Uninorms on Bounded Lattices with Given Underlying Operations

  • Slavka Bodjanova
  • Martin KalinaEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 981)


The main goal of this paper is to construct uninorms on a bounded lattice L which are neither conjunctive nor disjunctive (i.e., are of the third type), and have a given underlying t-norm and t-conorm. Three different cases will be studied. The first one will present some (quite general) conditions under which it is possible to construct a uninorm of the third type, regardless of the type of underlying t-norm and t-conorm. Then, two different cases of idempotent uninorm will be presented. Finally, a uninorm with a given underlying t-norm and t-conorm will be presented.


Bounded lattice Idempotent uninorm t-conorm t-norm Uninorm Uninorm of the third type Uninorm which is neither conjunctive nor disjunctive 



The work of Martin Kalina has been supported from the VEGA grant agency, grant No. 2/0069/16 and 1/0006/19.


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Authors and Affiliations

  1. 1.Department of MathematicsTexas A&M University-KingsvilleKingsvilleUSA
  2. 2.Department of Mathematics, Faculty of Civil EngineeringSlovak University of Technology in BratislavaBratislavaSlovakia

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