A Parameter-tunable Triangular Norm with Monotonic Genes
In order to study the optimization of Zadeh operator, a definition of parameter-tunable triangular norm with monotonic genes is given.First, we defined a kind of triangular norm Fλin the general sense generated by monotone functions using elementary operations, and then a definition of triangular...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | zho |
| Published: |
Harbin University of Science and Technology Publications
2023-02-01
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| Series: | Journal of Harbin University of Science and Technology |
| Subjects: | |
| Online Access: | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2188 |
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| Summary: | In order to study the optimization of Zadeh operator, a definition of parameter-tunable triangular norm with monotonic genes is given.First, we defined a kind of triangular norm Fλin the general sense generated by monotone functions using elementary operations, and then a definition of triangular conorm Gλin the general sense is given by using duality.This type of definition unifies the optimal Zadeh operator proposed by some authors.Next, this definition is applied to generate a new pair of triangular norms. It is proved that the triangular norm and triangular conorm conditions are satisfied to verify the feasibility of the definition for constructing fuzzy operators, which gives new direction in the construction of triangular norms.Finally, we studied the variation of some operators parameter tuning and the relationship with the Zadeh operator.Fλand Gλmake the intersection and merging of fuzzy sets more reasonable, and the data usage more efficient to avoid information loss.On the basis of triangular conorm Gλ, the definition and theorem of g-λmeasure are given, which enriches the theory of fuzzy measure. |
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| ISSN: | 1007-2683 |