Showing papers on "Rough set published in 2002"

An application of soft sets in a decision making problem

Abstract: In this paper, we apply the theory of soft sets to solve a decision making problem using rough mathematics.

Data mining in soft computing framework: a survey

Abstract: 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.

Rough approximation by dominance relations

Abstract: In this article we are considering a multicriteria classification that differs from usual classification problems since it takes into account preference orders in the description of objects by condition and decision attributes. To deal with multicriteria classification we propose to use a dominance-based rough set approach (DRSA). This approach is different from the classic rough set approach (CRSA) because it takes into account preference orders in the domains of attributes and in the set of decision classes. Given a set of objects partitioned into pre-defined and preference-ordered classes, the new rough set approach is able to approximate this partition by means of dominance relations (instead of indiscernibility relations used in the CRSA). The rough approximation of this partition is a starting point for induction of if-then decision rules. The syntax of these rules is adapted to represent preference orders. The DRSA keeps the best properties of the CRSA: it analyses only facts present in data, and possible inconsistencies are not corrected. Moreover, the new approach does not need any prior discretization of continuous-valued attributes. In this article we characterize the DRSA as well as decision rules induced from these approximations. The usefulness of the DRSA and its advantages over the CRSA are presented in a real study of evaluation of the risk of business failure.

Decision Table Reduction based on Conditional Information Entropy

Abstract: This paper analyzes the information view of rough set theory and compares it with the algebra view of rough set theory Some equivalence relations and other kind of relations like inclusion relation between the information view and the algebra view of rough set theory are resulted through comparing each other Two novel heuristic knowledge reduction algorithms are developed based on conditional information entropy, that is, conditional entropy based algorithm for reduction of knowledge with computing core (CEBARKCC) and conditional entropy based algorithm for reduction of knowledge without computing core (CEBARKNC) These two algorithms are compared with a mutual information based algorithm for reduction of knowledge (MIBARK) of Duoqian Miao through theoretical analysis and experimental simulation CEBARKCC algorithm and CEBARKNC algorithm have good performance in simulation

Rough Sets: Mathematical Foundations

Abstract: 1 Rough Set Theory: An Introduction.- 2 The Sentential Calculus.- 3 Logical Theory of Approximations.- 4 Many-Valued Sentential Calculi.- 5 Propositional Modal Logic.- 6 Set Theory.- 7 Topological Structures.- 8 Algebraic Structures.- 9 Predicate Calculus.- 10 Independence, Approximation.- 11 Topology of Rough Sets.- 12 Algebra and Logic of Rough Sets.- 13 Infinite-valued Logical Calculi.- 14 From Rough to Fuzzy.- List of Symbols.

Rough set theory and its applications

Abstract: In this paper rudiments of the theory will be outlined, and basic concepts of the theory will be illustrated by a simple tutorial example, concerning churn modeling in telecommunications. Real life applications require more advanced extensions of the theory but we will not discuss these extensions here. Rough set theory has an overlap with many other theories dealing with imperfect knowledge, e.g., evidence theory, fuzzy sets, Bayesian inference and others. Nevertheless, the theory can be regarded as an independent, complementary, not competing, discipline in its own rights.

Data mining, rough sets and granular computing

Abstract: 1: Granular Computing - A New Paradigm.- Some Reflections on Information Granulation and its Centrality in Granular Computing, Computing with Words, the Computational Theory of Perceptions and Precisiated Natural Language.- 2: Granular Computing in Data Mining.- Data Mining Using Granular Computing: Fast Algorithms for Finding Association Rules.- Knowledge Discovery with Words Using Cartesian Granule Features: An Analysis for Classification Problems.- Validation of Concept Representation with Rule Induction and Linguistic Variables.- Granular Computing Using Information Tables.- A Query-Driven Interesting Rule Discovery Using Association and Spanning Operations.- 3: Data Mining.- An Interactive Visualization System for Mining Association Rules.- Algorithms for Mining System Audit Data.- Scoring and Ranking the Data Using Association Rules.- Finding Unexpected Patterns in Data.- Discovery of Approximate Knowledge in Medical Databases Based on Rough Set Model.- 4: Granular Computing.- Observability and the Case of Probability.- Granulation and Granularity via Conceptual Structures: A Perspective From the Point of View of Fuzzy Concept Lattices.- Granular Computing with Closeness and Negligibility Relations.- Application of Granularity Computing to Confirm Compliance with Non-Proliferation Treaty.- Basic Issues of Computing with Granular Probabilities.- Multi-dimensional Aggregation of Fuzzy Numbers Through the Extension Principle.- On Optimal Fuzzy Information Granulation.- Ordinal Decision Making with a Notion of Acceptable: Denoted Ordinal Scales.- A Framework for Building Intelligent Information-Processing Systems Based on Granular Factor Space.- 5: Rough Sets and Granular Computing.- GRS: A Generalized Rough Sets Model.- Structure of Upper and Lower Approximation Spaces of Infinite Sets.- Indexed Rough Approximations, A Polymodal System, and Generalized Possibility Measures.- Granularity, Multi-valued Logic, Bayes' Theorem and Rough Sets.- The Generic Rough Set Inductive Logic Programming (gRS-ILP) Model.- Possibilistic Data Analysis and Its Similarity to Rough Sets.

Modal-style operators in qualitative data analysis

Abstract: We explore the usage of the modal possibility operator (and its dual necessity operator) in qualitative data analysis, and show that it-quite literally-complements the derivation operator of formal concept analysis; we also propose a new generalization of the rough set approximation operators. As an example for the applicability of the concepts we investigate the Morse data set which has been frequently studied in multidimensional scaling procedures.

Extension of rough set under incomplete information systems

Abstract: The classical rough set theory is based on complete information systems. It classifies objects using upper-approximation and lower-approximation defined on an indiscernibility relation that is a kind of equivalent relation. In order to process incomplete information systems, the classical rough set theory needs to be extended, especially, the indiscernibility relation needs to be extended to some inequivalent relation. There are several extensions for the indiscernibility relation at present, such as tolerance relation, non-symmetric similarity relation, and valued tolerance relation. Unfortunately, these extensions have their own limitation. We develop a new extension of rough set theory that is based on a limited tolerance relation.

The algorithm on knowledge reduction in incomplete information systems

Abstract: Rough set theory is emerging as a powerful tool for reasoning about data, knowledge reduction is one of the important topics in the research on rough set theory. It has been proven that finding the minimal reduct of an information system is a NP-hard problem, so is finding the minimal reduct of an incomplete information system. Main reason of causing NP-hard is combination problem of attributes. In this paper, knowledge reduction is defined from the view of information, a heuristic algorithm based on rough entropy for knowledge reduction is proposed in incomplete information systems, the time complexity of this algorithm is O(|A|2|U|). An illustrative example is provided that shows the application potential of the algorithm.

Organic food consumption: A multi‐theoretical framework of consumer decision making

Abstract: An approach is introduced to combine survey data with multi‐agent simulation models of consumer behaviour to study the diffusion process of organic food consumption. This methodology is based on rough set theory, which is able to translate survey data into behavioural rules. The topic of rule induction has been extensively investigated in other fields and in particular in learning machine, where several efficient algorithms have been proposed. However, the peculiarity of the rough set approach is that the inconsistencies in a data set about consumer behaviour are not aggregated or corrected since lower and upper approximation are computed. Thus, we expect that rough sets theory is suitable to extract knowledge in the form of rules within a consistent theoretical framework of consumer behaviour.

A New Version of Rough Set Exploration System

Abstract: We introduce a new version of the Rough Set Exploration System - a software tool featuring a library of methods and a graphical user interface supporting variety of rough-set-based computations. Methods, features and abilities of the implemented software are discussed and illustrated with a case study in data analysis.

Rough sets perspective on data and knowledge

Abstract: Rough set theory was proposed by Zdzislaw Pawlak (1982, 1991) in the early 1980s. Since then we have witnessed a systematic, worldwide growth of interest in rough set theory and its applications. The rough set approach has been introduced to deal with vague or imprecise concepts, to derive knowledge from data, and to reason about knowledge derived from data. In the first part of this chapter we outline the basic notions of rough sets, especially those that are related to knowledge extraction from data. Searching for knowledge is usually guided by some constraints (Langley et al., 1987). A wide class of such constraints can be expressed by discernibility of objects. Knowledge derived from data by the rough set approach consists of different constructs. Among them there are reducts, which are the central construct in the rough set approach, different kinds of rules (such as decision rules or association rules), dependencies, and patterns (templates), or classifiers. The reducts are of special importance since all other constructs can be derived from different kinds of reducts using the rough set approach. Strategies for searching reducts apply Boolean (propositional) reasoning (Brown, 1990), since the constraints (e.g., constraints related to the discernibility of objects) are expressible by propositional formulas. Moreover, using Boolean reasoning, minimal description-length data models (Mitchell, 1997; Rissanen, 1978) can be induced since they correspond to constructs of Boolean functions called prime implicants (or their approximations). The second part of this chapter includes illustrative examples of applications of this general scheme to inducing from data various forms of knowledge.

Connections between rough set theory and Dempster-Shafer theory of evidence

Abstract: In rough set theory there exists a pair of approximation operators, the upper and lower approximations, whereas in Dempster-Shafer theory of evidence there exists a dual pair of uncertainty measures, the plausibility and belief functions. It seems that there is some kind of natural connection between the two theories. The purpose of this paper is to establish the relationship between rough set theory and Dempster-Shafer theory of evidence. Various generalizations of the Dempster-Shafer belief structure and their induced uncertainty measures, the plausibility and belief functions, are first reviewed and examined. Generalizations of Pawlak approximation space and their induced approximation operators, the upper and lower approximations, are then summarized. Concepts of random rough sets, which include the mechanisms of numeric and non-numeric aspects of uncertain knowledge, are then proposed. Notions of the Dempster-Shafer theory of evidence within the framework of rough set theory are subsequently formed a...

Extension of rough set under incomplete information systems

Abstract: The classical rough set theory developed by professor Pawlak is based on complete information systems. It classifies objects using upper-approximation and lower-approximation defined on an indiscernibility relation that is a kind of equivalent relation. In order to process incomplete information systems, the classical rough set theory needs to be extended, especially, the indiscernibility relation needs to be extended to some inequivalent relation. There are several extensions for the indiscernibility relation now, such as tolerance relation, non-symmetric similarity relation, and valued tolerance relation. Unfortunately, these extensions have their own limitation. Presented in this paper is a new extension of rough set based on limited tolerance relation. The performances of these extended rough set models are also compared.

Axiomatization of utility, outranking and decision-rule preference models for multiple-criteria classification problems under partial inconsistency with the dominance principle

Abstract: Multiple-criteria classification (sorting) problem con­ cerns assignment of actions (objects) to some pre-defined and prefer­ ence-ordered decision classes. The actions are described by a finite set of criteria, i.e. attributes, with preference-ordered scales. To per­ form the classification, criteria have to be aggregated into a prefer­ ence model which can be: utility (discriminant) function, or outrank­ ing relation, or "if. .. , then ... " decision rules. Decision rules involve partial profiles on subsets of criteria and dominance relation on these profiles. A challenging problem in multiple-criteria decision making is the aggregation of criteria with ordinal scales. We show that the decision rule model we propose has advantages over a general utility function, over the integral of Sugeno, conceived for ordinal criteria, and over an outranking relation. This is shown by basic axioms characterizing these models. Moreover, we consider a more general decision rule model based on the rough set theory. The advantage of the rough set approach compared to competitive methodologies is the possibility of handling partially inconsistent data that are often encountered in preferential information, due to hesitation of decision makers, unstable character of their preferences, imprecise or incom­ plete knowledge and the like. We show that these inconsistencies can be represented in a meaningful way by "if. .. , then ... " decision rules induced from rough approximations. The theoretical results reported in this paper show that the decision rule model is the most general aggregation model among all the considered models. Keywords: multiple-criteria classification, preference modeling, decision rules, conjoint measurement, ordinal criteria, rough sets, axiomati7.ation _

Granular computing using information tables

Abstract: A simple and more concrete granular computing model may be developed using the notion of information tables. In this framework, each object in a finite nonempty universe is described by a finite set of attributes. Based on attribute values of objects, one may decompose the universe into parts called granules. Objects in each granule share the same or similar description in terms of their attribute values. Studies along this line have been carried out in the theories of rough sets and databases. Within the proposed model, this paper reviews the pertinent existing results and presents their generalizations and applications.

Learning rules from incomplete training examples by rough sets

Abstract: Machine learning can extract desired knowledge from existing training examples and ease the development bottleneck in building expert systems. Most learning approaches derive rules from complete data sets. If some attribute values are unknown in a data set, it is called incomplete. Learning from incomplete data sets is usually more difficult than learning from complete data sets. In the past, the rough-set theory was widely used in dealing with data classification problems. In this paper, we deal with the problem of producing a set of certain and possible rules from incomplete data sets based on rough sets. A new learning algorithm is proposed, which can simultaneously derive rules from incomplete data sets and estimate the missing values in the learning process. Unknown values are first assumed to be any possible values and are gradually refined according to the incomplete lower and upper approximations derived from the given training examples. The examples and the approximations then interact on each other to derive certain and possible rules and to estimate appropriate unknown values. The rules derived can then serve as knowledge concerning the incomplete data set.

On the Structure of Rough Approximations

Abstract: We study rough approximations based on indiscernibility relations which are not necessarily reflexive, symmetric or transitive. For this, we define in a lattice-theoretical setting two maps which mimic the rough approximation operators and note that this setting is suitable also for other operators based on binary relations. Properties of the ordered sets of the upper and the lower approximations of the elements of an atomic Boolean lattice are studied.

Fuzzy-rough sets for descriptive dimensionality reduction

Abstract: One of the main obstacles facing current fuzzy modelling techniques is that of dataset dimensionality. To enable these techniques to be effective, a redundancy-removing step is usually carried out beforehand. Rough set theory (RST) has been used as such a dataset pre-processor with much success, however it is reliant upon a crisp dataset; important information may be lost as a result of quantization. The paper proposes a dimensionality reduction technique that employs a hybrid variant of rough sets, fuzzy-rough sets, to avoid this information loss.