This paper deals with minimum spanning tree problems where each edge weight is a fuzzy random variable. In order to consider the imprecise nature of the decision maker's judgment, a fuzzy goal for the objective function is introduced. A novel decision making model is constructed based on possibility theory and on a stochastic programming model. It is shown that the problem including both randomness and fuzziness is reduced to a deterministic equivalent problem. Finally, a polynomial-time algorithm is provided to solve the problem.

A system based on application of Fuzzy Cognitive Map (FCM) to perform on-line fault diagnosis is presented. The diagnostic part of the system is composed of two diagnostic schemes. The first one (basic diagnostic algorithm) can be considered as a simple transition of Shiozaki's signed directed graph approach to FCM framework. The second one is an extended version of the basic diagnostic algorithm where an important concept, the temporal associative memories (TAM) recall of FCM, is adopted. In on-line application, self-generated fault FCM model generates predicted pattern sequence through the TAM recall process, which is compared with observed pattern sequence to declare the origin of fault. As the resultant diagnosis scheme takes short computation time, it can be used for on-line fault diagnosis of large and complex processes, and even for incipient fault diagnosis. In practical case, since real observed pattern sequence may be different from predicted one through the TAM recall owing to propagation delay between process variables, the time indexed fault FCM model incorporating delay time is proposed. The utility of the proposed system is illustrated in fault diagnosis of a tank-pipe system.