Discussion of arithmetic defuzzifications for fuzzy production inventory models

Abstract

Inventory management is often very unreliable because of the variability of the demand and the uncertainty of the forecast. Taking human subjective into consideration, the collection of historical data and the inaccuracy of linguistic hedges, recently fuzzy theory has been applied to construct the uncertain factors in an inventory which was hard to describe before. This paper is an extension of the paper by Hsieh, published in Information Sciences 146 (2002) 29-40 which examined a production inventory model under a fuzzy environment. This paper purposes three major points. Firstly, we provided a patchwork to improve Hsieh’s approach to show that the application of Taha’s algorithm of the extended Lagrangean method results in a tedious iterative computation. Secondly, we generalize the Graded Mean Integration Representation method to a weighted average operation. Thirdly, we studied the consistency between two arithmetic defuzzifications to obtain the final minimum crisp estimation under a fuzzy environment. Numerical examples are provided to illustrate our findings. Key words: Fuzzy production inventory, function principle, graded mean integration representation, fuzzy optimization.