Title: Preferable Pareto optimal solutions for specified key objective functions to multiple objective linear programming problems using trade-off ratios under fuzzy environment: an iterative process

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, one general iterative process is proposed for obtaining preferable Pareto optimal solutions, based on specified key objective functions, to multiple objective linear programming problems under fuzzy environment. In reality, decision maker usually specifies one key objective function to such problems. But there are known disadvantages in applying existing fuzzy optimisation techniques, in which weights, utility functions etc. are used; whereas in other techniques, none of the objective functions can be specified effectively as key objective function. Moreover, correlation between key objective function and other objective functions may not be exactly known to the decision maker. In existing interactive fuzzy optimisation techniques, initially developed by Sakawa et al. (1984), all such reference levels of fuzzy objective functions are taken as unity. But we may find it unrealistic to expect each of conflicting objective functions to attain individual goals simultaneously. In this paper, we propose to employ trade-off ratios of membership functions of fuzzy objective functions to determine corresponding reference membership levels analytically and develop one iterative process to find preferable Pareto optimal solutions under fuzzy environment. Numerical examples further illustrate our proposed iterative process. Finally conclusions are drawn.

Keywords: fuzzy decision-making; fuzzy optimisation; iterative process; key objective functions; multiple objective linear programming; Pareto optimal solutions; reference membership levels; trade-off ratios.

DOI: 10.1504/IJOR.2019.100727

International Journal of Operational Research, 2019 Vol.35 No.2, pp.245 - 262

Available online: 05 Jul 2019 *

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