AGOP 2019: New Trends in Aggregation Theory pp 106-114

# The Relation Between F-partial Order and Distributivity Equation

• Emel Aşıcı
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 981)

## Abstract

The notations of the order induced by triangular norms, nullnorms and uninorms have been studied widely. Nullnorms have been produced from triangular norms and triangular conorms with a zero element in the interior of the unit interval. They have been proved to be useful in several fields like expert systems, neural networks, fuzzy quantifiers. Also, the distributivity equation has been studied involving different classes of aggregation functions from triangular norms and triangular conorms to nullnorms. So, the study of the distributive property becomes very interesting, since nullnorms have been used several fields. In this paper we investigate distributivity equation for nullnorms on the unit interval [0, 1] and we give sufficient condition for two nullnorms to be equivalent.

## Notes

### Acknowledgement

Second author was supported of grants VEGA 1/0006/19.

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