Abstract
We explore questions related to the aggregation operators and aggregation of fuzzy sets. No preliminary knowledge of the aggregation operators theory and of the fuzzy sets theory are required, because all necessary information is given in Section 2. Later we introduce a new class of γ‐aggregation operators, which “ignore” arguments less than γ. Due to this property γ‐aggregation operators simplify the aggregation process and extend the area of possible applications. The second part of the paper is devoted to the generalized aggregation problem. We use the definition of generalized aggregation operator, introduced by A. Takaci in [7], and study the pointwise extension of a γ‐agop.
Highlights
We explore questions related to the aggregation operators and aggregation of fuzzy sets, i.e. elements of the class F (R) = {P |P : R → [0, 1]}
Let P1, . . . , Pn ∈ F (R), A : ∪n∈NF (R)n → F (R) and A be an ordinary agop on the unit interval, Ais a pointwise extension of A if the following holds: (E1) : (∀x ∈ R, A(P1, . . . , Pn)(x) = A(P1(x), . . . , Pn(x)), where A(P1, . . . , Pn) is a resulting fuzzy set obtained by means of application the operator Ato the fuzzy subsets P1, . . . , Pn
The notion of γ-agop and its pointwise extension is central in this paper
Summary
We explore questions related to the aggregation operators and aggregation of fuzzy sets, i.e. elements of the class F (R) = {P |P : R → [0, 1]}.
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