Aggregation of fuzzy truth values

Examples of Aggregation Operators on Membership Degrees of Type-2 Fuzzy Sets

“…According to the Zadeh's extension principle [24], Z. Takáč [16,17] extended the n-ary aggregation operator on [0,1] (see Definition 11) to the following n-ary operator on M.…”

“…Z. Takáč [16,17] also determined that if A is a continuous n-ary aggregation operator on [0,1], thenà is an aggregation operator on L* (that is a subset of L). Nevertheless he did not give any aggregation operator on L, or on M, as the closure properties given in those papers were established only on L*.…”

“…[2]). Then, Z. Takáč [16,17] introduced the definition of aggregation operator on M and applied the Zadeh's extension principle in order to extend the type-1 aggregation operators to T2FSs. Nevertheless, S. Zhou et al [25] had previously given an approximation with the extension of the ordinary aggregation operators so-called OWA (Ordered Weighted Averaging, see [22]).…”

“…The purpose of this paper is to introduce a family of operators on M, more general than that given in [16,17] and study some of their properties in order to determine under which conditions these operators are aggregation operators on L. Furthermore, we analyze other set of operators on M, different to those obtained in [16] and [17].…”

“…Takáč in [16] introduced the aggregation operators on any subalgebra of M (set of all fuzzy membership degrees of the type-2 fuzzy sets, that is, the functions from [0,1] to [0,1]). Furthermore, he applied the Zadeh's extension principle (see [24]) to obtain in [16,17] a set of aggregation operators on L* (the strongly normal and convex functions of M). In this paper, we introduce the aggregation operators on any partially ordered and bounded set (poset).…”