Ranking efficient decision-making units in data envelopment analysis using fuzzy concept

This paper introduces a new mathematical method for improving the discrimination power of data envelopment analysis and to completely rank the efficient decision-making units (DMUs). Fuzzy concept is utilised. For this purpose, first all DMUs are evaluated with the CCR model. Thereafter, the resulted weights for each output are considered as fuzzy sets and are then converted to fuzzy numbers. The introduced model is a multi-objective linear model, endpoints of which are the highest and lowest of the weighted values. An added advantage of the model is its ability to handle the infeasibility situation sometimes faced by previously introduced models.

A stepwise fuzzy linear programming model with possibility and necessity relations

Linear programming (LP) is the most widely used optimization technique for solving real-life problems because of its simplicity and efficiency. Although conventional LP models require precise data, managers and decision makers dealing with real-world optimization problems often do not have access to exact values. Fuzzy sets have been used in the fuzzy LP (FLP) problems to deal with the imprecise data in the decision variables, objective function and/or the constraints. The imprecisions in the FLP problems could be related to (1) the decision variables; (2) the coefficients of the decision variables in the objective function; (3) the coefficients of the decision variables in the constraints; (4) the right-hand-side of the constraints; or (5) all of these parameters. In this paper, we develop a new stepwise FLP model where fuzzy numbers are considered for the coefficients of the decision variables in the objective function, the coefficients of the decision variables in the constraints and the right-hand-side of the constraints. In the first step, we use the possibility and necessity relations for fuzzy constraints without considering the fuzzy objective function. In the subsequent step, we extend our method to the fuzzy objective function. We use two numerical examples from the FLP literature for comparison purposes and to demonstrate the applicability of the proposed method and the computational efficiency of the procedures and algorithms. © 2013-IOS Press and the authors. All rights reserved.

Reliability of vegetation community information derived using decorana ordination and fuzzy c-means clustering

Descriptions of vegetation communities are often based on vague semantic terms describing species presence and dominance. For this reason, some researchers advocate the use of fuzzy sets in the statistical classification of plant species data into communities. In this study, spatially referenced vegetation abundance values collected from Greek phrygana were analysed by ordination (DECORANA), and classified on the resulting axes using fuzzy c-means to yield a point data-set representing local memberships in characteristic plant communities. The fuzzy clusters matched vegetation communities noted in the field, which tended to grade into one another, rather than occupying discrete patches. The fuzzy set representation of the community exploited the strengths of detrended correspondence analysis while retaining richer information than a TWINSPAN classification of the same data. Thus, in the absence of phytosociological benchmarks, meaningful and manageable habitat information could be derived from complex, multivariate species data. We also analysed the influence of the reliability of different surveyors' field observations by multiple sampling at a selected sample location. We show that the impact of surveyor error was more severe in the Boolean than the fuzzy classification. © 2007 Springer.

Development of a probabilistic graphical structure from a model of mental health clinical expertise

This thesis explores the process of developing a principled approach for translating a model of mental-health risk expertise into a probabilistic graphical structure. Probabilistic graphical structures can be a combination of graph and probability theory that provide numerous advantages when it comes to the representation of domains involving uncertainty, domains such as the mental health domain. In this thesis the advantages that probabilistic graphical structures offer in representing such domains is built on. The Galatean Risk Screening Tool (GRiST) is a psychological model for mental health risk assessment based on fuzzy sets. In this thesis the knowledge encapsulated in the psychological model was used to develop the structure of the probability graph by exploiting the semantics of the clinical expertise. This thesis describes how a chain graph can be developed from the psychological model to provide a probabilistic evaluation of risk that complements the one generated by GRiST’s clinical expertise by the decomposing of the GRiST knowledge structure in component parts, which were in turned mapped into equivalent probabilistic graphical structures such as Bayesian Belief Nets and Markov Random Fields to produce a composite chain graph that provides a probabilistic classification of risk expertise to complement the expert clinical judgements

Developing a probabilistic graphical structure from a model of mental-health clinical risk expertise

This paper explores the process of developing a principled approach for translating a model of mental-health risk expertise into a probabilistic graphical structure. The Galatean Risk Screening Tool [1] is a psychological model for mental health risk assessment based on fuzzy sets. This paper details how the knowledge encapsulated in the psychological model was used to develop the structure of the probability graph by exploiting the semantics of the clinical expertise. These semantics are formalised by a detailed specification for an XML structure used to represent the expertise. The component parts were then mapped to equivalent probabilistic graphical structures such as Bayesian Belief Nets and Markov Random Fields to produce a composite chain graph that provides a probabilistic classification of risk expertise to complement the expert clinical judgements. © Springer-Verlag 2010.

Semisupervised learning of hierarchical latent trait models for data visualization

Recently, we have developed the hierarchical Generative Topographic Mapping (HGTM), an interactive method for visualization of large high-dimensional real-valued data sets. In this paper, we propose a more general visualization system by extending HGTM in three ways, which allows the user to visualize a wider range of data sets and better support the model development process. 1) We integrate HGTM with noise models from the exponential family of distributions. The basic building block is the Latent Trait Model (LTM). This enables us to visualize data of inherently discrete nature, e.g., collections of documents, in a hierarchical manner. 2) We give the user a choice of initializing the child plots of the current plot in either interactive, or automatic mode. In the interactive mode, the user selects "regions of interest," whereas in the automatic mode, an unsupervised minimum message length (MML)-inspired construction of a mixture of LTMs is employed. The unsupervised construction is particularly useful when high-level plots are covered with dense clusters of highly overlapping data projections, making it difficult to use the interactive mode. Such a situation often arises when visualizing large data sets. 3) We derive general formulas for magnification factors in latent trait models. Magnification factors are a useful tool to improve our understanding of the visualization plots, since they can highlight the boundaries between data clusters. We illustrate our approach on a toy example and evaluate it on three more complex real data sets. © 2005 IEEE.

Task-based image annotation and retrieval

In order to address problems of information overload in digital imagery task domains we have developed an interactive approach to the capture and reuse of image context information. Our framework models different aspects of the relationship between images and domain tasks they support by monitoring the interactive manipulation and annotation of task-relevant imagery. The approach allows us to gauge a measure of a user's intentions as they complete goal-directed image tasks. As users analyze retrieved imagery their interactions are captured and an expert task context is dynamically constructed. This human expertise, proficiency, and knowledge can then be leveraged to support other users in carrying out similar domain tasks. We have applied our techniques to two multimedia retrieval applications for two different image domains, namely the geo-spatial and medical imagery domains. © Springer-Verlag Berlin Heidelberg 2007.

An overall profit Malmquist productivity index with fuzzy and interval data

Although crisp data are fundamentally indispensable for determining the profit Malmquist productivity index (MPI), the observed values in real-world problems are often imprecise or vague. These imprecise or vague data can be suitably characterized with fuzzy and interval methods. In this paper, we reformulate the conventional profit MPI problem as an imprecise data envelopment analysis (DEA) problem, and propose two novel methods for measuring the overall profit MPI when the inputs, outputs, and price vectors are fuzzy or vary in intervals. We develop a fuzzy version of the conventional MPI model by using a ranking method, and solve the model with a commercial off-the-shelf DEA software package. In addition, we define an interval for the overall profit MPI of each decision-making unit (DMU) and divide the DMUs into six groups according to the intervals obtained for their overall profit efficiency and MPIs. We also present two numerical examples to demonstrate the applicability of the two proposed models and exhibit the efficacy of the procedures and algorithms. © 2011 Elsevier Ltd.