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http://ifigenia.org/wiki/issue:nifs/9/3/22-25
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| Title of paper:
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Some ways and means to define addition and multiplication operations between intuitionistic fuzzy sets
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| Author(s):
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| Radoslav Tzvetkov
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| Centre for Biomedical Engineering - Bulgarian Academy of Sciences, Bl. 105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria
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| rado_tzv@clbme.bas.bg
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| Presented at:
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Seventh International Conference on IFSs, Sofia, 23-24 August 2003
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| Published in:
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"Notes on Intuitionistic Fuzzy Sets", Volume 9 (2003) Number 3, pages 22-25
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| Download:
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 PDF (2204 Kb, File info)
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| Abstract:
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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.
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| References:
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- Atanassov, K., Intuitionistic Fuzzy Sets, Physica Verlag, 1999.
- Lang, S., Algebra, Mir, Moscow, 1968 (Russian translation).
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| Citations:
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