Forecasting 3PL demand of warehousing services with interval type-3 fuzzy logic and GM (1,1)

Real-world information can be vague or imprecise, not reliable, where the information is presented in fragments, ambiguity in the data, or even contradictory information, these can lead to uncertainty, but even this uncertainty we need to take decisions [1]. Part of this uncertainty can be handled by different un-certainty models, such: grey systems [2-3], type-1, type-2 [4-7] or typ-3 fuzzy systems, all used represent this uncertainty with numbers. But some-times, there more complex situations are, it is extremely difficult to find the precise numeric value or model to provide accurate value for any uncertain entity. This paper pro-vides a state-of-the-art review on the different applications of the type-3 [8-18]and grey systems [19-30] and proposes the application of Type-3 fuzzy logic for demand forecasting within the supply chain combined with the preciseness GM (1,1) of the grey systems theory (GST), applied for predicting the demand of warehousing services (3PL) in the industry. While utilizing interval type-3 fuzzy logic helps handling the uncertainty in the decision-making when forecasting re-duces its effect, the GM (1,1) improves its accuracy. Type-3 Fuzzy Logic is a robust and capable model to cope with high-order uncertainties associated with non-stationary time-dependent features of the GM (1,1). The main objective this paper is to present Type-3 fuzzy logic, denoted as A3, combined with a GM (1,1) model, which provides better results than its individual application. The hybrid approach is formed by an interval type-3 fuzzy model structured by fuzzy if then rules that, utilize as inputs the linear GM (1,1) equation. The contribution is the new scheme based on interval Type-3 Fuzzy Logic and the linear GM (1,1), which has not been proposed before, aiming to achieve and accurate forecast of multivariable forecasts time series, while reducing the mathematical complexity of the model. The fuzzy rules can be established with the Mandami reasoning meth-od, but in this paper were established with the Sugeno-Takagi-Kang approach. The proposed method has been compared with previous works and its results confirm the superiority of the Type-3 Fuzzy Logic combined with the GM (1,1).