Extension of TOPSIS for Group Decision-Making Based on the Type-2 Fuzzy Positive and Negative Ideal Solutions

Abstract In this paper based on the interval type-2 fuzzy sets, we introduce an extension of fuzzy TOPSIS for handling fuzzy multiple attributes group decision making problems. In the proposed method the fuzzy positive ideal solution and fuzzy negative ideal solution are obtained in the form of interval type-2 fuzzy sets without ranking the elements of decision matrix, using the proposed method the solution of decision problem is obtained with less computational attempt than existing methods

Calculating Super Efficiency of DMUs for Ranking Units in Data Envelopment Analysis Based on SBM Model

There are a number of methods for ranking decision making units (DMUs), among which calculating super efficiency and then ranking the units based on the obtained amount of super efficiency are both valid and efficient. Since most of the proposed models do not provide the projection of Pareto efficiency, a model is developed and presented through this paper based on which in the projection of Pareto-efficient is obtained, in addition to calculating the amount of super efficiency. Moreover, the model is unit invariant, and is always feasible and makes the amount of inefficiency effective in ranking

A New Method for Defuzzification and Ranking of Fuzzy Numbers Based on the Statistical Beta Distribution

Granular computing is an emerging computing theory and paradigm that deals with the processing of information granules, which are defined as a number of information entities grouped together due to their similarity, physical adjacency, or indistinguishability. In most aspects of human reasoning, these granules have an uncertain formation, so the concept of granularity of fuzzy information could be of special interest for the applications where fuzzy sets must be converted to crisp sets to avoid uncertainty. This paper proposes a novel method of defuzzification based on the mean value of statistical Beta distribution and an algorithm for ranking fuzzy numbers based on the crisp number ranking system on R. The proposed method is quite easy to use, but the main reason for following this approach is the equality of left spread, right spread, and mode of Beta distribution with their corresponding values in fuzzy numbers within (0,1) interval, in addition to the fact that the resulting method can satisfy all reasonable properties of fuzzy quantity ordering defined by Wang et al. The algorithm is illustrated through several numerical examples and it is then compared with some of the other methods provided by literature

Using Enhanced Russell Model to Solve Inverse Data Envelopment Analysis Problems

This paper studies the inverse data envelopment analysis using the nonradial enhanced Russell model. Necessary and sufficient conditions for inputs/outputs determination are introduced based on Pareto solutions of multiple-objective linear programming. In addition, an approach is investigated to identify extra input/lack output in each of input/output components (maximum/minimum reduction/increase amounts in each a of input/output components). In addition, the following question is addressed: if among a group of DMUs, it is required to increase inputs and outputs to a particular unit and assume that the DMU maintains its current efficiency level with respect to other DMUs, how much should the inputs and outputs of the DMU increase? This question is discussed as inverse data envelopment analysis problems, and a technique is suggested to answer this question. Necessary and sufficient conditions are established by employing Pareto solutions of multiple-objective linear programming as well

A New Method for Solving Fuzzy DEA Models by Trapeziodal Approximation

. Data envelopment analysis is a technique for measuring the relative efficiency of a set of decision making units with crisp data, but in this paper we explain a new method for evaluating of decision making units with fuzzy data. At first, we introduce fuzzy data envelopment analysis models with parameters as trapezoidal membership function. Then we extend this method for solving models with general parameter

Measuring Overall Profit Efficiency with Fuzzy Data

Data Envelopment Analysis (DEA) is a technique for measuring the efficiency of a set of Decision Making Units (DMUs) with common data, but in general it is not practical. This paper presents a framework where DEA is used to measure overall profit efficiency with fuzzy data. Specifically, it is shown that as the inputs, outputs and price vectors are fuzzy numbers, the DMUs cannot be easily evaluated. Thus, presenting a new method for computing the efficiency of DMUs with fuzzy data will be benefic. Also, it presents where DEA is used to measure overall profit of efficiency with interval and fuzzy inputs and outputs and an interval will be defined for the efficiency. The proposed method give the best and the worst overall profit efficiency for DMUs. The method is illustrated by solving numerical examples

A Full Ranking for Decision Making Units Using Ideal and Anti-Ideal Points in DEA

We propose a procedure for ranking decision making units in data envelopment analysis, based on ideal and anti-ideal points in the production possibility set. Moreover, a model has been introduced to compute the performance of a decision making unit for these two points through using common set of weights. One of the best privileges of this method is that we can make ranking for all decision making units by solving only three programs, and also solving these programs is not related to numbers of decision making units. One of the other advantages of this procedure is to rank all the extreme and nonextreme efficient decision making units. In other words, the suggested ranking method tends to seek a set of common weights for all units to make them fully ranked. Finally, it was applied for different sets holding real data, and then it can be compared with other procedures

A Linear Programming DEA Model for Selecting a Single Efficient Unit

In recent years, several mixed integer linear programming (MILP) models have been proposed for finding the most efficient decision-making unit (DMU) in data envelopment analysis. This paper introduces a new linear programming (LP) model to determine the most BCC-efficient decision-making unit. Unlike previous models, which are not convex, the new model is linear programming and so that it can be solved efficiently to discover the most efficient DMU. Moreover, it is mathematically proved that the new model identifies only a single BCC-efficient DMU by a common set of optimal weights. To show the applicability of the proposed model, a numerical example which contains a real data set of nineteen facility layout designs (FLDs) is used