Catálogo de publicaciones - libros

This paper focuses on a rough set method to analyze human evaluation data with much ambiguity such as sensory and feeling data. In order to handle totally ambiguous and probabilistic human evaluation data, we propose a probabilistic approximation based on information gains of equivalent classes. Furthermore, we propose a two-stage method to simply extract uncertain – rules using decision functions of approximate regions. Finally, we applied the proposed method to practical human sensory evaluation data and examined the effectiveness of the proposed method. The result shown that our proposed rough set method is more applicable to human evaluation data.

In this paper, we study variable precision rough set models based on multiple decision tables. The models can control the admissible level of classification error in each table, the ratio of supporting decision tables to all decision tables and the ratio of opposing decision tables to all decision tables. As the classical rough set model plays a key role in analysis of decision tables such as reduction, rule induction, etc., the proposed variable precision rough set models will play a key role in analysis of multiple decision tables.

A generalization of the original idea of rough sets and variable precision rough sets is introduced. This generalization is based on the concept of absolute and relative rough membership. Similarly to variable precision rough set model, the generalization called parameterized rough set model, is aimed at modeling data relationships expressed in terms of frequency distribution rather than in terms of a full inclusion relation used in the classical rough set approach. However, differently from variable precision rough set model, one or more parameters modeling the degree to which the condition attribute values confirm the decision attribute value, are considered. The properties of this extended model are investigated and compared to the classical rough set model and the variable precision rough set model.

We examine methods of valued tolerance relations where the conventional methods based on rough sets are extended in order to handle incomplete information. The methods can deal with missing values probabilistically interpreted. We propose a correctness criterion to the extension of the conventional methods. And then we check whether or not the correctness criterion is satisfied in a method of valued tolerance relations. As a result, we conclude that the method does not satisfy the correctness criterion. Therefore, we show how to revise the method of valued tolerance relations so that the correctness criterion can be satisfied.

Pawlak recently introduced (RSFGs) as a graphical framework for reasoning from data. Each rule is associated with three coefficients, which have been shown to satisfy Bayes’ theorem. Thereby, RSFGs provide a new perspective on Bayesian inference methodology.

In this paper, we show that inference in RSFGs takes polynomial time with respect to the largest domain of the variables in the decision tables. Thereby, RSFGs provide an efficient tool for uncertainty management. On the other hand, our analysis also indicates that a RSFG is a special case of conventional Bayesian network and that RSFGs make implicit assumptions regarding the problem domain.

In this paper, we study rough set approximations under fuzzy and random environments. A fuzzy set-valued mapping defines a pair of upper and lower fuzzy rough approximations. Properties of fuzzy approximation operators are examined and the crisp representations of fuzzy approximation operators are presented. A fuzzy random variable from a universe to a universe carries a probability measure defined over subsets of into a system of upper and lower probabilities over subsets of . The connections between fuzzy approximation spaces and fuzzy belief structures are also established.

This paper is concerned with describing and analyzing the control actions which are accomplished by a human operator, who controls a complex dynamic system. The decision model is expressed by means of a decision table with fuzzy attributes. Decision tables are generated by the fuzzification of crisp data, basing on a set of fuzzy linguistic values of the attributes. A T-similarity relation is chosen for comparing the elements of the universe. Fuzzy partitions of the universe with respect to condition and decision attributes are generated. The task of stabilization of the aircraft’s altitude performed by a pilot is considered as an illustrative example. The limit-based and mean-based variable precision fuzzy rough approximations are determined. The measure of -approximation quality is used for evaluating the consistency of the human operator’s decision model, and assessing the importance of particular condition attributes in the control process.

Rough set theory is developed based on the notion of equivalence relation, but the property of equivalence has limited its application fields, which may not provide a realistic description of real-world relationships between elements. The paper presents a transition from the equivalence relation to the compatibility relation, called Compatibility Rough Set Theory or, in short, CRST. A specific type of fuzzy compatibility relations, called conditional probability relations, is discussed. All basic concepts or rough set theory are extended. Generalized rough set approximations are defined by using coverings of the universe induced by a fuzzy compatibility relation. Generalized rough membership functions are defined and their properties are examined.

In this paper, to deal with practical situations where a fuzzy classification must be approximated by available knowledge expressed in terms of a Pawlak’s approximation space, we investigate an extension of approximation quality measure to a fuzzy classification aimed at providing a numerical characteristic for such situations. Furthermore, extensions of related coefficients such as the precision measure and the significance measure are also discussed. A simple example is given to illustrate the proposed notions.

A method of constructing a classifier that uses fuzzy reasoning is described in this paper. Rules for this classifier are obtained by means of algorithms relying on a tolerance rough sets model. Got rules are in so called sharp” form, a genetic algorithm is used for fuzzification of these rules. Presented results of experiments show that the proposed method allows getting a smaller rules set with similar (or better) classification abilities.