Abstract
Abstract Aim of the paper is to propose a new tool for a decision supporting system concerning the financial project evaluation. It is based on the determination of the internal rate of return (IRR) of a investment project in which all expenditure and anticipated incomes are vague, and described by Ordered Fuzzy Numbers (OFNs). It means that the probabilistic approach is neglected in this paper and the use of the well developed arithmetics of OFNs is made to find a positive fuzzy root of a fuzzy polynomial representing the fuzzy net present value of the project. Since in the space of OFNs a partial order relation is defined together with a number of defuzzification functionals, the authors can construct a decision support system for investors helping them in acceptance procedure of most profitable investment projects.
Highlights
An increasing role of small and medium enterprizes requires new tools for supporting their activities in the nowadays economics
Aim of the paper is to propose a new tool for a decision supporting system concerning the financial project evaluation. It is based on the determination of the internal rate of return (IRR) of a investment project in which all expenditure and anticipated incomes are vague, and described by Ordered Fuzzy Numbers (OFNs)
We may use the order relation existing in the space of Ordered Fuzzy Numbers (OFN) in ranking all projects, from the highest to the lowest according to their fuzzy IRR values, without referring to any defuzzification method
Summary
An increasing role of small and medium enterprizes requires new tools for supporting their activities in the nowadays economics. Future returns, already are always uncertain and a possible model of this uncertainty is to use fuzzy numbers It was Buckley, who in his first paper [1] on the subject of fuzzy internal rate of return used triangular fuzzy numbers to present net cash flow of a proposed investment project over n periods of time. In this paper we confine our interest to propose tools to a decision supporting system when OFN appear It will be a system for investors which helps them in the process of selection of business plan in the case of imprecise data concerning expenditures and the future cash flows modeled using OFN. It contains the main definitions of discounted values of cash flows, net present value and internal rate of return. The existence of a fuzzy solution for IRR’s equation has been proved based on the classical result of the algebra: the root of a polynomial is a continuous function of the polynomial coefficients
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