Fuzzy compatibility structures in new product development

This paper deals with the problem of generalizing the concept of crisp compatibility structures developed by the authors in [J. Hohenegger, A. Bufardi, P. Xirouchakis, A new concept of compatibility structure in new product development. Advanced Engineering Informatics, in press, doi:10.1016/g.aei.2006.09.005], to the case of binary fuzzy relations. This generalization is very important because the compatibility modeling problem for which the compatibility structure is developed takes place at the early phases of new product development which are characterized by imprecision. For this generalization, the Łukasiewicz triplet is shown to be a suitable choice for the fuzzy De Morgan triplet. The class of fuzzy compatibility structures without incomparability deserves a particular attention and is investigated in more detail. Its minimal representation is provided and the construction of fuzzy compatibility structures without incomparability from the fuzzy impacts is considered. A case study illustrating the evaluation of the fuzzy compatibility relations between alternatives is provided.