Rough-fuzzy granular approach in natural computing framework is considered. The concept of rough set theoretic knowledge encoding and the role f-granulation for its improvement are addressed. Some examples of their judicious integration for tasks like case generation, classification/ clustering, feature selection and information measures are described explaining the nature, roles and characteri...

Different components of soft computing (e.g., fuzzy logic, artificial neural networks, rough sets and genetic algorithms) and machine intelligence, and their relevance to pattern recognition and data mining are explained. Characteristic features of these tools are described conceptually. Various ways of integrating these tools for application specific merits are described. Tasks like case (prot...

In this paper, we discuss rough inclusions defined in Rough Mereology – a paradigm for approximate reasoning introduced by Polkowski and Skowron – as a basis for common models for rough as well as fuzzy set theories. We justify the point of view that tolerance (or, similarity) is the motif common to both theories. To this end, we demonstrate in Sect. 6 that rough inclusions (which represent a h...

Structure of Rough Approximations Based on Molecular Lattices p. 69 Rough Approximations under Level Fuzzy Sets p. 78 Fuzzy-Rough Modus Ponens and Modus Tollens as a Basis for Approximate Reasoning p. 84 Logic and Rough Sets Rough Truth, Consequence, Consistency and Belief Revision p. 95 A Note on Ziarko's Variable Precision Rough Set Model and Nonmonotonic Reasoning p. 103 Fuzzy Reasoning Base...

Dominance-based Rough Set Approach (DRSA) was introduced as a generalization of the rough set approach for reasoning about preferences. While data describing preferences are ordinal by the nature of decision problems they concern, the ordering of data is also important in many other problems of data analysis. Even when the ordering seems irrelevant, the presence or the absence of a property (po...

Pawlak’s Rough set theory was originally proposed as a general mathematical tool for dealing with uncertainty in modeling imperfect knowledge. The purpose of this paper is to introduce the concept of multifuzzy rough sets by combining the multi-fuzzy set and rough set models. Some operations such as Complement, Union, Intersection etc. are defined for multi-fuzzy rough sets and De Morgan’s laws...

fuzzy rough n-ary subhypergroups are introduced and characterized.

A granular neural network for identifying salient features of data, based on the concepts of fuzzy set and a newly defined fuzzy rough set, is proposed. The formation of the network mainly involves an input vector, initial connection weights and a target value. Each feature of the data is normalized between 0 and 1 and used to develop granulation structures by a user defined α-value. The input ...

Recently, the rough set and fuzzy set theory have generated a great deal of interest among more and more researchers. Granular computing (GrC) is an emerging computing paradigm of information processing and an approach for knowledge representation and data mining. The purpose of granular computing is to seek for an approximation scheme which can effectively solve a complex problem at a certain ...