A Novel Entropy of Interval Valued Fuzzy Set

The main attribution of this paper is to propose two methods to construct entropy of interval valued fuzzy sets (IVFSs). First, we use an IVFS to construct two FSs and define entropy by similarity measure of the two FSs; then we use an IVFS to construct two IVFSs and also define entropy by similarity measure of the two IVFSs. At the same time, we give two examples to show that our methods are effective.

[1]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1972, Inf. Control..

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

[3]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU) - an outline , 2005, GrC.

[4]  Miin-Shen Yang,et al.  Fuzzy entropy on intuitionistic fuzzy sets , 2006, Int. J. Intell. Syst..

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

[6]  Weixin Xie,et al.  Distance measure and induced fuzzy entropy , 1999, Fuzzy Sets Syst..

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

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

[9]  Janusz Kacprzyk,et al.  Entropy for intuitionistic fuzzy sets , 2001, Fuzzy Sets Syst..

[10]  Changlin Mei,et al.  Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure , 2009, Knowl. Based Syst..

[11]  Hai Liu,et al.  Entropy on intuitionistic fuzzy soft sets and on interval-valued fuzzy soft sets , 2013, Inf. Sci..

[12]  Liu Xuecheng,et al.  Entropy, distance measure and similarity measure of fuzzy sets and their relations , 1992 .

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

[14]  Zeshui Xu,et al.  Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making , 2007, Fuzzy Optim. Decis. Mak..

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

[16]  Guo-Jun Wang,et al.  Intuitionistic fuzzy sets and L-fuzzy sets , 2000, Fuzzy Sets Syst..

[17]  I. Turksen Interval valued fuzzy sets based on normal forms , 1986 .

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

[19]  Wenyi Zeng,et al.  Relationship between similarity measure and entropy of interval valued fuzzy sets , 2006, Fuzzy Sets Syst..

[20]  Humberto Bustince,et al.  Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets , 2000, Int. J. Approx. Reason..

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

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

[23]  Chang Wang,et al.  Entropy, similarity measure and distance measure of vague soft sets and their relations , 2013, Inf. Sci..

[24]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[25]  Wenyi Zeng,et al.  Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship , 2008, Inf. Sci..