In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

Various expanded rough set models based on tolerance relations enlarge the application fields of rough set theory. Through generating tolerance relations to fuzzy tolerance relations and combining with dominance relations, a tolerance class of a fuzzy tolerance relation is further decomposed into a positive fuzzy tolerance class, a negative fuzzy tolerance class and a purely fuzzy tolerance cla...

This paper presents some highlights in the application of neural networks, fuzzy logic, genetic algorithms, and rough sets to automated knowledge acquisition. These techniques are capable of dealing with inexact and imprecise problem domains and have been demonstrated to be useful in the solution of classification problems. It addresses the issue of the application of appropriate evaluation cri...

A generalized hybrid unsupervised learning algorithm, which is termed as rough-fuzzy possibilistic c-means (RFPCM), is proposed in this paper. It comprises a judicious integration of the principles of rough and fuzzy sets. While the concept of lower and upper approximations of rough sets deals with uncertainty, vagueness, and incompleteness in class definition, the membership function of fuzzy ...

Fuzzy rough set method provides an effective approach to data mining and knowledge discovery from hybrid data including categorical values and numerical values. However, its time-consumption is very intolerable to analyze data sets with large scale and high dimensionality. Many heuristic fuzzy-rough feature selection algorithms have been developed however, quite often, these methods are still c...

Granular computing is a computational paradigm in which a granule represents a structure of patterns evolved by performing operations on the individual patterns. Two granular neural networks are described for performing the pattern analysis tasks like classification and clustering. The granular neural networks are designed by integrating fuzzy sets and fuzzy rough sets with artificial neural ne...