International Journal of Nonlinear Analysis and Applications
Grey flexible mathematical programming problems: Feasibility and efficiency concepts of the solution
Document Type : Research Paper
Authors
1 Mazandaran
2 Guangzhou University, China
3 Foshan University, China
Abstract
Grey System theory was initiated in 1982 and Grey mathematics is the mathematical foundation of Grey System (GS) theory. After successful applications of grey systems, this theory has been developed in many areas and disciplines such as ecology, economy, geology, earthquake, industry, material science sports, traffic, management, decision sciences, transportation, medicine, agriculture, diet problem, and etc. Because of the ability to deal with poor, incomplete, or uncertainty problems with grey systems, most of the real-world processes in decision problems are in the grey stage due to lack of information and uncertainty. This is one of the main reasons to emphasize that grey optimization provides a useful tool for decision-making problems under such uncertainties. The GS clearness of logic and ease of use impelled researchers to develop this theory as well as fuzzy sets theory in the field of Linear Programming (LP) too. Early applications of Grey Linear Programming (GLP) incorporated grey numbers into the objective function, constraint matrix, right-hand sides of constraints, and sometimes all of the above. However, the flexibility assumption in decision making is more comfortable for the Decision Maker (DM), hence in this paper, we concentrate on Grey Flexible Linear Programming (GFLP) problems as a reasonable extension of GLP models in which is more adept with the real situations. For this aim, after defining the classical GFLP model, we first introduce a new concept of α ̅-feasibility and α-efficiency to these problems, and then we propose a two-phase approach to solve the mentioned problems. Furthermore, for supporting and also verifying the proposed solving process, we give some fundamental theorems and results. We believe that this approach will be open a new window to the modelling of the problems in the real world in the flexibility conditions.
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