Fuzzy net present values for capital investments in an uncertain environment

This work presents a series of pragmatic algorithms for calculating the net present values of capital investments in an environment, which are subject to uncertainty from randomness of outcomes and vagueness of estimation. Linguistic terms is adopted to assess the possibilities of future economic scenarios, and fuzzy numbers are then used to represent the linguistic assessments and estimate cash flows and costs of capital. Utilizing the standard fuzzy arithmetic, the text presents the equations of the expected fuzzy net present values for a single project, expected fuzzy equivalent annuity for mutually exclusive projects with equal life spans, and expected fuzzy equivalent annuity to infinity for projects with unequal risks (jointly called expected FNPVs). By further applying the fuzzy arithmetic with requisite constraints, novel equations are proposed for computing the fuzzy variance and standard deviation. The selection of the target is based on the rule of high return (expected FNPVs), low absolute risk (fuzzy standard deviation), and/or low relative risk (coefficient of variation). In addition to efficiently integrating the quantitative information, the developed algorithms are anticipated to measure the subjective qualitative information more effectively than the traditional method.