Showing papers by "Zdzisław Pawlak published in 2003"

Flow graphs and decision algorithms

Abstract: In this paper we introduce a new kind of flow networks, called flow graphs, different to that proposed by Ford and Fulkerson. Flow graphs are meant to be used as a mathematical tool to analysis of information flow in decision algorithms, in contrast to material flow optimization considered in classical flow network analysis. In the proposed approach branches of the flow graph are interpreted as decision rules, while the whole flow graph can be understood as a representation of decision algorithm. The information flow in flow graphs is governed by Bayes' rule, however, in our case, the rule does not have probabilistic meaning and is entirely deterministic. It describes simply information flow distribution in flow graphs. This property can be used to draw conclusions from data, without referring to its probabilistic structure.

A rough set view on Bayes' theorem

Abstract: Rough set theory offers new perspective on Bayes' theorem. The look on Bayes' theorem offered by rough set theory reveals that any data set (decision table) satisfies the total probability theorem and Bayes' theorem. These properties can be used directly to draw conclusions from objective data without referring to subjective prior knowledge and its revision if new evidence is available. Thus, the rough set view on Bayes' theorem is rather objective in contrast to subjective “classical” interpretation of the theorem. © 2003 Wiley Periodicals, Inc.

Decision algorithms and flow graphs: A rough set approach

Abstract: This paper concerns some relationship between Bayes’ theorem and rough sets. It is revealed that any decision algorithm satisfies Bayes’ theorem, without referring to either prior or posterior probabilities inherently associated with classical Bayesian methodology. This leads to a new simple form of this theorem, which results in new algorithms and applications. Besides, it is shown that with every decision algorithm a flow graph can be associated. Bayes’ theorem can be viewed as a flow conservation rule of information flow in the graph. Moreover, to every flow graph the Euclidean space can be assigned. Points of the space represent decisions specified by the decision algorithm, and distance between points depicts distance between decisions in the decision algorithm.

Rough Measures, Rough Integrals and Sensor Fusion

Abstract: This paper introduces a family of discrete rough integrals defined relative to rough measures. Rough set theory yields a rough measure based on a recently discovered rough membership set function. The particular form of 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 classical rough integral introduced by Z. Pawlak is revisited in the context of rough measure spaces. The family of rough integrals presented in this paper 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 problemsolving effort such as classification of a perceived phenomenon in the environment of an agent. By way of practical application, an approach to fusion of homogeneous sensors is considered. The form of sensor fusion considered in this paper consists in selecting only those sensors considered relevant in solving a problem.

Decision Algorithms, Bayes’ Theorem and Flow Graphs

Abstract: The paper concerns some relationships between decision algorithms, Bayes’ theorem and flow graphs. It is shown it this paper that every decision algorithm reveals probabilistic properties, particularly it satisfies the total probability theorem and Bayes’ theorem. This leads to a new look on Bayesian inference methodology, showing that Bayes’ theorem can be used to reason directly from data without referring to prior and posterior probabilities, inherently associated with Bayesian inference. Besides, a new form of Bayes’ theorem is introduced, based on the strength of decision rules, which simplifies essentially computations. Moreover it is shown that decision algorithms can be depicted in a form of a flow graph in which flow is ruled by the total probability theorem and Bayes’ theorem. This leads to a new class of flow networks, unlike to those introduced by Ford and Fulkerson. Interpretation of flow graphs as a kind of neural network is briefly discussed.

Decision Rules and Dependencies

Abstract: We proposed in this paper to use some ideas of Jan Lukasiewicz, concerning independence of logical formulas, to study dependencies in databases.

Bayes’ Theorem — the Rough Set Perspective

Abstract: Rough set theory offers new insight into Bayes’ theorem. It does not refer either to prior or posterior probabilities, inherently associated with Bayesian reasoning, but reveals some probabilistic structure of the data being analyzed. This property can be used directly to draw conclusions from data.