Fuzzy goal and possibility programming with imprecise goal hierarchy

In this paper, the fuzzy goal programming is investigated when both the coefficients and the aspiration levels are considered fuzzy numbers with either trapezoidal or triangular membership functions. The possibility programming approach has been utilised in the case of exceedance possibility and the case of strict exceedance possibility. In many situations, the decision‐maker cannot set a precise priority structure for the possibility functions of the fuzzy goals. A membership function for the imprecise relation between different pairs of possibilities has been defined. This function reflects a scale for the degree of importance between any pair of goals. This scale starts from 'almost not important' to 'certainly more important'. Accordingly, there are two types of the membership functions. The first represents the possibility functions of all fuzzy goals, while the second is the membership functions of the imprecise importance relations. The weighted max‐min approach is utilised for the two types. The suggested approach is illustrated by a numerical example.