Rough Set Based Uncertain Knowledge Expressing and Processing

Uncertainty exists almost everywhere. In the past decades, many studies about randomness and fuzziness were developed. Many theories and models for expressing and processing uncertain knowledge, such as probability & statistics, fuzzy set, rough set, interval analysis, cloud model, grey system, set pair analysis, extenics, etc., have been proposed. In this paper, these theories are discussed. Their key idea and basic notions are introduced and their difference and relationship are analyzed. Rough set theory, which expresses and processes uncertain knowledge with certain methods, is discussed in detail.

[1]  J. Goguen L-fuzzy sets , 1967 .

[2]  Dorota Kuchta,et al.  Further remarks on the relation between rough and fuzzy sets , 1992 .

[3]  E. Kerre A First View on the Alternatives of Fuzzy Set Theory. , 2001 .

[4]  Humberto Bustince,et al.  Vague sets are intuitionistic fuzzy sets , 1996, Fuzzy Sets Syst..

[5]  Sun Hong-an On Operations of the Extension Set , 2007 .

[6]  Jerry M. Mendel,et al.  Type-2 fuzzy logic systems , 1999, IEEE Trans. Fuzzy Syst..

[7]  Qiang Wu,et al.  Real formal concept analysis based on grey-rough set theory , 2009, Knowl. Based Syst..

[8]  Etienne E. Kerre,et al.  On the relationship between some extensions of fuzzy set theory , 2003, Fuzzy Sets Syst..

[9]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[10]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[11]  W.-L. Gau,et al.  Vague sets , 1993, IEEE Trans. Syst. Man Cybern..

[12]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[13]  Yang Chun New Definition of Extension Set , 2001 .

[14]  M. Zettler,et al.  Robustness analysis of polynomials with polynomial parameter dependency using Bernstein expansion , 1998, IEEE Trans. Autom. Control..

[15]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[16]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[17]  Z. Pawlak Rough sets and fuzzy sets , 1985 .