The use of the mathematical tool of fuzzy interval-valued numbers for the estimation of undetermined parameters of investment projects and their efficiency criteria

Abstract

Real investment management is the most important area of modern businesses. Real investments, particularly related to providing new capital (for new companies, new productions), are associated with various kinds of uncertainty. When choosing an investment project, it is necessary to consider uncertainty factors characterizing the state of the competitive environment, risk of undesired events, the cost of investment resources, random swings of demand and market prices, various political and economic risks. The presence of uncertainty factors results in the failure to consider the parameters of investment project financial flows determined; simulation tools, which would allow considering uncertainty, fuzziness, stochastic nature of project implementation and getting project efficiency estimations addressing the main risk and uncertainty factors subject to simulation and/or expert evaluation, are necessary. This paper proposes using the mathematical tool of fuzzy interval-valued numbers to simulate undetermined parameters of an investment project and calculate net present value. Interval-valued fuzzy numbers, which are often interpreted as second-order fuzzy numbers or ultra-fuzzy numbers, allow simulating not only the uncertainty of a value on the reference axis (carrier) of a parameter but also the uncertainty related to the membership function value. The paper proposes an algorithm for constructing fuzzy triangular interval-valued numbers based on processing expert information and an algorithm for generating project net present value estimation based on operations with interval-valued fuzzy numbers.