In this study, we present the operator-dependent sigmoid function, which is derived from a universal unary operator called kappa function. Here, describe how generalized function related to representable uninorms (i.e., Dombi's aggregative operator). Namely, show that inverse of an additive generator operator. We provide necessary and sufficient conditions for form transforms into conjunctive o...

This article discusses Lipschitz properties of generated aggrega-tion functions. Such generated functions include triangular norms and conorms, quasi-arithmetic means, uninorms, nullnorms and continuous generated functions with a neutral element. The Lipschitz property guarantees stability of aggregation operations with respect to input inaccuracies, and is important for applications. We provid...

Recently, the distributivity of fuzzy implications over t-norms, t-conorms and uninorms was studied in many articles. In this paper we characterize functions which satisfy one of the four generalized distributivity equations of classical implication in the case when t-conorms are continuous and Archimedean. Using the obtained characterizations we describe some solutions which are fuzzy implicat...

Aggregation functions on [0, 1] with annihilator 0 can be seen as a generalized product on [0, 1]. We study the generalized product on the bipolar scale [−1, 1], stressing the axiomatic point of view ( compare also [9]). Based on newly introduced bipolar properties, such as the bipolar increasingness, bipolar unit element, bipolar idempotent element, several kinds of generalized bipolar product...

This paper proposes a hybrid architecture based on neural networks, fuzzy systems, and n-uninorms for solving pattern classification problems, termed as ENFS-Uni0 (short evolving neuro-fuzzy system uni-nullneurons). The model can produce knowledge in an on-line (single-pass) learning context particular form of rules representing the dependencies among input features through IF-THEN type relatio...