A comprehensive fuzzy DEA model for emerging market assessment and selection decisions

The changing economic conditions have challenged many financial institutions to search for more efficient and effective ways to assess emerging markets. Data envelopment analysis (DEA) is a widely used mathematical programming technique that compares the inputs and outputs of a set of homogenous decision making units (DMUs) by evaluating their relative efficiency. In the conventional DEA model, all the data are known precisely or given as crisp values. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague. In addition, performance measurement in the conventional DEA method is based on the assumption that inputs should be minimized and outputs should be maximized. However, there are circumstances in real-world problems where some input variables should be maximized and/or some output variables should be minimized. Moreover, real-world problems often involve high-dimensional data with missing values. In this paper we present a comprehensive fuzzy DEA framework for solving performance evaluation problems with coexisting desirable input and undesirable output data in the presence of simultaneous input–output projection. The proposed framework is designed to handle high-dimensional data and missing values. A dimension-reduction method is used to improve the discrimination power of the DEA model and a preference ratio (PR) method is used to rank the interval efficiency scores in the resulting fuzzy environment. A real-life pilot study is presented to demonstrate the applicability of the proposed model and exhibit the efficacy of the procedures and algorithms in assessing emerging markets for international banking.     

An OWA-TOPSIS method for multiple criteria decision analysis

A hybrid approach integrating OWA (Ordered Weighted Averaging) aggregation into TOPSIS (technique for order performance by similarity to ideal solution) is proposed to tackle multiple criteria decision analysis (MCDA) problems. First, the setting of extreme points (ideal and anti-ideal points) in TOPSIS is redefined and extended for handling the multiple extreme points situation where a decision maker (DM) or multiple DMs can provide more than one pair of extreme points. Next, three different aggregation schemes are designed to integrate OWA into the TOPSIS analysis procedure. A numerical example is provided to demonstrate the proposed approach and the results are compared for different aggregation settings and confirm the robustness of rankings from different scenarios.     

Fuzzy dynamic multi-objective Data Envelopment Analysis model

Data Envelopment Analysis (DEA) is a managerial powerful tool to evaluate the relative efficiency of each decision making unit (DMU). Nowadays, multi-objective DEA models in static environment are an attractive technique for evaluation quantity and quality aspects of performance analysis because there is some weakness in single objective DEA such as one-dimensional performance analysis and also it is important to consider the decision maker(s) preference over the potential adjustments of various inputs and outputs when DEA is employed. In this paper, a fuzzy dynamic multi-objective DEA model is presented in which data are changing sequentially. This paper assesses the performance of the railways using presented model as a numerical example to evaluate the results of the model. Results indicate that the multiple objective program model improves discriminating power of classical DEA models with just one time calculation of the efficiency achievement for all DUMs.     

Clustering and group selection of multiple criteria alternatives with application to space-based networks

In many real-world problems, the range of consequences of different alternatives are considerably different. In addition, sometimes, selection of a group of alternatives (instead of only one best alternative) is necessary. Traditional decision making approaches treat the set of alternatives with the same method of analysis and selection. In this paper, we propose clustering alternatives into different groups so that different methods of analysis, selection, and implementation for each group can be applied. As an example, consider the selection of a group of functions (or tasks) to be processed by a group of processors. The set of tasks can be grouped according to their similar criteria, and hence, each cluster of tasks to be processed by a processor. The selection of the best alternative for each clustered group can be performed using existing methods; however, the process of selecting groups is different than the process of selecting alternatives within a group. We develop theories and procedures for clustering discrete multiple criteria alternatives. We also demonstrate how the set of alternatives is clustered into mutually exclusive groups based on 1) similar features among alternatives; 2) ideal (or most representative) alternatives given by the decision maker; and 3) other preferential information of the decision maker. The clustering of multiple criteria alternatives also has the following advantages. 1) It decreases the set of alternatives to be considered by the decision maker (for example, different decision makers are assigned to different groups of alternatives). 2) It decreases the number of criteria. 3) It may provide a different approach for analyzing multiple decision makers problems. Each decision maker may cluster alternatives differently, and hence, clustering of alternatives may provide a basis for negotiation. The developed approach is applicable for solving a class of telecommunication networks problems where a set of objects (such as routers, processors, or intelligent autonomous vehicles) are to be clustered into similar groups. Objects are clustered based on several criteria and the decision maker's preferences.     

Common set of weights in data envelopment analysis under prospect theory

Data envelopment analysis (DEA) is a data‐driven tool for performance evaluation, measuring decision‐making units (DMUs) and designating them with specific weightings. The standard DEA model typically sets up that decision‐makers (DMs) are wholly rational to select the most favourable weights to obtain the maximum performance score, but does not take into account their attitude toward risk during the assessment. The prospect theory generally matches humans' psychological behaviours. Thus, our study captures the non‐rational behaviours of DMs, performing under risk scenarios, in order to construct a novel common‐weights DEA model that maximizes the total prospect value, which can vary more steeply for losses than for gains, hence obtaining a more realistic common weight scheme. Our proposed model not only generates DMUs, with higher total prospect values, but also greater degrees of satisfaction. The current study shows that the prospect theory can be aptly extended to the DEA research area, supplying a proper guideline for future DEA research.     

Using interactive multiobjective methods to solve DEA problems with value judgements

Data envelopment analysis (DEA) is a performance measurement tool that was initially developed without consideration of the decision maker (DM)'s preference structures. Ever since, there has been a wide literature incorporating DEA with value judgements such as the goal and target setting models. However, most of these models require prior judgements on target or weight setting. This paper will establish an equivalence model between DEA and multiple objective linear programming (MOLP) and show how a DEA problem can be solved interactively without any prior judgements by transforming it into an MOLP formulation. Various interactive multiobjective models would be used to solve DEA problems with the aid of PROMOIN, an interactive multiobjective programming software tool. The DM can then search along the efficient frontier to locate the most preferred solution where resource allocation and target levels based on the DM's value judgements can be set. An application on the efficiency analysis of retail banks in the UK is examined. Comparisons of the results among the interactive MOLP methods are investigated and recommendations on which method may best fit the data set and the DM's preferences will be made.     

Fuzzy stochastic data envelopment analysis with application to base realignment and closure (BRAC)

Data envelopment analysis (DEA) is a non-parametric method for evaluating the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and outputs. Conventional DEA models assume that inputs and outputs are measured by exact values on a ratio scale. However, the observed values of the input and output data in real-world problems are often vague or random. Indeed, decision makers (DMs) may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. Several researchers have proposed various fuzzy methods for dealing with the ambiguous and random data in DEA. In this paper, we propose three fuzzy DEA models with respect to probability-possibility, probability-necessity and probability-credibility constraints. In addition to addressing the possibility, necessity and credibility constraints in the DEA model we also consider the probability constraints. A case study for the base realignment and closure (BRAC) decision process at the U.S. Department of Defense (DoD) is presented to illustrate the features and the applicability of the proposed models.     

Two-stage DEA model with additional input in the second stage and part of intermediate products as final output

Data envelopment analysis (DEA) has been proved to be an excellent approach for measuring performance of decision making units (DMUs) that use multiple inputs to generate multiple outputs. In many real world scenarios, inputs or outputs may be shared among various activities. This paper proposes a two-stage DEA model with additional input in the second stage and part of intermediate products as final output. We first discuss the non-cooperative condition in order to determine the upper and lower bounds of the efficiencies of sub-DMUs in different stages. A parametric transformation is described to solve the non-linear programming of the overall cooperative efficiency model. An application is provided.     

Type-2 fuzzy multi-objective DEA model: An application to sustainable supplier evaluation

In the last 10 years, sustainable supply chain management (SSCM) has become one of the important topics in business and academe. Sustainable supplier performance evaluation and selection play a significant role in establishing an effective SSCM. One of the techniques that can be used for evaluating sustainable supplier performance is data envelopment analysis (DEA). The conventional DEA methods require accurate measurement of both input and output variables present in the problem. In practice, the observed values of the input and output data present in real-world problems are often imprecise. To cope with this situation, fuzzy DEA models were constructed for expressing relative fuzzy efficiencies of decision-making units (DMUs). However, fuzzy DEA is still limited to fuzzy input/output data while some inputs and outputs might be affected by various factors of uncertainty and information granularity, meaning that they could be better modeled in terms of fuzzy sets of type-2. In this paper, we develop a multi-objective DEA model in a setting of type-2 fuzzy modeling to evaluate and select the most appropriate sustainable suppliers. In the proposed model, both efficiency and effectiveness are considered to describe the integrated productivity of suppliers. In sequel, chance constrained programming, critical value-based reduction methods and equivalent transformations are considered to solve the problem. A detailed case study is employed to show the advantages of the proposed model in terms of measuring effectiveness, efficiency and productivity in an uncertain environment expressed at different confidence levels. At the same time, the results demonstrate that the model is capable of helping decision makers to balance economic, social, and environmental factors when selecting sustainable suppliers.     

An ideal-seeking fuzzy data envelopment analysis framework

Data envelopment analysis (DEA) is a widely used mathematical programming approach for evaluating the relative efficiency of decision making units (DMUs) in organizations. Crisp input and output data are fundamentally indispensable in traditional DEA evaluation process. However, the input and output data in real-world problems are often imprecise or ambiguous. In this study, we present a four-phase fuzzy DEA framework based on the theory of displaced ideal. Two hypothetical DMUs called the ideal and nadir DMUs are constructed and used as reference points to evaluate a set of information technology (IT) investment strategies based on their Euclidean distance from these reference points. The best relative efficiency of the fuzzy ideal DMU and the worst relative efficiency of the fuzzy nadir DMU are determined and combined to rank the DMUs. A numerical example is presented to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms.     

Sensing degree of fuzziness in MCDM model using modified flexible S -curve MF

It is hard to sense the degree of vagueness while using a Multiple Criteria Decision-Making (MCDM) model in industrial engineering problems. Selection of best candidate-alternative is an important issue when the attributes of the candidate-alternatives are conflicting in nature and they have incommensurable units. An MCDM model makes it possible to select the candidate-alternative that suits best for the investor. An example illustrating an MCDM model applied in plant-site selection problem has been considered in this article to demonstrate the veracity of the proposed methodology. The degree of vagueness hidden in the proposed approach has been investigated using a flexible modified logistic membership function (MF). The approach presented here provides feedback to the decision maker, implementer and analyst and gives a clear indication about the appropriate application and usefulness of the MCDM model. The key objective of this article is to guide decision makers in finding out the best candidate-alternative with higher degree of satisfaction and lesser degree of vagueness.     

Multiproduct aggregate production planning with fuzzy demands and fuzzy capacities

Given the uncertain market demands and capacities in production environment, this paper discusses some practical approaches to modeling multiproduct aggregate production planning problems with fuzzy demands, fuzzy capacities, and financial constraints. By formulating the fuzzy demand, fuzzy equation, and fuzzy capacities, a fuzzy production-inventory balance equation for single period and a dynamic balance equation are formulated as fuzzy/soft equations and they represent the possibility levels of meeting the market demands. Using this formulation and interpretation, a fuzzy multiproduct aggregate production planning model is developed, and its solutions using parametric programming, best balance and interactive techniques are introduced to cater to different scenarios under various decision making preferences. Using the proposed models and techniques, first, the decision maker can select a preferred production plan with a common satisfaction level or different combinations of preferred possibility level and satisfaction levels, according to the market demands and available production capacities, and second, the obtained structure of the optimal solution can help decision maker in aggregate production planning. The decision maker can also make a preferred and reasonable production plan corresponding to one's most concerned criteria. Hence, decision makers not only can come up with a reasonable aggregate production plan with minimum efforts, but also have more choices of making a preferred aggregate plan based on his most concerned criteria. These models can effectively enhance the capability of an aggregate plan to give feasible family disaggregation plans under different scenarios with fuzzy demands and capacities. Simulation and the results of analysis on the proposed techniques are also given in detail in this paper.     

A Case-Based Micro Interactive Genetic Algorithm (CBMIGA) for interactive learning and search: Methodology and application to groundwater monitoring design

Interactive optimization algorithms use real–time interaction to include decision maker preferences based on the subjective quality of evolving solutions. In water resources management problems where numerous qualitative criteria exist, use of such interactive optimization methods can facilitate in the search for comprehensive and meaningful solutions for the decision maker. The decision makers using such a system are, however, likely to go through their own learning process as they view new solutions and gain knowledge about the design space. This leads to temporal changes (nonstationarity) in their preferences that can impair the performance of interactive optimization algorithms. This paper proposes a new interactive optimization algorithm – Case-Based Micro Interactive Genetic Algorithm – that uses a case-based memory and case-based reasoning to manage the effects of nonstationarity in decision maker’s preferences within the search process without impairing the performance of the search algorithm. This paper focuses on exploring the advantages of such an approach within the domain of groundwater monitoring design, though it is applicable to many other problems. The methodology is tested under non-stationary preference conditions using simulated and real human decision makers, and it is also compared with a non-interactive genetic algorithm and a previous version of the interactive genetic algorithm.     

Using fuzzy super-efficiency slack-based measure data envelopment analysis to evaluate Taiwan’s commercial bank efficiency

Data envelopment analysis (DEA) mainly utilizes envelopment technology to replace production function in microeconomics. The input and output of decision making units (DMUs) are projected into the attributes to evaluate or measure their performance. However, if the inputs and outputs are linguistically termed or are fuzzy-numbered, conventional DEA can not easily measure the performance. Therefore, we propose the use of a fuzzy super-efficiency slack-based measure DEA to analyze the operational performance of 24 commercial banks facing problems on loan and investment parameters with vague characteristics. After our analysis, we find that the fuzzy slack-based measure of efficiency (Fuzzy SBM)/fuzzy super-efficiency slack-based measure of efficiency (Fuzzy Super SBM) can not only effectively characterize uncertainty, but also have a higher capability to evaluate bank efficiency than the conventional Fuzzy DEA approach.     

Developing a fuzzy TOPSIS approach based on subjective weights and objective weights

Multiple criteria decision making (MCDM) is widely used in ranking one or more alternatives from a set of available alternatives with respect to multiple criteria. Inspired by MCDM to systematically evaluate alternatives under various criteria, we propose a new fuzzy TOPSIS for evaluating alternatives by integrating using subjective and objective weights. Most MCDM approaches consider only decision maker’s subjective weights. However, the end-user attitude can be a key factor. We propose a novel approach that involves end-user into the whole decision making process. In this proposed approach, the subjective weights assigned by decision makers (DM) are normalized into a comparable scale. In addition, we also adopt end-user ratings as an objective weight based on Shannon’s entropy theory. A closeness coefficient is defined to determine the ranking order of alternatives by calculating the distances to both ideal and negative-ideal solutions. A case study is performed showing how the propose method can be used for a software outsourcing problem. With our method, we provide decision makers more information to make more subtle decisions.     

A mathematical framework to optimize ATR systems with non-declarations and sensor fusion

Combat identification is one example where incorrect automatic target recognition (ATR) output labels may have substantial decision costs. For example, the incorrect labeling of hostile targets vs. friendly non-targets may have high costs; yet, these costs are difficult to quantify. One way to increase decision confidence is through fusion of data from multiple sources or from multiple looks through time. Numerous methods have been published to determine a Bayes’ optimal fusion decision if decision costs are well known. This research presents a novel mathematical programming ATR evaluation framework. A new objective function inclusive of time is introduced to optimize and compare ATR systems. Constraints are developed to enforce both decision maker preferences and traditional engineering measures of performance. This research merges rejection and receiver operating characteristic (ROC) analysis by incorporating rejection and ROC thresholds as decision variables. The rejection thresholds specify non-declaration regions, while the ROC thresholds explore viable true positive and false positive tradeoffs for output target labels. This methodology yields an optimal ATR system subject to decision maker constraints without using explicit costs for each type of output decision. A sample application is included for the fusion of two channels of collected polarized radar data for 10 different ground targets. A Boolean logic and probabilistic neural network fusion method are optimized and compared. Sensitivity analysis of significant performance parameters then reveals preferred regions for each of the fusion algorithms.     

Evaluation and ranking DMUs in the presence of both undesirable and ordinal factors in data envelopment analysis

In the last decade,ranking units in data envelopment analysis(DEA) has become the interests of many DEA researchers and a variety of models were developed to rank units with multiple inputs and multiple outputs.These performance factors(inputs and outputs) are classified into two groups:desirable and undesirable.Obviously,undesirable factors in production process should be reduced to improve the performance.Also,some of these data may be known only in terms of ordinal relations.While the models developed in the past are interesting and meaningful,they didn t consider both undesirable and ordinal factors at the same time.In this research,we develop an evaluating model and a ranking model to overcome some deficiencies in the earlier models.This paper incorporates undesirable and ordinal data in DEA and discusses the efficiency evaluation and ranking of decision making units(DMUs) with undesirable and ordinal data.For this purpose,we transform the ordinal data into definite data,and then we consider each undesirable input and output as desirable output and input,respectively.Finally,an application that shows the capability of the proposed method is illustrated.     

Using simulation and multi-criteria methods to provide robust solutions to dispatching problems in a flow shop with multiple processors

Dispatching rules are important to the performance of a manufacturing system. Selective applications of different priority rules at different processing stages in a multiple workstation manufacturing system have a positive impact on shop performance. This type of problem is a combinatorial dispatching decision. However, no dispatching rule can consistently produce better performance than all other rules under a variety of operating conditions and criteria. It is the purpose of this study to provide a robust solution for a dispatching decision that will have ‘good’ performance under different operating scenarios. In this paper a simulation case of a flow shop with multiple processors is proposed, specifically a multi-layer ceramic capacitor manufacturing system. Two multiple criteria decision-making methods – techniques for order preference by similarity to ideal solution (TOPSIS) and an analytic hierarchy process (AHP) – in combination with Taguchi orthogonal array are used to find the most suitable dispatching rule for every workstation. The results show that for 15 production scenarios and 4 criteria this combinatorial dispatching rule is robust, in the sense that it outperforms other commonly employed strategies.     

Interactive cartography—An analytical tool for management information systems

An interactive time-sharing graphical system has been developed at Princeton University for applications in education, engineering design, and management information systems. Graphical processors have been integrated into a general purpose interactive computer system, providing for easy graphical input and output in a time-sharing mode. The present report discusses the capabilities of the interactive system for applications in which cartographical displays serve as tools for analysis and reporting. The interactiveness of the system permits the analyst and the policy decision maker to quickly explore alternative solutions.     

Data transformation in the evidential reasoning-based decision making process

This paper describes the application of an evidential reasoning (ER)‐based decision making process to multiple‐criteria decision making (MCDM) problems having both quantitative and qualitative criteria. The ER approach is based on the decision theory and the theory of evidence and it uses the concept of ‘degree of belief’ to assess decision alternatives on each attribute. When faced with MCDM problems, evaluation and selection or ranking of alternatives appear to be both challenging and vital to arrive at a rational and robust decision. In the presence of both qualitative and quantitative evaluations in an MCDM problem, it is necessary, when using the ER‐based decision making process, to transform or convert quantitative data into a belief structure using a number of grades so that the converted belief structure and the original quantitative data are equivalent in values or utilities. This paper suggests three scenarios for data transformation and examines how the ranking of decision alternatives is changed when different scenarios of data transformation are used. Ranking of UK universities using the ER approach is illustrated as an example.