Research Methodology of Fuzzy Characteristics of Real Options in Innovative Projects

The paper proposes generalization of the fuzzy random pairs approach for research of stochastic processes. The generalization is initiated by an approach to investigation of uncertainty in research project supported with an RFBR grant no. 15-06-06914. This project deals with the stochastic processes, which are the solution of one of the Geske model's modifications. The generalization essence is in the following: 1) time variable (t) in a random process xi(t) is replaced with a random value (u), distributed uniformly within a segment [0; T], which turns the process xi(t) into a two-dimensional random value V = (u, xi(u)), defined on [0; T] x R; 2) the random value V is transformed into a random pointwise set mapping using the interval transformation; 3) in order to transform the random pointwise set mapping into a fuzzy set and to build its membership function a stochastic algorithm is used; 4) for fuzzy set investigation of the obtained pointwise set mapping the fuzzy random pairs approach is used. The paper contains main definitions and adaptation of abstract procedures of fuzzy sets approach to the real innovative project aimed at organization of methyl chloride to ethylene processing and implemented in Russia.