A new insight of the distributivity for S-uninorms

Although the scholars studied the distributivity for S-uninorms, at least, the underlyinguninorm of one S-uninorm in the distributivity equations was assumed to be in Umin exceptthe distributivity for S-uninorms over t-(co)norms. In this paper, we further characterize thedistributivity for S-uninorms, where the conjunctive underlying uninorms of the S-uninormsin the distributivity equations are not fixed in Umin but arbitrary. Firstly, we discuss thedistributivity between S-uninorms. Secondly, we analyze the distributivity for S-uninormsover T-uninorms. Moreover, we obtain the distributivity for T-uninorms over S-uninorms byduality. Thirdly, we investigate the distributivity for S-uninorms over disjunctive uninorms.Because S-uninorms in those distributivity equations are arbitrary, our results are extensionsof the previous results on the distributivity for S-uninorms.

کلیدواژه ها:

Aggregation operators ، distributivity ، uninorms ، S-uninorms ، T-uninorms