Logical, algebraic, analytic, and probabilistic aspects of triangular norms

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Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm (2012, background): “…Einstein, Hamacher and Frank t-conorms and t-norms or others, and some of them have been applied to intuitionistic fuzzy set, which contains three functions: the membership function, the nonmembership function and the hesitancy function describing uncertainty and fuzziness more objectively.”
Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems (2016, background): “Deﬁnition 1 (Klement & Mesiar, 2005; Nguyen & Walker, 1997) Deﬁnition 2 (Klement & Mesiar, 2005; Nguyen & Walker, 1997) Deﬁnition 3 (Klement & Mesiar, 2005; Nguyen & Walker, 1997) : A t-norm function T ( x, y ) is called an Archimedean t-norm if it is continuous and T ( x, x ) < x for all x ∈ (0 ,…”
Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems (2014, unknown): “…1] → [0, 1] is called t -conorm if it satisfies the following conditions: (1) ∀𝑥 ∈ [0, 1], 𝑆(0, 𝑥) = 𝑥 ; (2) ∀𝑥, 𝑦 ∈ [0, 1], 𝑆(𝑥, 𝑦) = 𝑆(𝑦, 𝑥) ; (3) ∀𝑥, 𝑦, 𝑧 ∈ [0, 1], 𝑆(𝑥, 𝑆(𝑦, 𝑧)) = 𝑆(𝑆(𝑥, 𝑦), 𝑧) ; (4) if 𝑥 ≤ 𝑥 󸀠 , 𝑦 ≤ 𝑦 󸀠 , then 𝑆(𝑥, 𝑦) ≤ 𝑆(𝑥 󸀠 , 𝑦 󸀠 ) .”