Inexact discretionary inputs in data envelopment analysis

In this chapter, the relationship between fuzzy concepts and the efficiency score in Data envelopment analysis (DEA) is dealt with.A new DEA model for handling crisp data using fuzzy concept is proposed.In addition, the relationship between possibility sets and the efficiency score in the traditional crisp CCR model is presented.The relationship provides an alternative perspective of viewing efficiency.With the usage of the appropriate fuzzy and possibility sets to represent certain characteristics of the input data, many DEA models involving input data with various characteristics could be studied.Furthermore, based upon the proposed models, two nondiscretionary models are introduced in which some inputs or outputs, in a fuzzy sense, are inexact discretionary variables.For this purpose, a two-stage algorithm will be presented to treat the DEA model in the presence of an inexact discretionary variable.With this relationship, a new perspective of viewing and exploring other DEA models is now made possible

Using data envelopment analysis to defuzzify a group of dependent fuzzy numbers

The defuzzification process converts fuzzy numbers to crisp ones and is an important stage in the implementation of fuzzy systems. In many actual applications, relationships among data indicate their mathematical dependence on one another. Hence, this study proposes a new method based on the Data Envelopment Analysis (DEA) model to defuzzify a group of dependent fuzzy numbers. It also aims to obtain the crisp points that satisfy the characteristics of these data as a group by approximating the optimal solutions within the production possibility set of the DEA model.The proposed method partitions the fuzzy numbers, and the relationships among these numbers are observed as constraints. Finally, the usefulness of this new method is illustrated in a real-world problem

Group decision via usage of analytic hierarchy process and preference aggregation method (Keputusan berkumpulan menggunakan proses hierarki analisis dan kaedah pengagregatan keutamaan)

The Analytic Hierarchy Process (AHP) is a recognised modern approach to solve decision making problems. Initially introduced by Saaty in 1971 as a tool for handling individual decision making situation, the method has since been extended to incorporate groups. In this paper, a new method for AHP group decision making is proposed. The method integrates AHP with a Data Envelopment Analysis (DEA)-based preferential aggregation method. It manipulates the preferential weights and ranking aspect of each decision maker in coming up with an optimisation model that determines the best efficiency score of each alternatives. These efficiency scores are then used to rank the alternatives and determine the group decision weights. A comparative analysis of the method with another AHP group decision making method indicates a similar ‘satisfactory index’ level

A fuzzy interval weights approach in fuzzy goal programming for a multi-criteria problem

Goal Programming (GP) is an effective method to solve linear multi-objective problems.The weights play an important role for achieving the solution of the multi-objective programming problem according to the needs and desires of the decision makers (DMs), particularly in uncertain environments.To tackle such uncertain matter on the issue of weights, the proposed approach has taken the interval weights associated to the unwanted devotional variable in goal achievement function as triangular fuzzy numbers Hence, this study presents a new insight into interval weights to solve linear multi-objective fuzzy GP problems by introducing a defuzzification method based on the Data Envelopment Analysis (DEA) model to defuzzify groups of fuzzy interval weights.This method partitions these fuzzy numbers which cover all possible results in this interval, able to give us best and optimal weights. In the solution process, the interval weights which were derived from several pairwise interval judgment matrices associated with unwanted deviational variables are introduced to the goal achievement function with the objective of minimization of those deviations, and thus, realize the aspired goal levels of the problem. To illustrate the proposed approach, numerical examples are solved with the resulted real or crisp weights. An improved optimal solution is achieved when the interval weight is represented as fuzzy numbers with their middle points are geometric means as compared to normal interval weights associated with the maximum and minimum interval under same matrix for each standard GP model and fuzzy GP model