Computing, in its usual sense, is centered on manipulation of numbers and symbols. In contrast, computing with words, or CW for short, is a methodology in which the objects of computation are words and propositions drawn from a natural language, e.g., small, large, far, heavy, not very likely, the price of gas is low and declining, Berkeley is near San Francisco, it is very unlikely that there will be a significant increase in the price of oil in the near future, etc. Computing with words is inspired by the remarkable human capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Familiar examples of such tasks are parking a car, driving in heavy traffic, playing golf, riding a bicycle, understanding speech and summarizing a story. Underlying this remarkable capability is the brain’s crucial ability to manipulate perceptions – perceptions of distance, size, weight, color, speed, time, direction, force, number, truth, likelihood and other characteristics of physical and mental objects. Manipulation of perceptions plays a key role in human recognition, decision and execution processes. As a methodology, computing with words provides a foundation for a computational theory of perceptions – a theory which may have an important bearing on how humans make – and machines might make – perception-based rational decisions in an environment of imprecision, uncertainty and partial truth. A basic difference between perceptions and measurements is that, in general, measurements are crisp whereas perceptions are fuzzy. One of the fundamental aims of science has been and continues to be that of progressing from perceptions to measurements. Pursuit of this aim has led to brilliant successes. We have sent men to the moon; we can build computers

The present article provides a survey of the available literature on data mining using soft computing. A categorization has been provided based on the different soft computing tools and their hybridizations used, the data mining function implemented, and the preference criterion selected by the model. The utility of the different soft computing methodologies is highlighted. Generally fuzzy sets are suitable for handling the issues related to understandability of patterns, incomplete/noisy data, mixed media information and human interaction, and can provide approximate solutions faster. Neural networks are nonparametric, robust, and exhibit good learning and generalization capabilities in data-rich environments. Genetic algorithms provide efficient search algorithms to select a model, from mixed media data, based on some preference criterion/objective function. Rough sets are suitable for handling different types of uncertainty in data. Some challenges to data mining and the application of soft computing methodologies are indicated. An extensive bibliography is also included.

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.

The main objective of this paper is to advocate for formal and mathematical modeling of data mining, which unfortunately has not received much attention. A framework is proposed for rule mining based on granular computing. It is developed in the Tarski's style through the notions of a model and satisfiability. The model is a database consisting of a finite set of objects described by a finite set of attributes. Within this framework, a concept is defined as a pair consisting of the intension, an expression in a certain language over the set of attributes, and the extension, a subset of the universe, of the concept. An object satisfies the expression of a concept if the object has the properties as specified by the expression, and the object belongs to the extension of the concepts. Rules are used to describe relationships between concepts. A rule is expressed in terms of the intensions of the two concepts and is interpreted in terms of the extensions of the concepts. Two interpretations of rules are examined in detail, one is based on logical implication and the other on conditional probability.

It is a deep-seated tradition in science to view uncertainty as a province of probability theory. The generalized theory of uncertainty (GTU) which is outlined in this paper breaks with this tradition and views uncertainty in a much broader perspective. Uncertainty is an attribute of information. A fundamental premise of GTU is that information, whatever its form, may be represented as what is called a generalized constraint. The concept of a generalized constraint is the centerpiece of GTU. In GTU, a probabilistic constraint is viewed as a special––albeit important––instance of a generalized constraint. A generalized constraint is a constraint of the form X isr R, where X is the constrained variable, R is a constraining relation, generally non-bivalent, and r is an indexing variable which identifies the modality of the constraint, that is, its semantics. The

An importance of the idea of granularity of knowledge for approximate reasoning has been recently stressed in [6,9-10]. We address here the problem of synthesis of adaptive decision algorithms and we propose an approach to this problem based on the notion of a granule which we develop in the framework of rough mereology. This framework does encompass both rough and fuzzy set theories. Our approach may be applied in the problems of approximate synthesis of complex objects (solutions) in distributed systems of intelligent agents. Keywords--- rough sets, apporoximate reasoning, rough mereology, granules of knowledge I. Introduction: a notion of a granule In this introduction, we first present the rough set approach, then we outline the fuzzy set approach and finally we introduce elements of rough mereological theory [2], [7,8] by means of which we will define in the sequel the notion of a granule of knowledge in a unified way. We begin with rough set approach [5]. In this approach, kn...

Granular computing (GrC) may be regarded as a label of theories, methodologies, techniques, and tools that make use of granules, i.e., groups, classes, or clusters of a universe, in the process of problem solving. The main objective of this paper is to discuss basic issues of GrC, with emphasis on the construction of granules and computation with granules. After a brief review of existing studies, a set-theoretic model of GrC is proposed based on the notion of power algebras.

There are two objectives of this chapter. One objective is to examine the basic principles and issues of granular computing. We focus on the tasks of granulation and computing with granules. From semantic and algorithmic perspectives, we study the construction, interpretation, and representation of granules, as well as principles and operations of computing and reasoning with granules. The other objective is to study a partition model of granular computing in a set-theoretic setting. The model is based on the assumption that a finite set of universe is granulated through a family of pairwise disjoint subsets. A hierarchy of granulations is modeled by the notion of the partition lattice.

Information retrieval support systems (IRSS) are designed with the objective to provide the necessary utilities, tools, and languages that support a user to perform various tasks in finding useful information and knowledge. While existing information retrieval systems (IRS) focus on the search and browsing functionalities, an IRSS focuses on the supporting functionalities. IRSS are more flexible and combine the functionalities of IRS, Web browser and Web search engines. One objective of the paper is to demonstrate the needs for, and the potential benefits of, moving from IRS to IRSS. On the one hand, IRSS is an emerging important research topic, and on the other hand, there is a lack of a systematic study on the topic. Another objective of the paper is to present a framework for IRSS by drawing results from decision support systems (DSS) and intelligent systems. Basic issues of IRSS are discussed, and basic components of an IRSS, as well as its functionalities, are studied.

Abstract- A generalized decision logic language GDL is proposed for granular computing (GrC) in the Tarski’s style through the notions of a model and satisfiability. The model is an information table consisting of a finite set of objects described by a finite set of attributes. A concept or a granule is characterized by a pair consisting of the intension of the concept, a formula of the language GDL, and the extension of the concept, a subset of the universe. We discuss the application of GDL in formal concepts and decision rules. The former deals with description and interpretation of granules, and the latter deals with the relationships between granules. I.