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 problems, etc. Because of the ability to deal with poor, incomplete, or uncertain problems with grey systems, most of the real-world processes in decision problems are in the grey stage due to a 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 which are more adept with 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, to support and also verifying the proposed solving process, we give some fundamental theorems and results. We believe that this approach will open a  new window to the modelling of the problems in the real world in flexible conditions. 

Keywords


Articles in Press, Accepted Manuscript
Available Online from 17 February 2022
  • Receive Date: 19 July 2019
  • Accept Date: 28 September 2020