Abstract. The current research in granular computing is dominated by set-theoretic models such as rough sets and fuzzy sets. By recasting the existing studies in a wider context, we propose a unified framework of granular computing. The new framework extends results obtained in the set-theoretic setting and extracts high-level common principles from a wide range of scientific disciplines. The art of granular computing for problem solving emerges from the resulting common philosophy, methodology and information processing paradigm. Granular computing stresses not only the need for rigor, structure, conciseness and clarity, but also the importance of conscious effects and wisdom in using powerful strategies and heuristics in stating and solving problems.

arose as a synthesis of insights into human-centred information processing by Zadeh in the late ’90s and the Granular Computing name was coined, at this early stage, by T.Y Lin. Although the name is now in widespread use, or perhaps because of it, there are calls for a clarification of the distinctiveness of Granular Computing against the background of other human-centred information processing paradigms. This study examines the basic motivation for information granulation and casts Granular Computing as a structured combination of algorithmic and non-algorithmic information processing that mimics human, intelligent synthesis of knowledge from information.

Granular computing, as an emerging research field, provides a conceptual framework for studying many issues in data mining. This paper examines some of those issues, including data and knowledge representation and processing. It is demonstrated that one of the fundamental tasks of data mining is searching for the right level of granularity in data and knowledge representation. 1.

granule representation, granule relation, literature analysis. Knowledge plays a central role in human and artificial intelligence. One of the key characteristics of knowledge is its structured organization. Knowledge can be and should be presented in multiple levels and multiple views to meet people’s needs in different levels of granularities and from different perspectives. In this paper, we stand on the view point of granular computing and provide our understanding on multi-level and multi-view of knowledge through granular knowledge structures (GKS). Representation of granular knowledge structures, operations for building granular knowledge structures and how to use them are investigated. As an illustration, we provide some examples through results from an analysis of proceeding papers. Results show that granular knowledge structures could help users get better understanding of the knowledge source from set theoretical, logical and visual point of views. One may consider using them to meet specific needs or solve certain kinds of problems. 1

Abstract — Ptolemy II is a component-based design and modeling environment. It has a polymorphic type system that supports both the base types and structured types, such as arrays and records. The base type support was reported in [12]. This paper presents the extensions that support structured types. In the base type system, all the types are organized into a type lattice, and type constraints in the form of inequalities can be solved efficiently over the lattice. We take a hierarchical and granular approach to add structured types to the lattice, and extend the format of inequality constraints to allow arbitrary nesting of structured types. We also analyze the convergence of the constraint solving algorithm on an infinite lattice after structured types are added. To show the application of structured types, we present a Ptolemy II model that implements part of the IEEE 802.11 specifications. This model makes extensive use of record types to represent the protocol messages in the system. I.

Abstract — Granular computing unifies structured thinking, structured problem solving and structured information processing. In order to see the flexibility and universal applicability of this trinity model, we must demonstrate its effectiveness in solving real world problems. In this paper, we apply the basic ideas, principles, and strategies of granular computing to the specific problem solving task known as structured writing. Results from languages, human knowledge organization, rhetoric, writing, computer programming, and mathematical proving are summarized and cast in a setting for structured writing. The results bring new insights into granular computing. I.

The data explosion in (applied) biology and its associated data management problems of Internet-available resources is well-known (e.g. [3]), but how to solve it remains a big

Abstract — This paper introduces a new framework for privacy preserving computation to the granular computing community. The framework is called P4P (Peers for Privacy) and features a unique architecture and practical protocols for user data validation and vector addition-based computation. It turned out that many non-trivial and non-linear computations can be done using an iterative algorithm with vector-addition aggregation steps. Examples include voting, summation, SVD, regression, and ANOVA etc. P4P allows them to be carried out while preserving users privacy. To demonstrate its application in granular computing, we present two practical protocols that test the equality of user vectors in zero-knowledge. Our protocols only involve constant number of public key operations (independent of vector size) and are very efficient. These protocols can be used to perform granulation, which is a fundamental task of granular computing, in a privacy-preserving manner. They can also be of independent interest for other fields such as data mining as well. Index Terms — Privacy, zero-knowledge protocol, equivalence test, granulation.

Abstract—Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringbased rough sets through down-sets and up-sets. In this way, one can investigate covering-based rough sets from algebraic and topological points of view. Keywords—Covering, poset, down-set, lattice, topological space, topological base.

Abstract—Granular computing deals with representation of information in the form of some aggregates and related methods for transformation and analysis for problem solving. A granulation scheme based on clustering and Rough Set Theory is presented with focus on structured conceptualization of information has been presented in this paper. Experiments for the proposed method on four labeled data exhibit good result with reference to classification problem. The proposed granulation technique is semi-supervised imbibing global as well as local information granulation. To represent the results of the attribute oriented granulation a tree structure is proposed in this paper. Keywords—Granular computing, clustering, Rough sets, data mining.