A Class Of Twofold Uncertain Multi-objective Decision-making Model And Its Application To Inventory Problem

Multi-objective decision-making is an important part of modern decision-making science and an important branch of operational research. We usually face these practical decision-making problems which include some conflictive and unmeasured each other decision-making objective. It is the problem of certain multi-objective decision-making that how to optimize some objective functions or find the satisfied solution under finite resource. But as a result of some artificial or external factors, practical multi-objective decision-making problems are often with much uncertainy which usually exist many kinds of uncertainties, such as fuzzy, random, bifuzzy, fuzzy random and multifold uncertain variables.Fuzzy random variable is a kind of twofold uncertain variables. In many practical decision-making problems, the membership functions of some random variables is know, but some parameters about these membership functions are unknown. Based on the data analysis and experience accumulation, the experts and decision-makers make the uncertain parameters be fuzzy variables or random variables, and then they would become bifuzzy variables or fuzzy random variables. Bifuzzy programming or fuzzy random programming are for the problems which include bifuzzy variables or fuzzy random variables respectively. The elastic data structure and choice pattern will boost the descriptive and adaptive capability of programming models. When dealing with these multifold uncertain information, people are used to replacing uncertain parameters with deterministic quantities and replacing multifold uncertain parameters with onefold uncertain parameters, which may leave out much valuable information and can not reflect the essence of problems. In this paper, from two points of view about bifuzzy variables and fuzzy random variables, we have studied multi-objective programming problems with twofold uncertain coefficients and have been applied to practical inventory problems; and have solved a class of multi-objective inventory problems with twofold uncertain coefficients. On the other hand, we have gave the results of the fuzzy multi-objective programming problems under the same restrictive conditions. By comparing the two different results under different environment, we find that the multi-objective programming with twofold uncertain coefficients are much practical than that with fuzzy parameters, and the results of the multi-objective programming with twofold uncertain coefficients are satisfied by the decision-makers.In this paper, on the basis of summarizing the known researches, we propose a system of solutions for a class of multi-objective inventory problems with twofold uncertain coefficients and apply them to the practical inventory problems. The major achievements as follows:(1) The theory aspectWe propose theα-cut set of the bifuzzy variables and fuzzy random variables, and propose the solution of transforming bifuzzy variables and fuzzy random variables to trapezoidal fuzzy numbers, and propose a generic multi-objective programming with twofold uncertain coefficients and proved the method of solving (α,β)-satisfied solution.(2) The application aspectWe apply the programming model with twofold uncertain coefficients to the practical inventory problem. The bifuzzy and fuzzy random parameters reflect the management experience of the decision-makers and experts. On the basis of these, we propose the precise mathematics model about inventory problem and the solution about mathematics model. By comparing the results with that under fuzzy environment, we find the results under towfold uncertain environment make the decision-makers satisfied.This paper has referenced significance to accelerate the research of bifuzzy theory and fuzzy random theory.