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Fuzzy random classical and inverse median location problems

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Abstract

In many complex systems, fuzziness and randomness simultaneously appear in a system. Then the fuzzy random variable such that it can be an effective tool to determine some high-uncertainty phenomena. Moreover, in the real-world situation, the parameters of a location problem can be randomness and fuzziness at the same time. This means that, available random data of a location problem may be unsatisfactory, therefore the fuzzy information must be integrate with the random data. This paper deals with the classical and inverse median location problems on uncertain networks in which the vertex weights are fuzzy random variables. We introduce the new criteria probability-possibility, probability-necessity and probability-credibility to convert the fuzzy random p-median location problem into a quadratic programming problem on uncertain networks. For this purpose, new formula are introduced for the possibility, necessity and credibility criteria that are used for converting fuzzy variables into deterministic variables. Also, the inverse 1-median location problem with the fuzzy random vertex weights is reformulated as the deterministic inverse 1-median location problem under the probability-possibility, the probability-necessity and the probability-credibility criteria. Finally, using these criteria, the linear time algorithms are presented for the inverse 1-median location problems on the uncertain tree networks.

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  1. Department of Applied Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran

    Sepideh Taghikhani & Fahimeh Baroughi

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  1. Sepideh Taghikhani
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  2. Fahimeh Baroughi
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Correspondence to Fahimeh Baroughi.

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Taghikhani, S., Baroughi, F. Fuzzy random classical and inverse median location problems. Soft Comput 27, 8821–8839 (2023). https://doi.org/10.1007/s00500-023-08042-x

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