Fuzzy rough set theory for the interval-valued fuzzy information systems

Sun, Baiqing; Gong, Zengtai; Chen, Degang

doi:10.1016/j.ins.2008.03.001

Cited by 132 publications

(64 citation statements)

References 23 publications

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“…Sun et al [32] considered attribute reduction in interval-valued fuzzy information tables. The results may be applied to attribute reduction in interval-set-valued information tables.…”

Section: Studies Related To Interval Setsmentioning

confidence: 99%

Interval sets and interval-set algebras

Yao

2009

2009 8th IEEE International Conference on Cognitive Informatics

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An interval set is an interval in the power set lattice based on a universal set and is a family of subsets of the universal set. Interval sets and interval-set algebras provide a tool for modeling and processing partially known concepts and for approximating undefinable or complex concepts. Existing results on interval sets and interval-set algebras are reviewed and new results are given. Two types of interval-set algebras are examined based on an inclusion ordering and a knowledge ordering, respectively. Related studies are summarized.

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“…Sun et al [32] considered attribute reduction in interval-valued fuzzy information tables. The results may be applied to attribute reduction in interval-set-valued information tables.…”

Section: Studies Related To Interval Setsmentioning

confidence: 99%

Interval sets and interval-set algebras

Yao

2009

2009 8th IEEE International Conference on Cognitive Informatics

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“…Recently, rough set approximations have also been developed into fuzzy environment where the results are called rough fuzzy sets (Dubois and Prade 1990;Li and Zhang 2008;Thiele 2001;Wu et al 2006) and fuzzy rough sets (Dubois and Prade 1990;Radzikowska and Kerre 2002;Yeung et al 2005;Wu et al 2005Wu et al , 2003Wu and Zhang 2004;Tiwari et al 2013;Zhang et al 2009). Moreover, by combining rough set theory with the other uncertainty theory, such as intuitionistic fuzzy set theory, interval-valued fuzzy set theory, hesitant fuzzy set theory and interval-valued hesitant fuzzy set theory, lots of researchers proposed many new rough sets model (Cornelis et al 2003;Chakrabarty et al 1998;Nanda and Majumda 1992;Jena and Ghosh 2002;Rizvi et al 2002;Samanta and Mondal 2001;Zhang et al 2009Zhang et al , 2012Zhang et al , 2014Zhang et al , 2015Wu 2008, 2009;Sun et al 2008;Zhang et al 2012;Zhang 2012aZhang , b, 2013Yang et al 2014). Up to now, many of researches about rough sets are mainly focusing on the same universe.…”

Section: Introductionmentioning

confidence: 99%

Hesitant fuzzy rough set over two universes and its application in decision making

2015

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In this paper, we propose a general decisionmaking framework based on the HF rough set model over two universes. By a constructive approach, the HF rough set model over two universes is first presented and some properties of this model are further discussed. The union, the intersection and the composition of hesitant fuzzy approximation spaces are proposed, and some properties are also investigated. We then give a new approach of decision making in uncertainty environment using the hesitant fuzzy rough sets over two universes. Finally, two practical applications are provided to illustrate the validity of this approach.

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“…In order to establish applicable mathematical structures for these problems, covering-based rough sets are combined with some other theories and methods, such as fuzzy sets [7,27], topology [25,40] and lattice theory [6]. These interesting investigations not only enrich covering-based rough set theory, but also make it more adaptive to real-world applications.…”

Section: Introductionmentioning

confidence: 99%

Four matroidal structures of covering and their relationships with rough sets

Wang

Zhu

et al. 2013

International Journal of Approximate Reasoning

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Covering is a common form of data representation, and covering-based rough sets serve as an efficient technique to process this type of data. However, many important problems such as covering reduction in covering-based rough sets are NP-hard so that most algorithms to solve them are greedy. Matroids provide well-established platforms for greedy algorithm foundation and implementation. Therefore, it is necessary to integrate covering-based rough set with matroid. In this paper, we propose four matroidal structures of coverings and establish their relationships with rough sets. First, four different viewpoints are presented to construct these four matroidal structures of coverings, including 1-rank matroids, bigraphs, upper approximation numbers and transversals. The respective advantages of these four matroidal structures to rough sets are explored. Second, the connections among these four matroidal structures are studied. It is interesting to find that they coincide with each other. Third, a converse view is provided to induce a covering by a matroid. We study the relationship between this induction and the one from a covering to a matroid. Finally, some important concepts of covering-based rough sets, such as approximation operators, are equivalently formulated by these matroidal structures. These interesting results demonstrate the potential to combine covering-based rough sets with matroids.

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Fuzzy rough set theory for the interval-valued fuzzy information systems

Cited by 132 publications

References 23 publications

Interval sets and interval-set algebras

Interval sets and interval-set algebras

Hesitant fuzzy rough set over two universes and its application in decision making

Four matroidal structures of covering and their relationships with rough sets

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