An approach based on necessity measure to the fuzzy spanning tree problems

On the decision problems with defective information, the uncertain elements are often formulated as the random variables (the stochastic programming problems) even if they don't behave themselves stochastically. However, when uncertainty is mainly derived from the lack of amount of information and so on, we think, it is proper to recognize them as a kind of "fuzziness" and formulate them as the possibility variables on the fuzzy theory. In this paper, we propose the fuzzy spanning tree problems, in which the edge costs of the graph are possibility variables. At the time of its formulation, we pay attention to the analogy between the random variables and the possibility variables and adopt a model corresponding to the probability maximum one on the chance constrained programming problems for the stochastic programming, that is, the necessity measure maximum model on the modality constrained programming problems for the possibilistic programming. Moreover, in the solution, we propose the efficient algorithm based on the binary search, which fully exploits its problem structure.