  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 any
context of science - and represent this data by a complex or more general (A
Clifford algebra is introduced for this more general representation)
probability amplitude which matches a generalization of Born's rule. The
outcome from QLRA will introduce the formula of total probability with an
additional term of trigonometric, hyperbolic or hyper-trigonometric
interference and this is in fact a generalization of the familiar formula of
interference of probabilities.
  We study representation of statistical data (of any origin) by a probability
amplitude in a complex algebra and a Clifford algebra (algebra of hyperbolic
numbers). The statistical datas are collected from measurements of two
trichotomous observables and the complexity of the problem increased eventually
compared to the case of dichotomous observables. We see that only special
statistical data (satisfying a number of nonlinear constraints) have a
quantum-like representation. In this paper we will present a class of
statistical data which satisfy these nonlinear constraints and have a
quantum-like representation. This quantum-like representation induces
trigonometric-, hyperbolic- and hyper-trigonometric interferences
representation.
