Decision Models to Find a Promising Start-Up Firm with Qualiflex under Probabilistic Linguistic Circumstance

QUALIFLEX is a flexible method to solve the multi-criteria decision-making problem with a few alternatives. Moreover, the linguistic term is a very general way used by decision makers (DMs) to express their real perceptions. In particular, the probabilistic linguistic information, including the probability of each linguistic term, can simulate the vague perceptions of the DMs well. Therefore, the main contributions of this paper are constructing two novel QUALIFLEX with probabilistic linguistic information. First, based on the classical QUALIFLEX, it has been extended under probabilistic linguistic circumstance. Secondly, it is common for the DMs to have different risk attitudes for gains and losses when making their decisions under uncertainty, which is well explained by prospect theory (PT). Hence, PT has been integrated into the extended QUALIFLEX. Then, in this paper, a prospect QUALIFLEX is proposed as well. The feasibility and validity of the proposed methods have been verified by a numerical example in venture capital. The comparative and simulated analysis shows that the latter method with prospect framework is more appropriate than the former one because of the inherent psychological behaviors of the DMs and its excellent ability in identifying the similar alternatives. Furthermore, the ranking results derived from the prospect QUALIFLEX do not change with the different values of parameters. It reveals that the prospect QUALIFLEX is stable and reliable.