The Principle of Justifiable Granularity and an Optimization of Information Granularity Allocation as Fundamentals of Granular Computing

Witold Pedrycz 한국정보처리학회 2011 Journal of information processing systems Vol.7 No.3

Concepts and Design Aspects of Granular Models of Type-1 and Type-2

Witold Pedrycz 한국지능시스템학회 2015 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.15 No.2

In this study, we pursue a new direction for system modeling by introducing the concept of granular models, which produce results in the form of information granules (such as intervals, fuzzy sets, and rough sets). We present a rationale and several key motivating arguments behind the use of granular models and discuss their underlying design processes. The development of the granular model includes optimal allocation of information granularity through optimizing the criteria of coverage and specificity. The emergence and construction of granular models of type-2 and type-n (in general) is discussed. It is shown that achieving a suitable coverage-specificity tradeoff (compromise) is essential for developing granular models.

Associations Among Information Granules and Their Optimization in Granulation-Degranulation Mechanism of Granular Computing

Witold Pedrycz 한국지능시스템학회 2013 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.13 No.4

Knowledge representation realized by information granules is one of the essential facets of granular computing and an area of intensive research. Fuzzy clustering and clustering are general vehicles to realize formation of information granules. Granulation ? degranulation paradigm is one of the schemes determining and quantifying functionality and knowledge representation capabilities of information granules. In this study, we augment this paradigm by forming and optimizing a collection of associations among original and transformed information granules. We discuss several transformation schemes and analyze their properties. A series of numeric experiments is provided using which we quantify the improvement of the degranulation mechanisms offered by the optimized transformation of information granules.

Boosting of granular models

Pedrycz, Witold,Kwak, Keun-Chang North-Holland 2006 Fuzzy sets and systems Vol.157 No.22

<P><B>Abstract</B></P><P>In this study, we are concerned with the design of granular modeling being originally proposed by Pedrycz and Vasilakos. The enhancement of the development process comes in the form of the boosting mechanism applied to the generic model. In comparison with the original topology of the model studied so far, we augment it by a bias term and investigate its role in the overall architecture. Second, treating the granular model as a weak learner, we discuss the underlying mechanisms of boosting which in this setting has to be refined so that it handles the continuous case. From the design standpoint, we are interested in studying the following issues: (a) effectiveness of boosting when applied in this modeling framework along with its numeric quantification, and (b) impact of information granularity at which the granular models are developed on the improvements offered by boosting procedure itself. Numeric experiments help quantify the performance of the boosted granular models and gain a detailed view at the efficiency of the boosting strategy vis-à-vis different design scenarios.</P>

Associations Among Information Granules and Their Optimization in Granulation-Degranulation Mechanism of Granular Computing

Pedrycz, Witold Korean Institute of Intelligent Systems 2013 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.13 No.4

Knowledge representation realized by information granules is one of the essential facets of granular computing and an area of intensive research. Fuzzy clustering and clustering are general vehicles to realize formation of information granules. Granulation - degranulation paradigm is one of the schemes determining and quantifying functionality and knowledge representation capabilities of information granules. In this study, we augment this paradigm by forming and optimizing a collection of associations among original and transformed information granules. We discuss several transformation schemes and analyze their properties. A series of numeric experiments is provided using which we quantify the improvement of the degranulation mechanisms offered by the optimized transformation of information granules.

The Principle of Justifiable Granularity and an Optimization of Information Granularity Allocation as Fundamentals of Granular Computing

Pedrycz, Witold Korea Information Processing Society 2011 Journal of information processing systems Vol.7 No.3

Granular Computing has emerged as a unified and coherent framework of designing, processing, and interpretation of information granules. Information granules are formalized within various frameworks such as sets (interval mathematics), fuzzy sets, rough sets, shadowed sets, probabilities (probability density functions), to name several the most visible approaches. In spite of the apparent diversity of the existing formalisms, there are some underlying commonalities articulated in terms of the fundamentals, algorithmic developments and ensuing application domains. In this study, we introduce two pivotal concepts: a principle of justifiable granularity and a method of an optimal information allocation where information granularity is regarded as an important design asset. We show that these two concepts are relevant to various formal setups of information granularity and offer constructs supporting the design of information granules and their processing. A suite of applied studies is focused on knowledge management in which case we identify several key categories of schemes present there.

Data-based design of fuzzy sets

Witold Pedrycz,George Vukovich 한국지능시스템학회 1999 한국지능시스템학회논문지 Vol.9 No.3

Granular Bidirectional and Multidirectional Associative Memories: Towards a Collaborative Buildup of Granular Mappings

Pedrycz, Witold Korea Information Processing Society 2017 Journal of information processing systems Vol.13 No.3

Associative and bidirectional associative memories are examples of associative structures studied intensively in the literature. The underlying idea is to realize associative mapping so that the recall processes (one-directional and bidirectional ones) are realized with minimal recall errors. Associative and fuzzy associative memories have been studied in numerous areas yielding efficient applications for image recall and enhancements and fuzzy controllers, which can be regarded as one-directional associative memories. In this study, we revisit and augment the concept of associative memories by offering some new design insights where the corresponding mappings are realized on the basis of a related collection of landmarks (prototypes) over which an associative mapping becomes spanned. In light of the bidirectional character of mappings, we have developed an augmentation of the existing fuzzy clustering (fuzzy c-means, FCM) in the form of a so-called collaborative fuzzy clustering. Here, an interaction in the formation of prototypes is optimized so that the bidirectional recall errors can be minimized. Furthermore, we generalized the mapping into its granular version in which numeric prototypes that are formed through the clustering process are made granular so that the quality of the recall can be quantified. We propose several scenarios in which the allocation of information granularity is aimed at the optimization of the characteristics of recalled results (information granules) that are quantified in terms of coverage and specificity. We also introduce various architectural augmentations of the associative structures.

Concepts and Design Aspects of Granular Models of Type-1 and Type-2

Pedrycz, Witold Korean Institute of Intelligent Systems 2015 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.15 No.2

In this study, we pursue a new direction for system modeling by introducing the concept of granular models, which produce results in the form of information granules (such as intervals, fuzzy sets, and rough sets). We present a rationale and several key motivating arguments behind the use of granular models and discuss their underlying design processes. The development of the granular model includes optimal allocation of information granularity through optimizing the criteria of coverage and specificity. The emergence and construction of granular models of type-2 and type-n (in general) is discussed. It is shown that achieving a suitable coverage-specificity tradeoff (compromise) is essential for developing granular models.

Granular Bidirectional and Multidirectional Associative Memories: Towards a Collaborative Buildup of Granular Mappings

( Witold Pedrycz ) 한국정보처리학회 2017 Journal of information processing systems Vol.13 No.3

Associative and bidirectional associative memories are examples of associative structures studied intensively in the literature. The underlying idea is to realize associative mapping so that the recall processes (one-directional and bidirectional ones) are realized with minimal recall errors. Associative and fuzzy associative memories have been studied in numerous areas yielding efficient applications for image recall and enhancements and fuzzy controllers, which can be regarded as one-directional associative memories. In this study, we revisit and augment the concept of associative memories by offering some new design insights where the corresponding mappings are realized on the basis of a related collection of landmarks (prototypes) over which an associative mapping becomes spanned. In light of the bidirectional character of mappings, we have developed an augmentation of the existing fuzzy clustering (fuzzy c-means, FCM) in the form of a so-called collaborative fuzzy clustering. Here, an interaction in the formation of prototypes is optimized so that the bidirectional recall errors can be minimized. Furthermore, we generalized the mapping into its granular version in which numeric prototypes that are formed through the clustering process are made granular so that the quality of the recall can be quantified. We propose several scenarios in which the allocation of information granularity is aimed at the optimization of the characteristics of recalled results (information granules) that are quantified in terms of coverage and specificity. We also introduce various architectural augmentations of the associative structures.