Hierarchization process by possibilistic fuzzy clustering of fuzzy rules

This paper presents a possibilistic fuzzy clustering algorithm that is applied to a multidimensional fuzzy set or fuzzy rules. This method can be used to decompose the fuzzy system into an hierarchical structure. The methodology presented leads to a fuzzy partition of the fuzzy rules, one for each cluster, which corresponds to a new set of fuzzy sub-systems. This technique is tested to organize the fuzzy model into a new and more comprehensive structure

A Flexible Approach to the Multidimensional Model: The Fuzzy Datacube

As a result of the use of OLAP technology in new fields of knowledge and the merge of data from different sources, it has become necessary for models to support this technology. In this paper, we propose a new multidimensional model that can manage imprecision both in dimensions and facts. Consequently, the multidimensional structure is able to model data imprecision resulting from the integration of data from different sources or even information from experts, which it does by means of fuzzy logic

SymScal: symbolic multidimensional scaling of interval dissimilarities

Multidimensional scaling aims at reconstructing dissimilaritiesbetween pairs of objects by distances in a low dimensional space.However, in some cases the dissimilarity itself is unknown, but therange of the dissimilarity is given. Such fuzzy data fall in thewider class of symbolic data (Bock and Diday, 2000).Denoeux and Masson (2000) have proposed to model an intervaldissimilarity by a range of the distance defined as the minimum andmaximum distance between two rectangles representing the objects. Inthis paper, we provide a new algorithm called SymScal that is basedon iterative majorization. The advantage is that each iteration isguaranteed to improve the solution until no improvement is possible.In a simulation study, we investigate the quality of thisalgorithm. We discuss the use of SymScal on empirical dissimilarityintervals of sounds.iterative majorization;multidimensional scaling;symbolic data analysis;distance smoothing

Applying fuzzy-set theoretic poverty measures within a developmental local government context : the Khayelitsha - Mitchell's Plain case study

Includes bibliographical references (leaves 100-108).This paper attempts to demonstrate the importance of the linkage between the presence of poverty and the nature of governance, something largely omitted from poverty studies in South Africa. The context of this investigation was the establishment of the new local government model (i.e. Developmental Local Government), which puts governance at the forefront of addressing poverty effectively. The new governance model adopts a multidimensional poverty paradigm in its Integrated Development Planning (IDP). However, in this study we have examined whether the approach adopted (i.e. Basic Needs) is necessarily the best multidimensional approach available. We have given preference to the capabilities approach with its emphasis on well-being where people are the beneficiaries of development rather than the basic needs approach where the emphasis is on goods and services as a means to good life. Sen's Capabilities Approach was operationalised by adopting a relatively new methodology (Le. fuzzy-set theoretic poverty measures) for measuring multidimensional poverty in the Khayelitsha Mitchell's Plain (KMP) magisterial district using the Census 2001 dataset. Our results show that unemployment, housing and low incomes need the most attention in KMP. Furthermore, the fuzzy-set measures, which view poverty as opaque and vague, yield more detailed policy information, thus preventing the single-policy response dominating many IDPs at present. As a medium term policy response, it is suggested that the implementation of the extended public works programme in KMP has the potential to significantly address both the material and non-material capability failure existing in KMP

Comparison of different strategies of utilizing fuzzy clustering in structure identification

Fuzzy systems approximate highly nonlinear systems by means of fuzzy "if-then" rules. In the literature, various algorithms are proposed for mining. These algorithms commonly utilize fuzzy clustering in structure identification. Basically, there are three different approaches in which one can utilize fuzzy clustering; the �first one is based on input space clustering, the second one considers clustering realized in the output space, while the third one is concerned with clustering realized in the combined input-output space. In this study, we analyze these three approaches. We discuss each of the algorithms in great detail and o¤er a thorough comparative analysis. Finally, we compare the performances of these algorithms in a medical diagnosis classi�cation problem, namely Aachen Aphasia Test. The experiment and the results provide a valuable insight about the merits and the shortcomings of these three clustering approaches

Using Fuzzy Linguistic Representations to Provide Explanatory Semantics for Data Warehouses

A data warehouse integrates large amounts of extracted and summarized data from multiple sources for direct querying and analysis. While it provides decision makers with easy access to such historical and aggregate data, the real meaning of the data has been ignored. For example, "whether a total sales amount 1,000 items indicates a good or bad sales performance" is still unclear. From the decision makers' point of view, the semantics rather than raw numbers which convey the meaning of the data is very important. In this paper, we explore the use of fuzzy technology to provide this semantics for the summarizations and aggregates developed in data warehousing systems. A three layered data warehouse semantic model, consisting of quantitative (numerical) summarization, qualitative (categorical) summarization, and quantifier summarization, is proposed for capturing and explicating the semantics of warehoused data. Based on the model, several algebraic operators are defined. We also extend the SQL language to allow for flexible queries against such enhanced data warehouses