A method to solve linear programming problem with interval type-2 fuzzy parameters

Pradip Kundu (), Saibal Majumder (), Samarjit Kar () and Manoranjan Maiti ()
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Pradip Kundu: Indian Institute of Science Education and Research Kolkata
Saibal Majumder: National Institute of Technology, Durgapur
Samarjit Kar: National Institute of Technology, Durgapur
Manoranjan Maiti: Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University

Fuzzy Optimization and Decision Making, 2019, vol. 18, issue 1, No 6, 103-130

Abstract: 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

Keywords: Interval type-2 fuzzy variable; Membership function; Generalized credibility measure; Chance-constraint programming (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10700-018-9287-2

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