Rough sets theory for multicriteria decision analysis
TL;DR: The original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation, but is failing when preference-orders of attribute domains (criteria) are to be taken into account and it cannot handle inconsistencies following from violation of the dominance principle.
About: This article is published in European Journal of Operational Research.The article was published on 2001-02-15. It has received 1544 citations till now. The article focuses on the topics: Dominance-based rough set approach & Rough set.
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TL;DR: The basic concepts of rough set theory are presented and some rough set-based research directions and applications are pointed out, indicating that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences.
2,004 citations
TL;DR: Some extensions of the rough set approach are presented and a challenge for the roughSet based research is outlined and it is outlined that the current rough set based research paradigms are unsustainable.
1,161 citations
TL;DR: A comprehensive review of the work done, during the 1968-2005, in the application of statistical and intelligent techniques to solve the bankruptcy prediction problem faced by banks and firms is presented.
978 citations
References
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Book•
01 Jan 1976
TL;DR: This book develops an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions.
Abstract: Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental. The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions. This rule, together with the idea of "weights of evidence," leads to both an extensive new theory and a better understanding of the Bayesian theory. The book concludes with a brief treatment of statistical inference and a discussion of the limitations of epistemic probability. Appendices contain mathematical proofs, which are relatively elementary and seldom depend on mathematics more advanced that the binomial theorem.
14,565 citations
"Rough sets theory for multicriteria..." refers background in this paper
...Within Dempster±Shafer theory of evidence (Shafer, 1976), m A is interpreted as basic probability assignment....
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...Within Dempster±Shafer theory of evidence (Shafer, 1976), m A is interpreted as basic probability assignment....
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Book•
01 Jan 1976TL;DR: In this article, a confused decision maker, who wishes to make a reasonable and responsible choice among alternatives, can systematically probe his true feelings in order to make those critically important, vexing trade-offs between incommensurable objectives.
Abstract: Many of the complex problems faced by decision makers involve multiple conflicting objectives. This book describes how a confused decision maker, who wishes to make a reasonable and responsible choice among alternatives, can systematically probe his true feelings in order to make those critically important, vexing trade-offs between incommensurable objectives. The theory is illustrated by many real concrete examples taken from a host of disciplinary settings. The standard approach in decision theory or decision analysis specifies a simplified single objective like monetary return to maximise. By generalising from the single objective case to the multiple objective case, this book considerably widens the range of applicability of decision analysis.
8,895 citations
Book•
31 Oct 1991
TL;DR: Theoretical Foundations.
Abstract: I. Theoretical Foundations.- 1. Knowledge.- 1.1. Introduction.- 1.2. Knowledge and Classification.- 1.3. Knowledge Base.- 1.4. Equivalence, Generalization and Specialization of Knowledge.- Summary.- Exercises.- References.- 2. Imprecise Categories, Approximations and Rough Sets.- 2.1. Introduction.- 2.2. Rough Sets.- 2.3. Approximations of Set.- 2.4. Properties of Approximations.- 2.5. Approximations and Membership Relation.- 2.6. Numerical Characterization of Imprecision.- 2.7. Topological Characterization of Imprecision.- 2.8. Approximation of Classifications.- 2.9. Rough Equality of Sets.- 2.10. Rough Inclusion of Sets.- Summary.- Exercises.- References.- 3. Reduction of Knowledge.- 3.1. Introduction.- 3.2. Reduct and Core of Knowledge.- 3.3. Relative Reduct and Relative Core of Knowledge.- 3.4. Reduction of Categories.- 3.5. Relative Reduct and Core of Categories.- Summary.- Exercises.- References.- 4. Dependencies in Knowledge Base.- 4.1. Introduction.- 4.2. Dependency of Knowledge.- 4.3. Partial Dependency of Knowledge.- Summary.- Exercises.- References.- 5. Knowledge Representation.- 5.1. Introduction.- 5.2. Examples.- 5.3. Formal Definition.- 5.4. Significance of Attributes.- 5.5. Discernibility Matrix.- Summary.- Exercises.- References.- 6. Decision Tables.- 6.1. Introduction.- 6.2. Formal Definition and Some Properties.- 6.3. Simplification of Decision Tables.- Summary.- Exercises.- References.- 7. Reasoning about Knowledge.- 7.1. Introduction.- 7.2. Language of Decision Logic.- 7.3. Semantics of Decision Logic Language.- 7.4. Deduction in Decision Logic.- 7.5. Normal Forms.- 7.6. Decision Rules and Decision Algorithms.- 7.7. Truth and Indiscernibility.- 7.8. Dependency of Attributes.- 7.9. Reduction of Consistent Algorithms.- 7.10. Reduction of Inconsistent Algorithms.- 7.11. Reduction of Decision Rules.- 7.12. Minimization of Decision Algorithms.- Summary.- Exercises.- References.- II. Applications.- 8. Decision Making.- 8.1. Introduction.- 8.2. Optician's Decisions Table.- 8.3. Simplification of Decision Table.- 8.4. Decision Algorithm.- 8.5. The Case of Incomplete Information.- Summary.- Exercises.- References.- 9. Data Analysis.- 9.1. Introduction.- 9.2. Decision Table as Protocol of Observations.- 9.3. Derivation of Control Algorithms from Observation.- 9.4. Another Approach.- 9.5. The Case of Inconsistent Data.- Summary.- Exercises.- References.- 10. Dissimilarity Analysis.- 10.1. Introduction.- 10.2. The Middle East Situation.- 10.3. Beauty Contest.- 10.4. Pattern Recognition.- 10.5. Buying a Car.- Summary.- Exercises.- References.- 11. Switching Circuits.- 11.1. Introduction.- 11.2. Minimization of Partially Defined Switching Functions.- 11.3. Multiple-Output Switching Functions.- Summary.- Exercises.- References.- 12. Machine Learning.- 12.1. Introduction.- 12.2. Learning From Examples.- 12.3. The Case of an Imperfect Teacher.- 12.4. Inductive Learning.- Summary.- Exercises.- References.
7,826 citations
"Rough sets theory for multicriteria..." refers background in this paper
...The rough sets theory introduced by Pawlak (1982, 1991) has often proved to be an excellent mathematical tool for the analysis of a vague description of objects (called actions in decision problems)....
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TL;DR: The metric and dimensional assumptions that underlie the geometric representation of similarity are questioned on both theoretical and empirical grounds and a set of qualitative assumptions are shown to imply the contrast model, which expresses the similarity between objects as a linear combination of the measures of their common and distinctive features.
Abstract: The metric and dimensional assumptions that underlie the geometric representation of similarity are questioned on both theoretical and empirical grounds. A new set-theoretical approach to similarity is developed in which objects are represented as collections of features, and similarity is described as a feature-matching process. Specifically, a set of qualitative assumptions is shown to imply the contrast model, which expresses the similarity between objects as a linear combination of the measures of their common and distinctive features. Several predictions of the contrast model are tested in studies of similarity with both semantic and perceptual stimuli. The model is used to uncover, analyze, and explain a variety of empirical phenomena such as the role of common and distinctive features, the relations between judgments of similarity and difference, the presence of asymmetric similarities, and the effects of context on judgments of similarity. The contrast model generalizes standard representations of similarity data in terms of clusters and trees. It is also used to analyze the relations of prototypicality and family resemblance
7,251 citations
"Rough sets theory for multicriteria..." refers background in this paper
...As for the symmetry, one should notice that yRx, which means ``y is similar to x'', is directional; there is a subject y and a referent x, and in general this is not equivalent to the proposition ``x is similar to y'', as maintained by Tversky (1977)....
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18 Mar 1952
TL;DR: In this paper, an examination of elementary properties of a value for the essential case is presented, which is deduced from a set of three axioms, having simple intuitive interpretations.
Abstract: An examination of a number of elementary properties of a value for the essential case. This value is deduced from a set of three axioms, having simple intuitive interpretations.
7,208 citations
"Rough sets theory for multicriteria..." refers background in this paper
...Within game theory, the function l A is called characteristic function and represents the payo obtained by the coalition A N in a cooperative game (Shapley, 1953; Banzhaf, 1965); in a multicriteria decision problem, l A can be interpreted as the conjoint importance of the criteria from A N (Grabisch, 1994, 1996)....
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...Within game theory, the function l A is called characteristic function and represents the payo obtained by the coalition A N in a cooperative game (Shapley, 1953; Banzhaf, 1965); in a multicriteria decision problem, l A can be interpreted as the conjoint importance of the criteria from A N…...
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...The Shapley value (Shapley, 1953) for every i 2 N is de®ned by /S i X K Nÿfig nÿ jKj ÿ 1 !jKj! n! l K [ fig ÿ l K : The Banzhaf value (Banzhaf, 1965) for every i 2 N is de®ned by /B i 1 2nÿ1 X K Nÿfig l K [ fig ÿ l K : The Shapley value and the Banzhaf value can be interpreted as speci®c kinds of…...
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...The Shapley value (Shapley, 1953) for every i 2 N is de®ned by...
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