Qualitative analysis of basic notions in an iterative approach to possibilistic goal programming

This paper deals with the qualitative analysis of basic notions in an iterative approach to possibilistic general goal programming problems. The problem is considered by incorporating possibilistic distributions into the parametric goals of the goal programming. As apparatus to cope with this problem, the paper uses the concept of α-possibly optimal solutions for the problem. A necessary and sufficient condition for such a solution is established. The basic notions of stability (the solvability set, the stability set of the first kind and the stability set of the second kind) are redefined and analyzed qualitatively for the problem.