Tackling an MCDM-problem with the help of some results from fuzzy set theory

The problem to be addressed and tackled in this paper arose as a byproduct from some efforts at solving problems involving multiple goals by linking linear and goal programming models. The critical issue was that some forms for interdependence among the goals could not be handled in the programming models. Here we will deal with a set of goals — with realistic counterparts in a Finnish plywood industry — in which a subset of the goals are (i) conflicting, another subset (ii) unilaterally supporting and a third subset (iii) mutually supporting. It is furthermore observed that the elements of a studied set of goals may be partly independent and partly interdependent, which makes the context a fullfledged MCDM-problem. It is tackled with a technique which is based on the theory of fuzzy sets, the conceptual framework for fuzzy decisions and the algorithms developed for fuzzy mathematical programming. The resulting fuzzy multiobjective programming model is simplified and tested with the help of a fairly complex numerical example.