Publication details
Web-geometric view on uninorms
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Proceedings |
| Conference | FSTA 2012: Eleventh International Conference on Fuzzy Set Theory and Applications |
| Citation | |
| Description | The aim of this contribution is the study of a geometric look on uninorms leading to a characterization of uninorms in some special classes. We believe that our results will contribute to better understanding of uninorms and support their wider aplication in several areas, such as many-valued logics or multicriteria-decision making on bipolar scales. Inspired by the previous results, we intend to find a relation between associativity of uninorms and geometry of their level sets. As in the previous case, this task is done by adopting the concepts of web geometry which is a branch of differential geometry introduced in the first half of the twentieth century and which has offered intuitive visual tools to characterize algebraic properties of loops. These tools are called closure conditions; the one that is of our particular interest is the Reidemeister closure condition which characterizes the associative loops (i.e. groups). We modify the {Reidemeister closure condition}, stating some additional constraints, so that it describes associativity of uninorms in a similarly transparent manner. Two results are introduced, particularly, for general uninorms and for representable uninorms. |
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