Novel survival functions based on conditional aggregation operators

Choquet-Sugeno-like operator based on relation and conditional aggregation operators

“…All of this has been possible thanks to the conditional aggregation operator defined in [2] and the dependence relation between conditional sets proposed in the present paper. The relation can generate different aggregation styles in decision making and can be used in as diverse areas as graph theory, neural networks and fuzzy theory.…”

“…Conditional aggregation operator extends the concept of aggregation operator Agg(•) presented by Calvo et al [9] to all measurable functions. For some examples and methods of construction of conditional aggregation operators we refer to [2] 1 . By A = {A(•|D) : D ∈ Σ} we denote a family of conditional aggregation operators (FCA in short).…”

“…⊂ D 1 for any D i ∈ Σ 0 and all i ∈ [l]. For instance, for X = [2] we have Now we can define the Choquet-Sugeno-like operator. Note that we do not use the word "integral", as there is no unambiguous definition of an integral in the literature, see [2,10,23].…”

“…We say that a FCA A is idempotent if A(b½ X |D) = b for any b ∈ [0, ∞) and any A(•|D) ∈ A with D ∈ Σ 0 (see [2,Proposition 3.10]). Obviously, A inf and A sup are idempotent FCAs.…”

“…Let X =[2], f (1) = f (2) = 0.5 and µ ∈ M be symmetric such that µ(X) = 2 and µ({2}) = 1 = µ({1}). The operator C µ,µ ∧ does not depend on permutation, so for B (1) = X and |B (2) | = 1 we get…”