The theory of intuitionistic fuzzy sets based on the intuitionistic fuzzy special sets

Abstract In this paper, we build up a connection between intuitionistic fuzzy special set (IFSS) and intuitionistic fuzzy set (IFS). Firstly, by using the concept of IFSS, we present the concept of intuitionistic nested set (INS) and show that an IFS can be determined by an INS. Secondly, we introduce the concept of λ -cut sets of IFS and show that λ -cut sets of IFS have the same properties as the cut sets of Zadeh fuzzy set. Thirdly, by using the concepts of λ -cut set of IFS and INS, we build up the decomposition theorem, representation theorem and extension principle of IFS. Finally, we apply our theory to intuitionistic fuzzy algebra and obtain the concept of intuitionistic fuzzy subgroup.

[1]  Deng-Feng Li,et al.  Multiattribute decision making models and methods using intuitionistic fuzzy sets , 2005, J. Comput. Syst. Sci..

[2]  Krassimir T. Atanassov,et al.  Remark on the intuitionistic fuzzy logics , 1998, Fuzzy Sets Syst..

[3]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[4]  Young Bae Jun,et al.  On intuitionistic fuzzy sub-hyperquasigroups of hyperquasigroups , 2005, Inf. Sci..

[5]  Young Bae Jun,et al.  Intuitionistic nil radicals of intuitionistic fuzzy ideals and Euclidean intuitionistic fuzzy ideals in rings , 2007, Inf. Sci..

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

[7]  Young Bae Jun,et al.  Quotient structures of intuitionistic fuzzy finite state machines , 2007, Inf. Sci..

[8]  Huawen Liu,et al.  Multi-criteria decision-making methods based on intuitionistic fuzzy sets , 2007, Eur. J. Oper. Res..

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

[10]  Selma Özçağ,et al.  A NOTE ON CONNECTEDNESS IN INTUITIONISTIC FUZZY SPECIAL TOPOLOGICAL SPACES , 2000 .

[11]  George Gargov,et al.  Elements of intuitionistic fuzzy logic. Part I , 1998, Fuzzy Sets Syst..

[12]  Li Min.  Cut sets of intuitionistic fuzzy sets , 2007 .

[13]  Cheng-Der Fuh,et al.  Fuzzy Clustering Based On Intuitionistic Fuzzy Relations , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[14]  Josè A. Herencia.  Graded sets and points: A stratified approach to fuzzy sets and points , 1996, Fuzzy Sets Syst..

[15]  R. Saadati.  On the intuitionistic fuzzy topological spaces , 2005, math/0501149.

[16]  Dogan Çoker,et al.  An introduction to intuitionistic fuzzy topological spaces , 1997, Fuzzy Sets Syst..

[17]  Hans-Jürgen Zimmermann,et al.  Introduction to Fuzzy Sets , 1985 .

[18]  Miin-Shen Yang,et al.  On the J-divergence of intuitionistic fuzzy sets with its application to pattern recognition , 2008, Inf. Sci..

[19]  Young Bae Jun,et al.  Intuitionistic fuzzy Hv-submodules , 2006, Inf. Sci..

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

[21]  Anna Pankowska,et al.  General IF-sets with triangular norms and their applications to group decision making , 2006, Inf. Sci..

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

[23]  H. B. Mitchell.  Ranking-Intuitionistic Fuzzy Numbers , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[24]  Francisco Gallego Lupiáñez,et al.  Nets and filters in intuitionistic fuzzy topological spaces , 2006, Inf. Sci..

[25]  Zeshui Xu,et al.  Clustering algorithm for intuitionistic fuzzy sets , 2008, Inf. Sci..

[26]  Erdal Coskun.  Systems on intuitionistic fuzzy special sets and intuitionistic fuzzy special measures , 2000, Inf. Sci..