Modified hyperbolic tangent
The modified hyperbolic tangent (mtanh or mth) is a special S-shaped function based on the hyperbolic tangent, given by
This function was proposed by Elena Soboleva as a utility function for multi-objective optimization and choice modelling in decision-making.[1][2][3]
In other papers it is used for approximation of current-voltage characteristics of field-effect transistors[4] and light-emitting diodes.[citation needed]
With parameters a = b = c = d = 1 the modified hyperbolic tangent function reduces to the conventional tanh(x) function, whereas for a = b = 1 and c = d = 0, the term becomes equal to sinh(x).
See also[edit]
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- e (mathematical constant)
- Equal incircles theorem, based on sinh
- Inverse hyperbolic functions
- List of integrals of hyperbolic functions
- Poinsot's spirals
- Sigmoid function
References[edit]
- ↑ Soboleva, Elena V.; Beskorovainyi, V. V. (2008). The utility function in problems of structural optimization of distributed objects (in Russian). Kharkiv University of Air Force. p. 121.CS1 maint: Unrecognized language (link) Search this book on
- ↑ Soboleva, Elena V. (2009). The S-shaped utility function of individual criteria for multi-objective decision-making in design (in Russian). Kharkiv National University of Radioelectronics. p. 247.CS1 maint: Unrecognized language (link) Search this book on
- ↑ Beskorovainyi, V. V.; Soboleva, Elena V. (2010). "ИДЕНТИФИКАЦИЯ ЧАСТНОй ПОлЕЗНОСТИ МНОГОФАКТОРНЫХ АлЬТЕРНАТИВ С ПОМОЩЬЮ S-ОБРАЗНЫХ ФУНКЦИй" [Identification of utility functions in multi-objective choice modelling by using S-shaped functions] (PDF) (in Russian) (1). Kharkiv National University of Radioelectronics: 50–54. УДК 519.688: 004.896; БИОНИКА ИНТЕЛЛЕКТА 2010. No 1 (72).CS1 maint: Unrecognized language (link)
- ↑ Tuev, Vasily I.; Uzhanin, Maxim V. (2009). ПРИМЕНЕНИЕ МОДИФИЦИРОВАННОЙ ФУНКЦИИ ГИПЕРБОЛИЧЕСКОГО ТАНГЕНСА ДЛЯ АППРОКСИМАЦИИ ВОЛЬТАМПЕРНЫХ ХАРАКТЕРИСТИК ПОЛЕВЫХ ТРАНЗИСТОРОВ [Using modified hyperbolic tangent function to approximate the current-voltage characteristics of field-effect transistors] (in Russian). Tomsk Politehnic University. pp. 135–138. 4/314/2009. Archived from the original on 2017-08-15. Retrieved 2015-11-05.CS1 maint: Unrecognized language (link) Search this book on [1]
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