Triangular norms on product lattices

Incomparability with respect to the triangular order

“…Some sets were determined which, under some special conditions, are lattices with respect to T . For more details on t-norms on bounded lattices, we refer to [3,9,10,11,13,15,16,17,19].…”

“…In [7], an equivalence relation on the class of the t-norms on [0, 1] was defined. It was DOI: 10.14736/kyb-2016- [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] showed that the equivalence class of the weakest t-norm T D on [0, 1] contains a t-norm which was different from T D .…”

Semi-t-operators on a finite totally ordered set

“…It is pointed out that nullnorms and t-operators are equivalent since they have the same block structures in [0,1] 2 (see [11] for detail). The t-operators have the same properties that t-norms and t-conorms but without boundary conditions, i. e., the existence of any identity is not required and this condition is substituted simply by continuity on boundary.…”

S-Implications on Complete Lattices and the Interval Constructor

“…See, e.g., the works on L-fuzzy set theory [15], BL-algebras of Hájek [16] and Brouwerian lattices [29]. The notion of triangular norm (t-norm, for short) of partially ordered sets, which are more general mathematical structures than complete lattices, is considered in [8,2]. In [26,4], an extension of t-norms for bounded lattice was presented in the same sense as proposed by [8,2].…”

“…The notion of triangular norm (t-norm, for short) of partially ordered sets, which are more general mathematical structures than complete lattices, is considered in [8,2]. In [26,4], an extension of t-norms for bounded lattice was presented in the same sense as proposed by [8,2]. In [9,10] complete lattices were considered.…”