Aggregation of Fuzzy Systems in Multi-level Decisions

Abstract

Although the various approaches proposed for fuzzy multi-level programming in the previous chapter are very powerful, it is only a start in this fruitful direction. Further developments are needed to consider other aspects and thus to make the actual solution process more practical in the sense of solving more realistic problems with reduced computation. Two of the most important aspects which need to be considered are the problem of aggregation of the fuzzy representation and the representation of systems whose description is vague and not well defined. The first aspect is concerned with the basic problem of fuzzy combination, where, in the previous chapter, only the non-compensatory min is used. The second aspect is concerned with the handling of vague systems. Notice that the problem representing the system at each division or each level in the previous chapter is crisp, not fuzzy. The fuzziness comes from the mutual interaction or mutual competition of the different decision-makers in each level or each division. In this chapter, fuzzy systems represented by fuzzy parameters or fuzzy coefficients, not just fuzzy objectives and fuzzy decisions, will be considered.