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

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http://ifigenia.org/wiki/issue:nifs/9/3/22-25

Title of paper: Some ways and means to define addition and multiplication operations between intuitionistic fuzzy sets Author(s): Radoslav Tzvetkov Centre for Biomedical Engineering - Bulgarian Academy of Sciences, Bl. 105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria rado_tzv@clbme.bas.bg Presented at: Seventh International Conference on IFSs, Sofia, 23-24 August 2003 Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 9 (2003) Number 3, pages 22-25 Download:  PDF (2204  Kb, File info) Abstract: In this paper we introduce some operations on IFS [1]. P. Burillo and H. Bustince introduced [math]\displaystyle{ T }[/math]- and [math]\displaystyle{ S }[/math]- norms as follows: [math]\displaystyle{ 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]\displaystyle{ 0 \le T(\mu_A(x), \mu_B(x)) + S(\nu_A(x), \nu_B(x)) \le 1 }[/math] We shall define: [math]\displaystyle{ \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]\displaystyle{ \neg \overline{P} \equiv P }[/math], where [math]\displaystyle{ \equiv }[/math] is the "equivalence" relation between operations. References: Atanassov, K., Intuitionistic Fuzzy Sets, Physica Verlag, 1999. Lang, S., Algebra, Mir, Moscow, 1968 (Russian translation). Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.