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The quantum-like representation algorithm (QLRA) was introduced by A.Khrennikov \cite{K1,K2,K3,K4,K5} to solve the "inverse Born's rule problem",i.e. to construct a representation of probabilistic data - measured in anycontext of science - and represent this data by a complex or more general (AClifford algebra is introduced for this more general representation)probability amplitude which matches a generalization of Born's rule. Theoutcome from QLRA will introduce the formula of total probability with anadditional term of trigonometric, hyperbolic or hyper-trigonometricinterference and this is in fact a generalization of the familiar formula ofinterference of probabilities.  We study representation of statistical data (of any origin) by a probabilityamplitude in a complex algebra and a Clifford algebra (algebra of hyperbolicnumbers). The statistical datas are collected from measurements of twotrichotomous observables and the complexity of the problem increased eventuallycompared to the case of dichotomous observables. We see that only specialstatistical data (satisfying a number of nonlinear constraints) have aquantum-like representation. In this paper we will present a class ofstatistical data which satisfy these nonlinear constraints and have aquantum-like representation. This quantum-like representation inducestrigonometric-, hyperbolic- and hyper-trigonometric interferencesrepresentation.

On hyperbolic interferences in the quantum--like representation algorithm for the case of triple-valued observables