A neutrosophic approach in the optimal solution of a neutrosophic fuzzy capital budgeting problem

Abstract

This paper is proposed to apply neutrosophic fuzzy dynamic programming to solve neutrosophic fuzzy capital budgeting problems (NFCBPs). This paper proposes an optimal solution to a NFCBP with indefinite parameters. In this proposed approach, the revenues are taken as neutrosophic triangular fuzzy numbers (NTFNs). Neutrosophic numbers are used to state indeterminate and inconsistent information. In this paper, ÃN = (a1, a2, a3; b1, b2, b3; c1, c2, c3) is taken as a NTFN whose truth membership TÃN, indeterminacy membership IÃN and falsity membership FÃN are defined in such a way that 0 ≤ TÃN(x) + IÃN(x) + FÃN(x) ≤ 3, x ∈ ÃN. Both forward and backward recursive equations are formulated with neutrosophic fuzzy approach to find the fuzzy optimal solution. The approach is illustrated by a numerical example. This proposed approach will pave the way for further researches in fuzzy dynamic programming models with neutrosophic approach.