Abstract
In this paper, we propose a method to solve linear programming network problems with constraints using interval type-2 fuzzy variables. The method is developed using generalized credibility measure, and lower and upper membership functions of an interval type-2 fuzzy variable. This method has been applied to solve a solid transportation problem with availabilities and demands of a product, and conveyance capacities, which are represented by trapezoidal interval type-2 fuzzy variables. Moreover, we have also shown that different types of problems with objective function having interval type-2 fuzzy parameters can be solved using the proposed method. Apart from a solid transportation problem, we demonstrate its applicability by solving two different network problems: (i) a shortest path problem and (ii) a minimum spanning tree problem. Suitable numerical examples are provided to illustrate the proposed method
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The authors are deeply indebted to the Editor and the anonymous referees for their constructive and valuable suggestions to improve the overall quality of the manuscript. Moreover, Saibal Majumder, an INSPIRE fellow (No. DST/INSPIRE Fellowship/2015/IF150410) would like to acknowledge Department of Science & Technology (DST), Ministry of Science and Technology, Government of India, for providing him financial support for the work.
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Kundu, P., Majumder, S., Kar, S. et al. A method to solve linear programming problem with interval type-2 fuzzy parameters. Fuzzy Optim Decis Making 18, 103–130 (2019). https://doi.org/10.1007/s10700-018-9287-2
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DOI: https://doi.org/10.1007/s10700-018-9287-2