Entropy on Interval-Valued Intuitionistic Fuzzy Soft Set

In this paper, the concept of soft entropy is firstly proposed to measure the intrinsic uncertainty of a soft set. For interval-valued intuitionistic fuzzy soft sets, axiomatical definitions of intuitionistic entropy, fuzzy entropy and soft entropy are proposed. The corresponding calculate formulae are given respectively. Different types of uncertainties estimated by different information entropies are discussed.

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

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

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

[4]  K. Atanassov Operators over interval valued intuitionistic fuzzy sets , 1994 .

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

[6]  Tsau Young Lin,et al.  Combination of interval-valued fuzzy set and soft set , 2009, Comput. Math. Appl..

[7]  Pabitra Kumar Maji,et al.  More on Intuitionistic Fuzzy Soft Sets , 2009, RSFDGrC.

[8]  Xiu-Gang Shang,et al.  A note on fuzzy information measures , 1997, Pattern Recognit. Lett..

[9]  Guoyin Wang,et al.  Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing , 2013, Lecture Notes in Computer Science.

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

[11]  Hai Liu,et al.  Interval-valued intuitionistic fuzzy soft sets and their properties , 2010, Comput. Math. Appl..

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

[13]  L. Zadeh Probability measures of Fuzzy events , 1968 .

[14]  D. Molodtsov Soft set theory—First results , 1999 .

[15]  Nikhil R. Pal,et al.  Some new information measures for fuzzy sets , 1993, Inf. Sci..

[16]  A. R. Roy,et al.  A fuzzy soft set theoretic approach to decision making problems , 2007 .

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

[18]  Bart Kosko,et al.  Addition as fuzzy mutual entropy , 1993, Inf. Sci..

[19]  R. Yager ON THE MEASURE OF FUZZINESS AND NEGATION Part I: Membership in the Unit Interval , 1979 .

[20]  Athar Kharal,et al.  On Fuzzy Soft Sets , 2009, Adv. Fuzzy Syst..

[21]  Lei Ying-jie A technique for constructing intuitionistic fuzzy entropy , 2007 .

[22]  Shengyi Jiang,et al.  Some information measures for interval-valued intuitionistic fuzzy sets , 2010, Inf. Sci..

[23]  Pei Wang,et al.  Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications , 2011, Inf. Sci..

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