Fuzzy decision networks and deconvolution

Three kinds of networks, namely, fuzzy minimal spanning tree, fuzzy PERT, and fuzzy shortest path, are analyzed by the use of a recently developed fuzzy ranking method to handle the various fuzzy quantities. To overcome the problem of double-inclusion of the amounts of uncertainties involved in the fuzzy quantities when extended subtraction is used for problems such as fuzzy PERT, fuzzy deconvolution is used. Since we are only interested in the ranking and aggregation of the results, the existence or nonexistence of the results from deconvolution does not influence the resulting analysis. A technique based on the ranking method is developed to handle negative spreads in the resulting fuzzy quantities. With the use of this fuzzy ranking method, the structure of the network is maintained and conventional algorithms can be applied with appropriate modifications. Emphasis is placed on the use of the subjective decision maker's opinion in the proposed fuzzy network analysis approach. Numerical examples are given to illustrate the approach.