Stochastic Spanning Tree Problem on a Fuzzy Network
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概要
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We consider the fuzzy network with fuzzy edges and crisp vertexes. Existence of each edge is not necessarily certain and it is given by a certain value between 0 and 1. 1 means it exists certainly and 0 means it does not exist. Intermediate number is the possibility and higher value corresponds to high possibility of existence. Further each edge has a random cost independent to other edges. Under the above setting, we seek a spanning tree satisfying a certain chance constraint and maximizing the minimal possibility among edges in the spanning tree. Since usually there is no spanning tree optimizing both objectives at a time, we derive an efficient solution procedure to obtain a set of some non-dominated spanning trees after defining non-domination of spanning trees. Finally we discuss the further research problems.
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