Title: On solving linear programming problem by duality approach in neutrosophic environment

Authors: Tuhin Bera; Nirmal Kumar Mahapatra

Addresses: Department of Mathematics, Boror S.S. High School, Bagnan, Howrah-711312, WB, India ' Department of Mathematics, Panskura Banamali College, Panskura RS-721152, WB, India

Abstract: This paper extends the concept of crisp linear programming problem (lpp) by adopting the coefficients in objective function, technical coefficients, the right hand side coefficients and the decision variables as single valued triangular neutrosophic numbers (S_υtrn number). It is a special type of neutrosophic set. This modified concept is here called neutrosophic linear programming problem (N_lp problem). To develop this notion, a linear ranking function is newly constructed from geometrical concept first. Then the validity of existing crisp results are tested with the help of that ranking function in this new arena. An attempt is also taken to solve an N_lp problem by duality approach. For that, an efficient solution algorithm is developed by obeying the properties of ranking function. Finally, this proposed algorithm is demonstrated to solve a real life problem and some special cases are also illustrated by numerical examples.

Keywords: neutrosophic set; single valued triangular neutrosophic number; neutrosophic linear programming problem; duality.

DOI: 10.1504/IJMOR.2021.113576

International Journal of Mathematics in Operational Research, 2021 Vol.18 No.3, pp.310 - 335

Received: 01 Oct 2019
Accepted: 30 Dec 2019
Published online: 12 Mar 2021 *

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