Some methods to obtain t-norms and t-conorms on bounded lattices

Abstract

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An Alternative Characterization of t-norms and t-conorms On An Appropriate Bounded Lattice

“…In 2015, a modification of ordinal sums of t-norms and t-conorms resulting to a t-norms and tconorms on an arbitrary bounded lattice was shown by Ertugrul, Karaçal, Mesiar [16]. Further modifications were proposed by Çaylı [13,12], Aşıcı and Mesiar [4,5], Aşıcı [2,3], Ouyang, Zhang, Baets [22] and Dan, Hu, Qiao [14]. In 2020, a new ordinal sum construction of t-norms and t-conorms on bounded lattices based on interior and closure operators was proposed by Dvoȓák, Holcapek [15].…”

Triangular norms on bounded trellises

“…Notwithstanding the many achievements mentioned above, all situated in the comfortable setting of real analysis, it took until the 90s for the study of t-norms on more general structures to take off [12,13], in particular on partially ordered sets (posets, for short) and lattices, thus being related to the study of partially ordered semigroups [21]. Not surprisingly, research in this direction has been a lot slower, initially being focused on construction methods [1,2,7,25,28], and only recently more profound characterizations in terms of ordinal sums [16,33,34].…”

On the constructions of t-norms and t-conorms on some special classes of bounded lattices

“…In 2015, a modification of ordinal sums of t-norms and t-conorms resulting to a t-norms and t-conorms on an arbitrary bounded lattice was shown by Ertugrul, Karaçal, Mesiar [16]. Further modifications were proposed by Ç aylı [11,13], Aşıcı, Mesiar [3,4], Ouyang, Zhang, Baets [23] and Dan, Hu, Qiao [14]. In 2020, a new ordinal sum construction of t-norms and t-conorms on bounded lattices based on interior and closure operators was proposed by Dvoȓák, Holcapek [15].…”