t-Norm based cuts of intuitionistic fuzzy sets |
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Authors: | Vladim?´ r Jani&scaron |
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Affiliation: | Department of Mathematics, Faculty of Science, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica, Slovak Republic |
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Abstract: | We consider the system of intuitionistic fuzzy sets (IF-sets) in a universe X and study the cuts of an IF-set. Suppose a left continuous triangular norm is given. The t-norm based cut (level set) of an IF-set is defined in a way that binds the membership and nonmembership functions via the triangular norm. This is an extension of usual cuts of IF-sets. We show that the system of these cuts fulfils analogical properties as usual systems of cuts. However, it is not possible to reconstruct an IF-set from the system of t-norm based cuts. |
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Keywords: | Intuitionistic fuzzy set Cut Triangular norm |
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