Stochastic logistic fuzzy maps for the construction of integrated multirates scenarios in the financing of infrastructure projects

In general, the development of economic infrastructure systems requires a behavioural comprehensive analysis of different financial variables or rates to establish its long-term success with regards to the Equity Internal Rate of Return (EIRR) expectation. For this reason, several financial organizations have developed economic scenarios supported by computational techniques and models to identify the evolution of these financial rates. However, these models and techniques have shown a series of limitations with regard to the financial management process and its impact on EIRR over time. To address these limitations in an inclusive way, researchers have developed different approaches and methodologies focused on the development of financial models using stochastic simulation methods and computational intelligence techniques. This paper proposes a Stochastic Fuzzy Logistic Model (S-FLM) inspired by a Fuzzy Cognitive Map (FCM) structure to model financial scenarios. Where the input consists in financial rates that are characterized as linguistic rates through a series of adaptive logistic functions. The stochastic process that explains the behaviour of the financial rates over time and their partial effects on EIRR is based on a Monte Carlo sampling process carried out on the fuzzy sets that characterize each linguistic rate. The S-FLM was evaluated by applying three financing scenarios to an airport infrastructure system (pessimistic, moderate/base, optimistic), where it was possible to show the impact of different linguistic rates on the EIRR. The behaviour of the S-FLM was validated using three different models: (1) a financial management tool; (2) a general FCM without pre-loaded causalities among the variables; and (3) a Statistical S-FLM model (S-FLMS), where the causalities between the concepts or rates were obtained as a result of an independent effects analysis applying a cross modelling between variables and by using a statistical multi-linear model (statistical significance level) and a multi-linear neural model (MADALINE). The results achieved by the S-FLM show a higher EIRR than expected for each scenario. This was possible due to the incorporation of an adaptive multi-linear causality matrix and a fuzzy credibility matrix into its structure. This allowed to stabilize the effects of the financial variables or rates on the EIRR throughout a financing period. Thus, the S-FLM can be considered as a tool to model dynamic financial scenarios in different knowledge areas in a comprehensive manner. This way, overcoming the limitations imposed by the traditional computational models used to design these financial scenarios.