A Functional Equation Stemming from a Characterization of Power-based Implications | IEEE Conference Publication | IEEE Xplore

A Functional Equation Stemming from a Characterization of Power-based Implications


Abstract:

The so-called family of T-power based implications has been introduced recently by using Zadeh's quantifiers modelled by powers of t-norms in its definition. Most of thes...Show More

Abstract:

The so-called family of T-power based implications has been introduced recently by using Zadeh's quantifiers modelled by powers of t-norms in its definition. Most of these operators satisfy the invariance with respect to powers of a continuous t-norm, an important property in approximate reasoning. When this family of fuzzy implication functions was characterized, the property I(x, y) · I(y, z) = I(x, z) in a concrete sub-domain played a key role. This property, which ensures that T-power based implications are unidimensional T'-preorders with T' the product t-norm, seems to be related to the invariance property. Therefore, the natural question of characterizing some classes of fuzzy implications with this property arises naturally. We provide such a characterization in a fairly general setting, generalizing earlier known results.
Date of Conference: 23-26 June 2019
Date Added to IEEE Xplore: 11 October 2019
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Conference Location: New Orleans, LA, USA

References

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