‘FLIP’: Multiobjective Fuzzy Linear Programming Software with Graphical Facilities

Abstract

The paper presents a microcomputer implementation of a visual interactive method, called ‘FLIP’, for solving MOLP problems with fuzzy coefficients in the objective functions and on the both sides of the constraints. The idea of ‘FLIP’ relies on an observation that for given values of decision variables, the main question to be answered consists in the comparison of objectives and goals, and left-and right-hand-sides of the constraints which are fuzzy numbers. In result of application of a comparison principle, the fuzzy MOLP problem is transformed into a non-fuzzy multiobjective linear fractional programming (MOLFP) problem which is solved using an interactive sampling method. An evaluation of the quality of successive proposals (solutions) is based on the following characteristics: (i) scores of fuzzy objectives in relation to the goals, (ii) dispersion of values of the fuzzy objectives due to uncertainty, (iii) safety of solutions or risk of violation of the constraints. The graphics displayed by ‘FLIP’ provide the most comprehensive synthesis of these characteristics. The aim of this paper is to demonstrate that the kind of visual interaction organized by ‘FLIP’ is the most appropriate for solving MOLP problems under uncertainty and imprecision. In order to support this conclusion, a land-use planning problem is solved using the ‘FLIP’ software on a micro.