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

Z. Takac 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). This will allow us to suitably provide aggregation operators onM. In this sense, firstly we define a set of operators on M, more general than those given by Z. Takac, studying some of their properties. Secondly, we focus on some operators obtained through a very different way, proving that they are aggregation operators on L (set of normal and convex functions of M), and onM.