Research On Fuzzy Data Envelopment Analysis Model And Its Robustness

This paper is about transforming the data inputs and outputs exact observations intofuzzy number of observations, and uses interval fuzzy numbers to show. The differentfuzzy degrees of the input and output fuzzy numbers what are given by the data decisionunit lead different membership degree. Then introduce the membership into the classicalDEA model, transform the classic DEA model into the fuzzy DEA model, and give thefuzzy data envelopment analysis model which corresponds to classic data envelopmentanalysis model. When introduced the fuzzy numbers into the classical DEA model, thefrontier becomes an ‘envelope body’. Determine the effectiveness of fuzzy DMUsproduction becomes to determine whether the fuzzy DMUs outside of the ‘envelopebody’ or not. The envelope body is composed by the fuzzy DMUs enveloping surfacesand solving the envelope body is transformed into solving the envelope surfaces. Tosimplify the solving steps, this paper gives definition, nature and solving methods of theenvelope, aiming to get the envelope body. The relationship between fuzzy DMUs andthe envelope body is divided into: fuzzy DMUs overall in the envelope body, partly in theenvelope body, and is not located within the envelope body. This paper introduces DEAeffective degree to measure describe the location relationship between DMUs and theenvelope body.There are fuzzy DEA production possibility set, and this paper studies thenature of the production possibility set and puts forward two methods: the functionderivative method and fuzzy DEA model judgment method, then give the scale of thefuzzy DMUs effectiveness. In sorting, scale efficiency, technical efficiency, productionefficiency and the position relationship between fuzzy DMUs with envelope body asattributes, and all the fuzzy DMUs as the objects and each function of fuzzy DMU andattribute as binary relation. Definite model robustness, analysis the robustness of themodel, and indicate the fuzzy data envelopment analysis model can characterize thereality of production problems better.