Remarks on the Subtraction and Division Operations over Intuitionistic Fuzzy Sets and Interval-Valued Fuzzy Sets

Atanassov (Fuzzy Sets and Systems 20 (1986) 87-96) defined basic operations over the intuitionistic fuzzy sets. Here we shall introduce two operations, subtraction and division, derived from the deconvolution for equations using addition and multiplication operations, respectively. In addition, we shall give some conditions to examine the correctness regarding the defined operations. The remarks in this paper can be immediately expressed in terms of interval-valued fuzzy sets.

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

[2]  Wenyi Zeng,et al.  Note on "Some operations on intuitionistic fuzzy sets" [Fuzzy Sets and Systems 114 (2000) 477], , 2006, Fuzzy Sets Syst..

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

[4]  Ranjit Biswas,et al.  Some operations on intuitionistic fuzzy sets , 2000, Fuzzy Sets Syst..

[5]  Humberto Bustince,et al.  Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets , 1996, Fuzzy Sets Syst..

[6]  K. Atanassov New operations defined over the intuitionistic fuzzy sets , 1994 .

[7]  K. Atanassov More on intuitionistic fuzzy sets , 1989 .

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

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

[10]  Krassimir T. Atanassov,et al.  Remark on Two Operations over Intuitionistic Fuzzy Sets , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[11]  Chuntian Cheng,et al.  On properties of four IFS operators , 2005, Fuzzy Sets Syst..

[12]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

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