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Intuitionistic fuzzy sets: Difference between revisions
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<math>A | <math>A = \lbrace \langle x, \mu_A(x), \nu_A(x) \rangle \ | \ x \in E \rbrace</math> | ||
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Functions <math>\mu_A: E \to [0,1]</math> and <math>\nu_A: E \to [0,1]</math> represent ''degree of [[membership]] (validity, etc.)'' and ''[[non-membership]] (non-validity, etc.)''. | Functions <math>\mu_A: E \to [0,1]</math> and <math>\nu_A: E \to [0,1]</math> represent ''degree of [[membership]] (validity, etc.)'' and ''[[non-membership]] (non-validity, etc.)''. | ||
We can define also function <math>\pi_A: E \to [0,1]</math> through | We can define also function <math>\pi_A: E \to [0,1]</math> through <math>\pi(x) = 1 - \mu (x) - \nu (x)</math> | ||
and it corresponds to ''degree of [[indeterminacy]] (uncertainty, etc.)''. | and it corresponds to ''degree of [[indeterminacy]] (uncertainty, etc.)''. | ||
Obviously, for every ordinary [[fuzzy set]] <math>A</math>: <math>\pi_A(x) = 0</math> for each <math>x \in E</math> and these sets have the form <math>\lbrace \langle x, \mu_{A}(x), 1-\mu_{A}(x)\rangle |x \in E \rbrace.</math> | Obviously, for every ordinary [[fuzzy set]] <math>A</math>: <math>\pi_A(x) = 0</math> for each <math>x \in E</math> and these sets have the form <math>\lbrace \langle x, \mu_{A}(x), 1-\mu_{A}(x)\rangle |x \in E \rbrace.</math> | ||
[[Category:Intuitionistic fuzzy sets]] | [[Category:Intuitionistic fuzzy sets]] | ||
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Revision as of 15:05, 16 October 2008
Let us have a fixed universe [math]\displaystyle{ E }[/math] and its subset [math]\displaystyle{ A }[/math]. The set
[math]\displaystyle{ A = \lbrace \langle x, \mu_A(x), \nu_A(x) \rangle \ | \ x \in E \rbrace }[/math]
where [math]\displaystyle{ 0 \leq \mu_A(x) + \nu_A(x) \leq 1 }[/math] is called intuitionistic fuzzy set.
Functions [math]\displaystyle{ \mu_A: E \to [0,1] }[/math] and [math]\displaystyle{ \nu_A: E \to [0,1] }[/math] represent degree of membership (validity, etc.) and non-membership (non-validity, etc.).
We can define also function [math]\displaystyle{ \pi_A: E \to [0,1] }[/math] through [math]\displaystyle{ \pi(x) = 1 - \mu (x) - \nu (x) }[/math] and it corresponds to degree of indeterminacy (uncertainty, etc.).
Obviously, for every ordinary fuzzy set [math]\displaystyle{ A }[/math]: [math]\displaystyle{ \pi_A(x) = 0 }[/math] for each [math]\displaystyle{ x \in E }[/math] and these sets have the form [math]\displaystyle{ \lbrace \langle x, \mu_{A}(x), 1-\mu_{A}(x)\rangle |x \in E \rbrace. }[/math]