View source for Issue:Some ways and means to define addition and multiplication operations between intuitionistic fuzzy sets

[[Category:Publications on intuitionistic fuzzy sets|{{PAGENAME}}]]
[[Category:Publications in Notes on IFS|{{PAGENAME}}]]
[[Category:Publications in 2003 year|{{PAGENAME}}]]
[[Category:ICIFS conference publications|{{PAGENAME}}]]
{{issue/title
 | title           = Some ways and means to define addition and multiplication operations between intuitionistic fuzzy sets
 | shortcut        = nifs/9/3/22-25
}}
{{issue/author
 | author          = Radoslav Tzvetkov 
 | institution     = Centre for Biomedical Engineering - Bulgarian Academy of Sciences
 | address         = Bl. 105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria 
 | email-before-at = rado_tzv
 | email-after-at  = clbme.bas.bg
}}
{{issue/data
 | conference      = Seventh [[ICIFS|International Conference on IFSs]], Sofia, 23-24 August 2003
 | issue           = [[Notes on Intuitionistic Fuzzy Sets/09/3|"Notes on Intuitionistic Fuzzy Sets", Volume 9 (2003) Number 3]], pages 22-25
 | file            = NIFS-09-3-22-25.pdf
 | format          = PDF
 | size            = 2204
 | abstract        = In this paper we introduce some operations on IFS [1]. P. Burillo and H. Bustince introduced <math>T</math>- and <math>S</math>- norms as follows:

<math>P(A, B) = \{ \langle x, T(\mu_A(x), \mu_B(x)), S(\nu_A(x), \nu_B(x)) \rangle |x \in E \}</math>

where

<math>0 \le T(\mu_A(x), \mu_B(x)) + S(\nu_A(x), \nu_B(x)) \le 1</math>

We shall define:

<math>\overline{P}(A, B) = \{ \langle x, S(\mu_A(x), \mu_B(x)), T(\nu_A(x), \nu_B(x)) \rangle |x \in E \}.</math>

Therefore <math>\neg \overline{P} \equiv P</math>, where <math>\equiv</math> is the "equivalence" relation between operations. 
 | keywords        = 
 | references      = 
# Atanassov, K., [[Intuitionistic Fuzzy Sets: Theory and Applications|Intuitionistic Fuzzy Sets]], Physica Verlag, 1999.
# Lang, S., Algebra, Mir, Moscow, 1968 (Russian translation). 
 | citations       = 
 | see-also        = 
}}