Combined Models Of Grey System Theory And Data Envelopment Analysis (DEA) And Their Applications

After nearly three decades of development, taking"small sample","poor information"uncertain system as the research objects, the comparatively perfect theoretical framework , method groups and model groups have been gradually included in grey systems theory, and great superiority and vigorous vitality are shown when they are applied in various fields such as society, economy, life, production, etc. Data envelopment analysis (DEA) theory, taking efficiency analysis as the research starting point, nonparametric methods as characteristics, programming models as research tools, is a common system analysis method in management science research. When used for efficiency evaluation in uncertain systems, the traditional DEA models appear "stranded". DEA models with imprecise data which have been made some achievements but still not perfected need further in-depth study. There are the same application fields of grey system theory and data envelopment analysis from different research perspectives, and combined models with the advantages of the both theories have yet to be established and tested in practice.Combining with characteristics of grey system modeling technologies and data envelopment analysis methods, grey systems theory and data envelopment analysis are incorporated, sublimated and exploited in this paper. DEA models with grey interval data and three parameters grey interval data and inverse DEA model with grey interval data are researched; The new combined forecasting models of GM model and DEA model are established; The new combined decision-making models of cross evaluation theory in DEA and grey relational decision-making method are constructed; The combined models above are applied in the investment decision-making, the supplier selection, the sales forecasting, etc, and achieves the desired effect. The main research results and conclusions are as follows.1 From a new perspective, the classification and extraction methods of grey information are given; Definition of credibility degree of the comparison among grey interval numbers is extended to discrete numbers and three parameters grey interval numbers; It is proved that credibility degree of comparison among interval grey numbers and three parameters interval grey numbers satisfies complementary relationship. Based on the credibility degree matrix of the interval efficiencies, sorting way of decision making units is proposed.2 DEA models with grey interval data are further discussed. Renewed DEA models with grey interval data based on the credibility degree of comparison among grey interval data are given; The linear programming to solve the upper and lower boundaries of the efficiency intervals and their drifting values of decision making units is proposed; The modification methods of efficiency intervals and its drifting values when some of the input or output variables have same positioning coefficient or positioning coefficient in uniform interval are researched; The traditional DEA models are expanded to three parameters interval grey numbers, decision making units are classified according to their effectiveness, and sorting method of the efficiency interval of the decision making units is given. The above algorithm is proved to be reasonable and feasible by examples analysis.3 Inverse DEA model with grey interval data is researched preliminarily. Comparing the efficiency interval of the evaluated decision making unit after changing the inputs or outputs with its original efficiency interval, if credibility degree of the latter equal or greater than the former is equivalent to the credibility degree of the latter less or equal to former, then it is considered that efficiency level of the evaluated decision making unit remain unchanged; when the evaluated decision making unit is non DEA effective, sufficient and necessary conditions for existence of solution to inverse DEA model with grey interval data and the solution expressions are given; when the evaluated decision making unit is weak DEA effective, partial solution are shown .4 The grey relational analysis models with incomplete weights information are established based on cross-evaluation methods in DEA. Taking grey relation coefficients between the attribute value and the ideal value as inputs or outputs in DEA model and learning from cross-evaluation methods in DEA, weights is determined by evaluated objects'cross evaluation. In the new models, preference of the experts, decision maker, and evaluated objects are considered in different degrees: Initial weights set is provided by experts to reflect the objective important degrees of the attributes; the optimal weights are chose in weights set given by experts according to the evaluated objects'goals, and use their optimal weights to evaluate themselves and other evaluated objects; Decision maker's subjective preferences from experience judgment is reflected in subjective preferences vector. The application examples indicate: The new combined models are more close to reality, and the decision results could be accepted by evaluated objects and decision maker.5 A combined model of GM and DEA used to predict DEA effective outputs of the decision making units is constructed. Effective outputs of the decision making units are expressed as the sum of average outputs forecasted by GM model and increased outputs which reflect the difficult degree to realize effective outputs. The increased outputs are solved by a linear programming using DEA efficiency theory, in which a new sample whose inputs are equal to the budget in the issue no. n + 1 and outputs are forecasted by GM model is introduced. Modeling mechanism and an enterprise product sales forecasting example illustrate: The difficulty to give the initial conditions in the traditional model is avoided in the combined model, and more information about difficulty degree from average outputs to the optimal value and its realization way are supplied to decision-makers.