Showing papers by "Zdzisław Pawlak published in 2001"

Drawing conclusions from data—The rough set way

Abstract: In the rough set theory with every decision rule two conditional probabilities, called certainty and coverage factors, are associated. These two factors are closely related with the lower and the upper approximation of a set, basic notions of rough set theory. It is shown that these two factors satisfy the Bayes' theorem. The Bayes' theorem in our case simply shows some relationship in the data, without referring to prior and posterior probabilities intrinsically associated with Bayesian inference in our case and can be used to inverse decision rules, i.e., to find reasons (explanation) for decisions.

Rough Sets and their Applications

Abstract: The paper discusses basic concepts of rough set theory. Starting point of the theory are data tables which are used to define rudiments of the theory: approximations, dependency and reduction of attributes, decision rules and others. Various applications of the theory are outlined and future problems pointed out.

New look on Bayes' theorem The rough set outlook

Abstract: W: G. Hirano, M. Inuiguchi, and S. Tsumoto, editors, Proceedings of International Workshop on Rough Set Theory and Granular Computing (RSTGC 2001), Matshue, Shimane, Japan, 2001, pages 1-8, 2001. (see also Bayes' Theorem Revisited -The Rough Set View, in: T. Terano, T. Nishida, A. Namatame, S. Tsumoto, Y. Ohsawa, T., Washio (eds.) New Frontiers in Artificial Intelligence, Joint JSAI 2001 Workshop Post-Proceedings, LNAI 2253, Springer 2001, 240-250)

Rough Measures and Integrals: A Brief Introduction

Abstract: This paper introduces a measure defined in the context of rough sets. Rough set theory provides a variety of set functions that can be studied relative to various measure spaces. In particular, the rough membership function is considered. The particular rough membership function given in this paper is a non-negative set function that is additive. It is an example of a rough measure. The idea of a rough integral is revisited in the context of the discrete Choquet integral that is defined relative to a rough measure. This rough integral computes a form of ordered, weighted "average" of the values of a measurable function. Rough integrals are useful in culling from a collection of active sensors those sensors with the greatest relevance in a problem-solving effort such as classification of a "perceived" phenomenon in the environment of an agent.

Bayes' Theorem Revised - The Rough Set View

Abstract: Rough set theory offers new insight into Bayes' theorem. The look on Bayes' theorem offered by rough set theory is completely different from that used in the Bayesian data analysis philosophy. It does not refer either to prior or posterior probabilities, inherently associated with Bayesian reasoning, but it reveals some probabilistic structure of the data being analyzed. It states that any data set (decision table) satisfies total probability theorem and Bayes' theorem. This property can be used directly to draw conclusions from data without referring to prior knowledge and its revision if new evidence is available. Thus in the presented approach the only source of knowledge is the data and there is no need to assume that there is any prior knowledge besides the data. We simply look what the data are telling us. Consequently we do not refer to any prior knowledge which is updated after receiving some data.

Combining Rough Sets and Bayes' Rule

Abstract: In rough set theory with every decision rule two conditional probabilities, called certainty and coverage factors, are associated. These two factors are closely related with the lower and the upper approximation of a set, basic notions of rough set theory. It is shown that these two factors satisfy the Bayes' rule. The Bayes' rule in our case simply shows some relationship in the data, without referring to prior and posterior probabilities intrinsically associated with Bayesian inference. This relationship can be used to “invert” decision rules, i.e., to find reasons (explanation) for decisions thus providing inductive as well as deductive inference in our scheme.

Data analysis The rough set perspective

Abstract: Rough set theory is a new mathematical approach to vagueness and uncertainty The theory has found many interesting applications and can be viewed as a new methodology of data analysis. In this paper basic concepts of rough set theory will be defined and the methodology of applications briefly discussed. A tutorial illustrative example will be used to make the introduced notions more intuitive.

49. Rough Measures and Integrals: A Brief

Abstract: This paper introduces a measure defined in the context of rough sets. Rough set theory provides a variety of set functions that can be studied relative to various measure spaces. In particular, the rough membership function is considered. The particular rough membership function given in this paper is a non-negative set function that is additive. It is an example of a rough measure. The idea of a rough integral is revisited in the context of the discrete Choquet integral that is defined relative to a rough measure. This rough integral computes a form of ordered, weighted ”average” of the values of a measurable function. Rough integrals are useful in culling from a collection of active sensors those sensors with the greatest relevance in a problem-solving effort such as classification of a ”perceived” phenomenon in the environment of an agent.