Abstract

This paper is mainly devoted to solving the functional equations of modularity of special class of aggregation operators with 2-neutral elements. Our investigations are motivated by modular logical connectives and their generalizations used in fuzzy set theory e.g. triangular norms, conorms, uninorms and nullnorms. In this work the modularity of two binary operations from the family of 2-uninorms (\(\textbf{U}_{k(e,f)}\)) which generalizes both uninorms and nullnorms is considered. In particular, all of the possible solutions for one of the three classes of these operations depending on the position of its absorbing and neutral elements are characterized.KeywordsTriangular normTriangular conormNullnormUninormModularity equation2-uninorm

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