Just like rough set theory, fuzzy set theory addresses the topic of dealing with imperfect knowledge. Recent investigations have shown how both theories can be combined into a more flexible, more expressive framework for modelling and processing incomplete information in information systems. At the same time, intuitionistic fuzzy sets have been proposed as an attractive extension of fuzzy sets,...

A fuzzy rough set approach has been proposed without using any fuzzy logical connectives. By this approach, gradual decision rules are induced from a given decision table. Fuzzy-rough modus ponens and fuzzy-rough modus tollens have been formulated based on the gradual decision rules. The equivalence condition between fuzzy-rough modus ponens and fuzzy-rough modus tollens is discussed. The condi...

This paper presents an adaptive fuzzy evidential reasoning approach, for segmenting multi-modality MR brain images. A novel fuzzy evidence structure model is proposed under the assumption that each information source provides two types of evidence: probabilistic evidence and fuzzy evidence. A new information measure, called hybrid entropy, is employed for evaluating the overall uncertainty cont...

–Rough set theory is a powerful tool to extract classification rules from a database that usually is given in the form of information system in which information is expressed by attributes and their values. In this paper, we first evaluate every example data (tuple) using, not a singleton but, a fuzzy number (or, suppose the original information system is along with such fuzzy numbers), due to ...

Rough mereology allows for similarity measures (called rough inclusions) which in turn form a basis for the mechanism of granulation of knowledge. Granules of knowledge, defined as classes of satisfactorily similar objects, can be regarded as worlds in which properties of entities are evaluated. Obtained in this way granular rough mereological intensional logics reveal essential properties of r...

Since the early 1990s, many authors have studied fuzzy rough set models and their application in machine learning and data reduction. In this work, we adjust the β-precision and the ordered weighted average based fuzzy rough set models in such a way that the number of theoretical properties increases. Furthermore, we evaluate the robustness of the new models a-β-PREC and a-OWA to noisy data and...

Introducing rough sets in hesitant fuzzy set domain and using it for the various applications would open up new possibilities in rough set theory. For this purpose the notion of hesitant fuzzy relations is introduced. The foundation of equivalence hesitant fuzzy relation is laid. Definition of anti-reflexive kernel, symmetric kernel etc. is proposed and the formulae to evaluate them are derived...

This paper presents a general framework for the study of rough set approximation operators in fuzzy environment in which both constructive and axiomatic approaches are used. In constructive approach, a pair of lower and upper generalized fuzzy rough (and rough fuzzy, respectively) approximation operators is first defined. The representations of both fuzzy rough approximation operators and rough...

Multiple granulation rough set approach to ordered information systems Weihua Xu a b c , Wenxin Sun c , Xiaoyan Zhang c & Wenxiu Zhang d a School of Management, Xi'an Jiaotong University, Xi'an, 710049, P.R. China b The Key Lab of the Ministry of Education for Process Control and Efficiency Engineering, Xi'an, 710049, P.R. China c School of Mathematics and Statistics, Chongqing University of Te...