A Novel Lexicographic Optimization Method for Solving Shortest Path Problems with Interval-Valued Triangular Fuzzy Arc Weights
Santos Arteaga FJ
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Shortest path (SP) optimization problems arise in a wide range of applications such as telecommunications and transportation industries. The main purpose of these problems is to find a path between two predetermined nodes within a network as cheaply or quickly as possible. Conventional SP problems generally assume that the arc weights are defined by crisp variables, though imprecise data have been lately incorporated into the analysis. The present study formulates the SP problem in a directed interval-valued triangular fuzzy network. The resulting interval-valued fuzzy SP (IVFSP) problem is converted into a multi objective linear programming (MOLP) problem. Then, a lexicographic optimization structure is used to obtain the efficient solution of the resulting MOLP problem. The optimization process confirms that the optimum interval-valued fuzzy shortest path weight preserves the form of an interval-valued triangular fuzzy number. The applicability of the proposed approach is illustrated through an example dealing with wireless sensor networks.