Possibilistic and fuzzy clustering methods for robust analysis of non-precise data

This work focuses on robust clustering of data affected by imprecision. The imprecision is managed in terms of fuzzy sets. The clustering process is based on the fuzzy and possibilistic approaches. In both approaches the observations are assigned to the clusters by means of membership degrees. In fuzzy clustering the membership degrees express the degrees of sharing of the observations to the clusters. In contrast, in possibilistic clustering the membership degrees are degrees of typicality. These two sources of information are complementary because the former helps to discover the best fuzzy partition of the observations while the latter reflects how well the observations are described by the centroids and, therefore, is helpful to identify outliers. First, a fully possibilistic k-means clustering procedure is suggested. Then, in order to exploit the benefits of both the approaches, a joint possibilistic and fuzzy clustering method for fuzzy data is proposed. A selection procedure for choosing the parameters of the new clustering method is introduced. The effectiveness of the proposal is investigated by means of simulated and real-life data

Fuzziness in Performance Evaluation Problems Using Data Envelopment Analysis

Efficiency evaluation is an important part of decision making in many areas particularly in management and manufacturing sectors. Uncertainty and fuzziness of the real world problems have increased utilization of fuzzy sets theory in many research areas and data envelopment analysis is one of them. Utilizing data envelopment analysis to evaluate efficiency scores of decision making units in fuzzy environment requires fuzzy models and mathematical methods for solving fuzzy models with minimum calculation and maximum precision. Since current fuzzy data envelopment analysis models are not able to solve some problems in fuzzy environment, our attempt is to provide fuzzy data envelopment analysis models related to following various problems. Some problems include uncontrollable data (for manager) that regularly have fuzzy essence. An uncontrollable fuzzy data envelopment analysis model is represented for these types of problems. The advantages of the proposed model are in capability of it in including uncontrollable factors particularly those with fuzzy nature in problems with fuzzy data and controlling factor weights by additional constraints which can avoid the model to become infeasibility. The disadvantage of the method is in using too many restrictions (one restriction for each fuzzy data) which makes the model complicated and expensive to solve. For cases that interval efficiency scores are helpful, a method for solving fuzzy data envelopment analysis models is represented which interval efficiency scores can be achieved without adding restrictions to the model for each fuzzy data. In comparison with other methods, this method is simple, easy and with no additional constraint for each fuzzy data. In addition a fuzzy weights data envelopment analysis model is proposed to determine effect of data on the efficiency score. The model is informative in problems that the manager needs to know about uncertain effects of factors on efficiency score. The method of solving the model is simple and informative. By suggesting categorical data envelopment analysis method for problems with uncertain membership in various categories, we can help the decision maker to recognize the efficient decision making units fairly. In comparison with available method for categorical problems, our method is more informative and the traditional categorical method is a special case of our method. Finally, we provide a solution to comparison of production methods by utilizing fuzzy non-discretionary data envelopment analysis model. The proposed technique is more capable and informative while it includes factors with fuzzy essence that have effect on efficiency of production methods which is a real problem and may be its performance be effected by many fuzzy issues. categorical method is a special case of our method. Finally, we provide a solution to comparison of production methods by utilizing fuzzy non-discretionary data envelopment analysis model. The proposed technique is more capable and informative while it includes factors with fuzzy essence that have effect on efficiency of production methods which is a real problem and may be its performance be effected by many fuzzy issues

Measuring efficiency of a hierarchical organization with fuzzy DEA method

The paper analyses how the data envelopment analysis (DEA) and fuzzy set theory can be used to measure and evaluate the efficiency of a hierarchical system with n decision making units and a coordinating unit. It is presented a model for determining the of activity levels of decision making units so as to achieve both fuzzy objectives of achieving global target levels of coordination unit on the inputs and outputs and individual target levels of decision making units, and then some methods to resolve fuzzy models are proposed.fuzzy DEA, policy making in multi-level organisations, efficiency analysis

Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference

Spatial database implementation of fuzzy region connection calculus for analysing the relationship of diseases

Analyzing huge amounts of spatial data plays an important role in many emerging analysis and decision-making domains such as healthcare, urban planning, agriculture and so on. For extracting meaningful knowledge from geographical data, the relationships between spatial data objects need to be analyzed. An important class of such relationships are topological relations like the connectedness or overlap between regions. While real-world geographical regions such as lakes or forests do not have exact boundaries and are fuzzy, most of the existing analysis methods neglect this inherent feature of topological relations. In this paper, we propose a method for handling the topological relations in spatial databases based on fuzzy region connection calculus (RCC). The proposed method is implemented in PostGIS spatial database and evaluated in analyzing the relationship of diseases as an important application domain. We also used our fuzzy RCC implementation for fuzzification of the skyline operator in spatial databases. The results of the evaluation show that our method provides a more realistic view of spatial relationships and gives more flexibility to the data analyst to extract meaningful and accurate results in comparison with the existing methods.Comment: ICEE201

Building interpretable fuzzy models for high dimensional data analysis in cancer diagnosis

Background: Analysing gene expression data from microarray technologies is a very important task in biology and medicine, and particularly in cancer diagnosis. Different from most other popular methods in high dimensional bio-medical data analysis, such as microarray gene expression or proteomics mass spectroscopy data analysis, fuzzy rule-based models can not only provide good classification results, but also easily be explained and interpreted in human understandable terms, by using fuzzy rules. However, the advantages offered by fuzzy-based techniques in microarray data analysis have not yet been fully explored in the literature. Although some recently developed fuzzy-based modeling approaches can provide satisfactory classification results, the rule bases generated by most of the reported fuzzy models for gene expression data are still too large to be easily comprehensible. Results: In this paper, we develop some Multi-Objective Evolutionary Algorithms based Interpretable Fuzzy (MOEAIF) methods for analysing high dimensional bio-medical data sets, such as microarray gene expression data and proteomics mass spectroscopy data. We mainly focus on evaluating our proposed models on microarray gene expression cancer data sets, i.e., the lung cancer data set and the colon cancer data set, but we extend our investigations to other type of cancer data set, such as the ovarian cancer data set. The experimental studies have shown that relatively simple and small fuzzy rule bases, with satisfactory classification performance, can be successfully obtained for challenging microarray gene expression datasets. Conclusions: We believe that fuzzy-based techniques, and in particular the methods proposed in this paper, can be very useful tools in dealing with high dimensional cancer data. We also argue that the potential of applying fuzzy-based techniques to microarray data analysis need to be further explored. </p

Medical image classification and symptoms detection using neuro fuzzy

The conventional method in medicine for brain MR images classification and tumor detection is by human inspection. Operator-assisted classification methods are impractical for large amounts of data and are also non-reproducible. MR images also always contain a noise caused by operator performance which can lead to serious inaccuracies classification. The use of artificial intelligent techniques, for instance, neural networks, fuzzy logic, neuro fuzzy have shown great potential in this field. Hence, in this project the neuro fuzzy system or ANFIS was applied for classification and detection purposes. Decision making was performed in two stages: feature extraction using the principal component analysis (PCA) and the ANFIS trained with the backpropagation gradient descent method in combination with the least squares method. The performance of the ANFIS classifier was evaluated in terms of training performance and classification accuracies and the results confirmed that the proposed ANFIS classifier has potential in detecting the tumors