FEATURE WEIGHTING FUZZY CLUSTERING INTEGRATING ROUGH SETS AND SHADOWED SETS

2012 ◽  
Vol 26 (04) ◽  
pp. 1250010 ◽  
Author(s):  
LINA WANG ◽  
JIANDONG WANG
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Clustering ◽  
Rough Sets ◽  
Granular Computing ◽  
Clustering Algorithms ◽  
Noisy Data ◽  
Real Data ◽  
Feature Weighting ◽  
Novel Method ◽  
Shadowed Sets

Associating features with weights is a common approach in clustering algorithms and determining the weight values is crucial in generating valid partitions. In this paper, we introduce a novel method in the framework of granular computing that incorporates fuzzy sets, rough sets and shadowed sets, and calculates feature weights automatically. Experiments on synthetic and real data patterns show that our algorithms always converge and are more effective in handling overlapping among clusters and more robust in the presence of noisy data and outliers.

Data Clustering Algorithms Using Rough Sets

2013 ◽  
pp. 297-327 ◽  
Author(s):  
B.K. Tripathy ◽  
Adhir Ghosh
Keyword(s):  
Comparative Study ◽  
Rough Set ◽  
Fuzzy Clustering ◽  
Fuzzy Set ◽  
Rough Sets ◽  
Data Clustering ◽  
Clustering Algorithms ◽  
Clustering Methods ◽  
Future Studies ◽  
Multiple Clusters

Developing Data Clustering algorithms have been pursued by researchers since the introduction of k-means algorithm (Macqueen 1967; Lloyd 1982). These algorithms were subsequently modified to handle categorical data. In order to handle the situations where objects can have memberships in multiple clusters, fuzzy clustering and rough clustering methods were introduced (Lingras et al 2003, 2004a). There are many extensions of these initial algorithms (Lingras et al 2004b; Lingras 2007; Mitra 2004; Peters 2006, 2007). The MMR algorithm (Parmar et al 2007), its extensions (Tripathy et al 2009, 2011a, 2011b) and the MADE algorithm (Herawan et al 2010) use rough set techniques for clustering. In this chapter, the authors focus on rough set based clustering algorithms and provide a comparative study of all the fuzzy set based and rough set based clustering algorithms in terms of their efficiency. They also present problems for future studies in the direction of the topics covered.

A GENERALIZED APPROACH TO POSSIBILISTIC CLUSTERING ALGORITHMS

2007 ◽  
Vol 15 (supp02) ◽  
pp. 117-138 ◽  
Author(s):  
JIAN ZHOU ◽  
CHIH-CHENG HUNG
Keyword(s):  
Set Theory ◽  
Fuzzy Clustering ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Clustering Algorithms ◽  
Infinite Family ◽  
Real Data ◽  
Point Of View ◽  
New Family ◽  
Possibilistic Clustering

Fuzzy clustering is an approach using the fuzzy set theory as a tool for data grouping, which has advantages over traditional clustering in many applications. Many fuzzy clustering algorithms have been developed in the literature including fuzzy c-means and possibilistic clustering algorithms, which are all objective-function based methods. Different from the existing fuzzy clustering approaches, in this paper, a general approach of fuzzy clustering is initiated from a new point of view, in which the memberships are estimated directly according to the data information using the fuzzy set theory, and the cluster centers are updated via a performance index. This new method is then used to develop a generalized approach of possibilistic clustering to obtain an infinite family of generalized possibilistic clustering algorithms. We also point out that the existing possibilistic clustering algorithms are members of this family. Following that, some specific possibilistic clustering algorithms in the new family are demonstrated by real data experiments, and the results show that these new proposed algorithms are efficient for clustering and easy for computer implementation.

Clustering Approaches in Decision Making Using Fuzzy and Rough Sets

2017 ◽  
pp. 116-136
Author(s):  
Deepthi P. Hudedagaddi ◽  
B. K. Tripathy
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Data Clustering ◽  
Geographical Information Systems ◽  
Clustering Algorithms ◽  
Real Life ◽  
Hybrid Models ◽  
The Individual ◽  
Few Data

Data clustering has been an integral and important part of data mining. It has wide applications in database anonymization, decision making, image processing and pattern recognition, medical diagnosis and geographical information systems, only to name a few. Data in real life scenario are having imprecision inherent in them. So, early crisp clustering techniques are very less efficient. Several imprecision based models have been proposed over the years like the fuzzy sets, rough sets, intuitionistic fuzzy sets and many of their generalized versions. Of late, it has been established that the hybrid models obtained as combination of these imprecise models are far more efficient than the individual ones. So, many clustering algorithms have been put forth using these hybrid models. The focus of this chapter is to discuss on some of the data clustering algorithms developed so far and their applications mainly in the area of decision making.

scholarly journals Modeling Decisions for Artificial Intelligence

2008 ◽  
Vol 12 (5) ◽  
pp. 408-408
Author(s):  
Vicenç Torra ◽  
◽  
Yasuo Narukawa ◽  
Keyword(s):  
Artificial Intelligence ◽  
Fuzzy Clustering ◽  
Rough Sets ◽  
Decision Procedure ◽  
Clustering Algorithms ◽  
Decision Makers ◽  
Rule Generation ◽  
Special Issue ◽  
Weather Information ◽  
The Third

In August 2007, the 4th International Conference on Modeling Decisions for Artificial Intelligence (MDAI1) was held in Kitakyushu, Japan. This special issue has its origins in the conference. We present nine papers related to soft computing tool applications. The first paper, by Honda and Okazaki, presents an axiomatization of a generalized Shaply value. The second paper, by García-Lapresta, also related to decision-making, introduces a multistage decision procedure in which decision-makers opinions are weighted by their contribution to an agreement. The third paper, by Torra and Miyamoto, concerns the problem of loading a container, outlining a system for loading nonorthogonal objects. The fourth paper, by Sakai, Koba, and Nakata, is devoted to rule generation based on rough sets. The fifth paper by Hiramatsu, Huynh, and Nakamori, deals with a fuzzy-based model applied to weather information. The sixth paper, by Inokuchi and Miyamoto, discuss fuzzy clustering algorithms for discrete data. The seventh paper, by Miyamoto, Kuroda, and Arai, studies an algorithm for the sequential extraction of clusters compared to mountain clustering. In the eighth paper, Miyamoto formulates fuzzy clustering using the calculus of variations. The ningth and final paper treats fuzzy clustering, in which Endo et al. discuss fuzzy c-means for data with tolerance. In closing, we thank the referees for their work on reviews and Prof. Hirota for editing this special issue. We also thank the Fuji Technology Press Ltd. staff for its advice. 1Work partially funded by Spanish MEC (projects ARES – CONSOLIDER INGENIO 2010 CSD2007-00004 – and eAEGIS – TSI2007-65406-C03-02)

Granular Computing

2011 ◽  
pp. 774-780
Author(s):  
Georg Peters
Keyword(s):  
Probability Theory ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Rough Sets ◽  
Granular Computing ◽  
Information Granularity ◽  
Relationship Of ◽  
The Relationship

It is well accepted that in many real life situations information is not certain and precise but rather uncertain or imprecise. To describe uncertainty probability theory emerged in the 17th and 18th century. Bernoulli, Laplace and Pascal are considered to be the fathers of probability theory. Today probability can still be considered as the prevalent theory to describe uncertainty. However, in the year 1965 Zadeh seemed to have challenged probability theory by introducing fuzzy sets as a theory dealing with uncertainty (Zadeh, 1965). Since then it has been discussed whether probability and fuzzy set theory are complementary or rather competitive (Zadeh, 1995). Sometimes fuzzy sets theory is even considered as a subset of probability theory and therefore dispensable. Although the discussion on the relationship of probability and fuzziness seems to have lost the intensity of its early years it is still continuing today. However, fuzzy set theory has established itself as a central approach to tackle uncertainty. For a discussion on the relationship of probability and fuzziness the reader is referred to e.g. Dubois, Prade (1993), Ross et al. (2002) or Zadeh (1995). In the meantime further ideas how to deal with uncertainty have been suggested. For example, Pawlak introduced rough sets in the beginning of the eighties of the last century (Pawlak, 1982), a theory that has risen increasing attentions in the last years. For a comparison of probability, fuzzy sets and rough sets the reader is referred to Lin (2002). Presently research is conducted to develop a Generalized Theory of Uncertainty (GTU) as a framework for any kind of uncertainty whether it is based on probability, fuzziness besides others (Zadeh, 2005). Cornerstones in this theory are the concepts of information granularity (Zadeh, 1979) and generalized constraints (Zadeh, 1986). In this context the term Granular Computing was first suggested by Lin (1998a, 1998b), however it still lacks of a unique and well accepted definition. So, for example, Zadeh (2006a) colorfully calls granular computing “ballpark computing” or more precisely “a mode of computation in which the objects of computation are generalized constraints”.

Sign in / Sign up

Export Citation Format

Share Document