On the Structure of Special Classes of Uninorms

0396682 - ÚI 2015 RIV NL eng J - Journal Article
Petrík, Milan - Mesiar, R.
On the Structure of Special Classes of Uninorms.
Fuzzy Sets and Systems. Roč. 240, 1 April (2014), s. 22-38. ISSN 0165-0114. E-ISSN 1872-6801
R&D Projects: GA ČR GPP201/12/P055
Grant - others:GA MŠk(CZ) EE2.3.20.0051; GA MŠk(CZ) ED1.1.00/02.0070
Program: ED
Institutional support: RVO:67985807
Keywords : associativity * contour * level set * Reidemeister closure condition * uninorm * web geometry
Subject RIV: BA - General Mathematics
Impact factor: 1.986, year: 2014

In this paper, the concept of the Reidemeister closure condition is adopted in order to characterize associativity of uninorms with a special attention paid to the class of representable uninorms. Thus, conditions replacing the associativity requirement for such uninorms are given. Further, the attention if focused on the uninorms where the underlying t-norm and t-conorm is idempotent or induce an involutive negator. Based on the aforementioned results, the structure of these classes of uninorms is fully described.
Permanent Link: http://hdl.handle.net/11104/0224409