Title: Solutions of multiple objective linear programming problems by applying T-sets in imprecise environment
Authors: Arindam Garai; Palash Mandal; Tapan Kumar Roy
Addresses: Department of Mathematics, Sonarpur Mahavidyalaya, Rajpur, Kolkata, WB, Pin: 700149, India ' Department of Mathematics, IIEST, Shibpur, Howrah, WB, Pin: 711103, India ' Department of Mathematics, IIEST, Shibpur, Howrah, WB, Pin: 711103, India
Abstract: In this paper, technique to find Pareto optimal solutions to multiple objective linear programming problems under imprecise environment is discussed. In imprecise environment, we observe that more preferable optimal values may be obtained by allowing membership functions to take arbitrary values, i.e., by removing constraints that impose membership values to fall in range between zero and one, than existing fuzzy optimisation techniques. Further, membership functions are not utilised as per definitions in existing fuzzy optimisation techniques. Also, such constraints may make the model infeasible. Consequently, one set viz. T-set is defined to supersede fuzzy set to represent impreciseness. Next, one general algorithm comprising T-sets, is given to find Pareto optimal solutions to multiple objective linear programming problems in imprecise environment. Numerical examples further illustrate proposed algorithm. Finally conclusions are drawn.
Keywords: multiple objective decision making; fuzzy set; fuzzy mathematical programming; linear programming problem; T-Pareto optimal solution; T-characteristic function; T-set; fuzzy decision making; optimisation.
International Journal of Operational Research, 2020 Vol.37 No.2, pp.198 - 219
Received: 31 Aug 2016
Accepted: 27 Feb 2017
Published online: 20 Feb 2020 *