

This paper proposes a method based on linear programming techniques to treat quasi-concave and non-concave fuzzy multi-objective programming (FMOP) problems. The proposed method initially presents a piecewise linear expression to interpreting a quasi-concave membership function. Then we find the convex-type break points and transform all quasi-concave membership functions into concave functions. After that, the converted program is solved by linear programming techniques to obtain a global optimum. In addition to not containing any of the zero-one variables, the proposed method does not require dividing the quasi-concave FMOP problem into large sub-problems as in conventional methods. The extension of the proposed method can treat general non-concave FMOP problems by merely adding less number of zero-one variables.