One method for modelling uncertain or inaccurate information is rough set analysis which was introduced and studied by Pawlak (1982) and his co–workers. Unlike other methods such as fuzzy set theory, Dempster – Shafer theory or statistical methods, rough set analysis requires no external parameters and uses only the information presented in the given data. In the present study we apply rough se...

Rough set theory has been proposed by Pawlak in the early 80s to deal with inconsistency problems following from information granulation. It operates on an information table composed of a set U of objects described by a set Q of condition and decision attributes. Decision attributes make a partition of U into decision classes. Basic concepts of rough set theory are: indiscernibility relation on...

Yager’s entropy was proposed to compute the information of fuzzy indiscernibility relation. In this paper we present a novel interpretation of Yager’s entropy in discernibility power of a relation point of view. Then some basic definitions in Shannon’s information theory are generalized based on Yager’s entropy. We introduce joint entropy, conditional entropy, mutual information and relative en...

The whole mathematical scenario has changed with the advent of the Rough Set Theory, a powerful tool to deal with uncertainty and incompleteness of knowledge in information system. With the advancement of research, the Soft Set Theory has emerged as an advanced mathematical tool to deal with data associated with uncertainty. The present chapter endeavors to forge a connection between soft set a...

Attribute reduction with fuzzy rough set is an effective technique for selecting most informative attributes from a given realvalued dataset. However, existing algorithms for attribute reduction with fuzzy rough set have to re-compute a reduct from dynamic data with sample arriving where one sample or multiple samples arrive successively. This is clearly uneconomical from a computational point ...

In digital-based information boom, the fuzzy covering rough set model is an important mathematical tool for artificial intelligence, and how to build the bridge between the fuzzy covering rough set theory and Pawlak’s model is becoming a hot research topic. In this paper, we first present the γ−fuzzy covering based probabilistic and grade approximation operators and double-quantitative approxim...

Shao-Han Liu Jzau-Sheng Lin, MEMBER SPIE National Chin-Yi Institute of Technology Department of Electronic Engineering No. 35, Lane 215, Sec. 1, Chung-Shan Rd Taiping, Taichung, Taiwan E-mail: [email protected] Abstract. A new fuzzy Hopfield-model net based on rough-set reasoning is proposed for the classification of multispectral images. The main purpose is to embed a rough-set learning...

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are s...

Data used in machine learning applications is prone to contain both vague and incomplete information. Many authors have proposed to use fuzzy rough set theory in the development of new techniques tackling these characteristics. Fuzzy sets deal with vague data, while rough sets allow to model incomplete information. As such, the hybrid setting of the two paradigms is an ideal candidate tool to c...