On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators

This paper presents a general framework for the study of relation-based (I,T)-intuitionistic fuzzy rough sets by using constructive and axiomatic approaches. In the constructive approach, by employing an intuitionistic fuzzy implicator I and an intuitionistic fuzzy triangle norm T, lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined. Properties of (I,T)-intuitionistic fuzzy rough approximation operators are examined. The connections between special types of intuitionistic fuzzy relations and properties of intuitionistic fuzzy approximation operators are established. In the axiomatic approach, an operator-oriented characterization of (I,T)-intuitionistic fuzzy rough sets is proposed. Different axiom sets characterizing the essential properties of intuitionistic fuzzy approximation operators associated with various intuitionistic fuzzy relations are explored.

[1]  Zeshui Xu,et al.  Intuitionistic preference relations and their application in group decision making , 2007, Inf. Sci..

[2]  Chris Cornelis,et al.  Classification Of Intuitionistic Fuzzy Implicators: An Algebraic Approach , 2002, JCIS.

[3]  Zun-Quan Xia,et al.  Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets , 2007, J. Comput. Syst. Sci..

[4]  Wei-Zhi Wu,et al.  Generalized fuzzy rough sets , 2003, Inf. Sci..

[5]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

[6]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[7]  Yee Leung,et al.  On characterizations of (I, J)-fuzzy rough approximation operators , 2005, Fuzzy Sets Syst..

[8]  Nehad N. Morsi,et al.  Axiomatics for fuzzy rough sets , 1998, Fuzzy Sets Syst..

[9]  Xiao-Ping Yang,et al.  Minimization of axiom sets on fuzzy approximation operators , 2007, Inf. Sci..

[10]  Xizhao Wang,et al.  On the generalization of fuzzy rough sets , 2005, IEEE Transactions on Fuzzy Systems.

[11]  Lei Zhou,et al.  On generalized intuitionistic fuzzy rough approximation operators , 2008, Inf. Sci..

[12]  Yee Leung,et al.  Generalized fuzzy rough sets determined by a triangular norm , 2008, Inf. Sci..

[13]  Yiyu Yao,et al.  Relational Interpretations of Neigborhood Operators and Rough Set Approximation Operators , 1998, Inf. Sci..

[14]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

[15]  Anna Maria Radzikowska,et al.  A comparative study of fuzzy rough sets , 2002, Fuzzy Sets Syst..

[16]  Yee Leung,et al.  An uncertainty measure in partition-based fuzzy rough sets , 2005, Int. J. Gen. Syst..

[17]  Degang Chen,et al.  Fuzzy rough set theory for the interval-valued fuzzy information systems , 2008, Inf. Sci..

[18]  Fei-Yue Wang,et al.  Reduction and axiomization of covering generalized rough sets , 2003, Inf. Sci..

[19]  Anna Maria Radzikowska,et al.  Rough Approximation Operations Based on IF Sets , 2006, ICAISC.

[20]  Tong-Jun Li,et al.  The minimization of axiom sets characterizing generalized approximation operators , 2006, Inf. Sci..

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

[22]  Danish Nadeem,et al.  Rough Intuitionistic Fuzzy Sets , 2002, JCIS.

[23]  Tsau Young Lin,et al.  Rough Approximate Operators: Axiomatic Rough Set Theory , 1993, RSKD.

[24]  Helmut Thiele,et al.  On Axiomatic Characterizations of Fuzzy Approximation Operators , 2000, Rough Sets and Current Trends in Computing.

[25]  Degang Chen,et al.  Fuzzy rough set theory for the interval-valued fuzzy information systems , 2008, Inf. Sci..

[26]  H. Thiele.  On axiomatic characterizations of fuzzy approximation operators. I. The fuzzy rough set based case , 2001 .

[27]  Helmut Thiele,et al.  On axiomatic characterization of fuzzy approximation operators. II. The rough fuzzy set based case , 2001, Proceedings 31st IEEE International Symposium on Multiple-Valued Logic.

[28]  Chris Cornelis,et al.  On the representation of intuitionistic fuzzy t-norms and t-conorms , 2004, IEEE Transactions on Fuzzy Systems.

[29]  Wen-Xiu Zhang,et al.  Rough fuzzy approximations on two universes of discourse , 2008, Inf. Sci..

[30]  Qinghua Hu,et al.  Information-preserving hybrid data reduction based on fuzzy-rough techniques , 2006, Pattern Recognit. Lett..

[31]  Helmut Thiele,et al.  On axiomatic characterisations of crisp approximation operators , 2000, Inf. Sci..

[32]  Chris Cornelis,et al.  Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge , 2003 .

[33]  C. J. V. Rijsbergen,et al.  Rough Sets, Fuzzy Sets and Knowledge Discovery , 1994, Workshops in Computing.

[34]  S. Nanda,et al.  Fuzzy rough sets , 1992 .

[35]  Wei-Zhi Wu,et al.  Constructive and axiomatic approaches of fuzzy approximation operators , 2004, Inf. Sci..

[36]  Ioannis K. Vlachos,et al.  Intuitionistic fuzzy information - Applications to pattern recognition , 2007, Pattern Recognit. Lett..

[37]  Xizhao Wang,et al.  Learning fuzzy rules from fuzzy samples based on rough set technique , 2007, Inf. Sci..

[38]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[39]  Chris Cornelis,et al.  INTUITIONISTIC FUZZY CONNECTIVES REVISITED , 2002 .

[40]  Chris Cornelis,et al.  Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application , 2004, Int. J. Approx. Reason..

[41]  Qinghua Hu,et al.  Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation , 2007, Pattern Recognit..

[42]  Dogan Çoker,et al.  Fuzzy rough sets are intuitionistic L-fuzzy sets , 1998, Fuzzy Sets Syst..

[43]  Yiyu Yao,et al.  Constructive and Algebraic Methods of the Theory of Rough Sets , 1998, Inf. Sci..

[44]  Didier Dubois,et al.  Terminological difficulties in fuzzy set theory - The case of "Intuitionistic Fuzzy Sets" , 2005, Fuzzy Sets Syst..

[45]  Yiyu Yao,et al.  Generalization of Rough Sets using Modal Logics , 1996, Intell. Autom. Soft Comput..

[46]  Wen-Xiu Zhang,et al.  An axiomatic characterization of a fuzzy generalization of rough sets , 2004, Inf. Sci..

[47]  Andrzej Skowron,et al.  Rough sets: Some extensions , 2007, Inf. Sci..

[48]  Philippe Smets,et al.  Implication in fuzzy logic , 1987, Int. J. Approx. Reason..

[49]  Gianpiero Cattaneo,et al.  Basic intuitionistic principles in fuzzy set theories and its extensions (A terminological debate on Atanassov IFS) , 2006, Fuzzy Sets Syst..

[50]  Etienne E. Kerre,et al.  On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision , 2007, Inf. Sci..

[51]  Humberto Bustince,et al.  Structures on intuitionistic fuzzy relations , 1996, Fuzzy Sets Syst..

[52]  Yiyu Yao,et al.  Two views of the theory of rough sets in finite universes , 1996, Int. J. Approx. Reason..

[53]  Yee Leung,et al.  On Generalized Rough Fuzzy Approximation Operators , 2006, Trans. Rough Sets.

[54]  Krassimir T. Atanassov,et al.  Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade's paper "Terminological difficulties in fuzzy set theory - the case of "Intuitionistic Fuzzy Sets" , 2005, Fuzzy Sets Syst..

[55]  R. Lowen,et al.  On the fundamentals of fuzzy sets. , 1984 .

[56]  Wei-Zhi Wu,et al.  Neighborhood operator systems and approximations , 2002, Inf. Sci..

[57]  Qiang Shen,et al.  Fuzzy-Rough Sets Assisted Attribute Selection , 2007, IEEE Transactions on Fuzzy Systems.