A Method to Construct an Extension of Fuzzy Information Granularity Based on Fuzzy Distance (original) (raw)
Related papers
2016
In fuzzy granular computing, a fuzzy granular structure is the collection of fuzzy information granules and fuzzy information granularity is used to measure the granulation degree of a fuzzy granular structure. In general, the fuzzy information granularity characterizes discernibility ability among fuzzy information granules in a fuzzy granular structure. In recent years, researchers have proposed some concepts of fuzzy information granularity based on partial order relations. However, the existing forms of fuzzy information granularity have some limitations when evaluating the fineness/coarseness between two fuzzy granular structures. In this paper, we propose an extension of fuzzy information granularity based on a fuzzy distance measure. We prove theoretically and experimentally that the proposed fuzzy information granularity is the best one to distinguish fuzzy granular structures.
Fuzzy Granular Structure Distance
IEEE Transactions on Fuzzy Systems, 2015
A fuzzy granular structure refers to a mathematical structure of the collection of fuzzy information granules granulated from a dataset, while a fuzzy information granularity is used to measure its uncertainty. However, the existing forms of fuzzy information granularity have two limitations. One is that when the fuzzy information granularity of one fuzzy granular structure equals that of the other, one can say that these two fuzzy granular structures possess the same uncertainty, but these two fuzzy granular structures may be not equivalent to each other. The other limitation is that existing axiomatic approaches to fuzzy information granularity are still not complete, under which when the partial order relation among fuzzy granular structures cannot be found, their coarseness/fineness relationships will not be revealed. To address these issues, a so-called fuzzy granular structure distance is proposed in this study, which can well discriminate the difference between any two fuzzy granular structures. Besides this advantage, the fuzzy granular structure distance has another important benefit: It can be used to establish a generalized axiomatic constraint for fuzzy information granularity. By using the axiomatic constraint, the coarseness/fineness of any two fuzzy granular structures can be distinguished. In addition, through taking the fuzzy granular structure distances of a fuzzy granular structure to the finest one and the coarsest one into account, we also can build a bridge between fuzzy information granularity and fuzzy information entropy. The applicable analysis on 12 real-world datasets shows that the fuzzy granular structure distance and the generalized fuzzy information granularity have much better performance than existing methods.
HISTORY AND DEVELOPMENT OF GRANULAR COMPUTING
1. Introduction 2. Information granularity and Granular Computing 3. Formal approaches to information granulation: an overview and generalizations 3.1. Formal platforms of information granularity 3.2. Information granules of higher type and higher order 3.3. Hybrid models of information granules 4. A design of information granules 4.1. The principle of justifiable granularity and design of fuzzy sets 4.2. Information granules as constructs of fuzzy clustering 4.3. Design of information granules with knowledge hints 5.
Multi-class granular approximation by means of disjoint and adjacent fuzzy granules
ArXiv, 2022
In granular computing, fuzzy sets can be approximated by granularly representable sets that are as close as possible to the original fuzzy set w.r.t. a given closeness measure. Such sets are called granular approximations. In this article, we introduce the concepts of disjoint and adjacent granules and we examine how the new definitions affect the granular approximations. First, we show that the new concepts are important for binary classification problems since they help to keep decision regions separated (disjoint granules) and at the same time to cover as much as possible of the attribute space (adjacent granules). Later, we consider granular approximations for multi-class classification problems leading to the definition of a multi-class granular approximation. Finally, we show how to efficiently calculate multiclass granular approximations for Lukasiewicz fuzzy connectives. We also provide graphical illustrations for a better understanding of the introduced concepts.
Granular Fuzzy Models: Construction, Analysis, and Design
2016
Building abstract concepts is essential to humans when acquiring knowledge, realizing processing (reasoning), and communicating findings. Abstraction comes hand in hand with information granules and information granulation. When analyzing digital images, we form groups (clusters) of pixels, colors, and textures that constitute familiar objects. This paramount ability of forming groups of objects (information granules), manipulating them, and producing sound conclusions, is realized in an almost subconscious manner. Information granules are critical when representing and processing knowledge. They become instrumental when solving Preface The research conducted in this thesis was performed under the supervision of Dr. Witold Pedrycz, and it was supported by the National Council of Science and Technology (CONACYT) Mexico under grant no. 213501/308562 and by the Autonomous University of Tlaxcala (UAT) Mexico. Most of the experiments presented in this thesis were completed by using the general Linux cluster for research use, provided and maintained by the Academic Information and Communication Technologies (AICT) department at the University of Alberta. Chapter 4 of this thesis has been published as O. F. Reyes-Galaviz, and W. Pedrycz, "Fuzzy relational structures: Learning alternatives for fuzzy modeling," Joint IFSA World Congress and
Towards Granular Computing: Classifiers Induced From Granular Structures
Granular computing as a paradigm is an area frequently studied within the Approximate Reasoning paradigm. Proposed by L. A.Zadeh granular computing has been studied within fuzzy as well as rough set approaches to uncertainty. It is manifest that both theories are immanently related to granulation as fuzzy set theory begins with fuzzy membership functions whose inverse images are prototype granules whereas rough set theory starts with indiscernibility relations whose classes are prototype, or, elementary granules. Many authors have devoted their works to analysis of granulation of knowledge, definitions of granules, methods for combining (fusing) granules into larger objects, applications of granular structures, see, quoted in references works by A. Skowron, T.Y. Lin, Y.Y.Yao, L.Polkowski and others. In this work, the emphasis is laid on granular decision (data) systems: they are introduced, methods of their construction with examples are pointed to, and applications are exhibited; those applications are founded on the basic although often implicit principle of data mining, viz., once a plausible for given data similarity measure is found, objects satisfactorily similar should reveal sufficiently close (or, for that matter identical) class values. In this work, this principle is applied to granules, following the idea presented by L.Polkowski at 2005, 2006 IEEE GrC conferences, that granules built on basis of a similarity relation from a given decision system should consists of objects similar to such a degree that averaging them would lead to new objects which together would constitute a new decision system preserving to a high degree knowledge represented by the original decision system. As knowledge in rough set theory is meant as the classification ability, it seems reasonable to test knowledge content with classifiers as classifier accuracy. This informal idea is tested in this work with some specific tools for granule construction, granular system building, and some well-tested classifiers known in literature for a few data sets from the UCI repository. In the following sections we outline: basic ideas of rough computing, granulation of knowledge, the idea of a granular decision system and we include the results of exemplary tests with real data.
Fuzzy information granules: a compact, transparent and efficient representation
2003
To illustrate the behavior of the proposed method a real-world information granulation problem has been used. Simulation results show that compact and robust fuzzy granules are attained, with the appreciable feature of being represented in a short functional form. In addition to the information granulation problem, a descriptive fuzzy model for a prediction benchmark has been developed to verify how much fuzzy granules identified form data through the proposed method are useful in providing good mapping properties.
Class-dependent rough-fuzzy granular space, dispersion index and classification
Pattern Recognition, 2012
A new rough-fuzzy model for pattern classification based on granular computing is described in the present article. In this model, we propose the formulation of class-dependent granules in fuzzy environment. Fuzzy membership functions are used to represent the feature-wise belonging to different classes, thereby producing fuzzy granulation of the feature space. The fuzzy granules thus generated possess better class discriminatory information that is useful in pattern classification with overlapping classes. Neighborhood rough sets are used in the selection of a subset of granulated features that explore the local/contextual information from neighbor granules. The model thus explores mutually the advantages of class-dependent fuzzy granulation and neighborhood rough set. The superiority of the proposed model to other similar methods is established with seven completely labeled data sets, including a synthetic remote sensing image, and two partially labeled real remote sensing images collected from satellites. Various performance measures, including a new method of dispersion estimation, are used for comparative analysis. The new measure called ''dispersion score'' quantifies the nature of distribution of the classified patterns among different classes so that lower is the dispersion, better is the classifier. The proposed model learns well even with a lower percentage of training set that makes the system fast. The model is seen to have lowest dispersion measure (i.e., misclassified patterns are confined to minimum number of classes) compared to others; thereby reflecting well the overlapping characteristics of a class with others, and providing a strong clue for the class-wise performance improvement with available higher-level information. The statistical significance of the proposed model is also supported by the w 2 test.