Mathematical justificaton of research method of fuzzy set properties of Geske model trajectories and its modifications
Abstract
The fuzzy random pairs approach is developed in [1] in order to study fuzzy set properties of random pointwise set mappings. The articles proposes generalization of the fuzzy random pairs approach for research of stochastic processes. The generalization is initiated by an approach to exploration of uncertainty in research project supported with an RFBR grant no. 15-06-06914, which is based on application of the Geske model modification. Mathematical description of the generalization is carried out for an example of a real venture-backed investment project aimed at organization of methyl chloride to ethylene processing.
The generalization essence is in the following: 1) time variable in a random process is replaced with a random value , distributed uniformly within a segment , which turns the process into a bidimensional random value , defined on ; 2) the random value value is translated into a random pointwise set mapping using the interval translation; 3) in order to translate the random pointwise set mapping into a fuzzy set and to build its membership function a stochastic algorithm is used; 4) for fuzzy set exploration of the resulting pointwise set mapping the fuzzy random pairs approach is used.
The solution of the Geske model is a stochastic process defined on a finite segment of time. The article contains main definitions and adaptations of abstract procedures of fuzzy set approach to the real investment project aimed at organization of methyl chloride to ethylene processing. A detailed research of this project attributes with the use of suggested fuzzy set approach lays beyond the frame of the article and should be the subject of an independent applied research.
About the Authors
A. O. Baranov
Institute of Economics and Industrial Engineering SB RAS, Novosibirsk
Novosibirsk State University, Novosibirsk
Russian Federation
Russian Federation
E. I. Muzyko
Novosibirsk State Technical University, Novosibirsk
Russian Federation
Russian Federation
V. N. Pavlov
4Peter the Great St.-Petersburg Polytechnic University, Saint-Petersburg
Russian Federation
Russian Federation
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For citations:
Baranov A.O., Muzyko E.I., Pavlov V.N. Mathematical justificaton of research method of fuzzy set properties of Geske model trajectories and its modifications. World of Economics and Management. 2016;16(2):78–88. (In Russ.)
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