On product-sum of triangular fuzzy numbers
Fuzzy Sets and Systems
On Hamacher sum of triangular fuzzy numbers
Fuzzy Sets and Systems
Introduction to artificial neural systems
Introduction to artificial neural systems
t-Norm-based addition of fuzzy intervals
Fuzzy Sets and Systems
On the principles of fuzzy neural networks
Fuzzy Sets and Systems
On the convergence of T-sum of L-R fuzzy numbers
Fuzzy Sets and Systems
Fuzzy neural networks: a survey
Fuzzy Sets and Systems
A note on t-norm-based addition of fuzzy intervals
Fuzzy Sets and Systems
A note to the T-sum of L-R fuzzy numbers
Fuzzy Sets and Systems
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Reasoning in Decision Making and Optimization
Fuzzy Reasoning in Decision Making and Optimization
T-sum of bell-shaped fuzzy intervals
Fuzzy Sets and Systems
T-sum of sigmoid-shaped fuzzy intervals
Information Sciences: an International Journal
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The extension principle defines the arithmetic operations on fuzzy intervals. In the extension principle one can use any t-norm for modeling the conjunction operator. It is therefore important to know, which t-norms are consistent with a particular type of fuzzy intervals. We call a t-norm consistent, if the arithmetic operation is closed. In this paper we investigate the addition of sigmoid and two bell-shaped membership functions which appear in many natural processes and are used in machine learning applications. We prove that the addition is closed if the Dombi operator is used. The calculation of sum is quite simple and can be used in various applications such as fuzzy-neural networks.