# An Integrated Risk Index Model Based on Hierarchical Fuzzy Logic for Underground Risk Assessment
## 1 Introduction  
Underground space and structures are hard to monitor because access to most of the underground facilities is difficult or almost impossible. Many issues are associated with underground facilities, such as leakage, liquefaction, collapse, distortion, and floods. Underground risk has to be evaluated periodically so that high-risk areas can be sustained in a timely fashion in order to make certain the protection of the people [1]. Different ways exist for assessing underground risks, such as assertion, sustainability, safety, and the environment; these are portrayed by risk ratings, such as high, low, or medium. The risk score is based on different criteria, it can be aggregated in order to find overall risk. Using overall risk the maintenance priority can be determined. Normally, underground risk assessment needs a large number of subjective judgments from the experts; these types of assessments are costly and time-consuming. Due to the complex non-linear relationship between the risk score and the risk mathematical rating, if a model is designed for this process in order to assess underground risk, it will be obviously of great benefit to underground agencies and Geo-environmental Engineers. These models can assess underground risk within no time or cost [2; 3]. An amount of construction accidents comprised of the failure of major infrastructure facilities, i.e., subways, bridges, and buildings, have happened because of less effective underground assessment. Hence, it is very obligatory to assess underground risk periodically in order to avoid these accidents. Most massive underground projects have a complex sequence of events and have complex procedural systems. For example, the rock mass is very complex and its association is with large suspicions. It is also very difficult to solve decision problems with underground construction and may lead to unforeseen results. When seeking to make improvements, the probabilistic decision and risk analysis can be used. The underground risk is an important element, and many qualitative and quantitative risk methods are available for risk assessment. To make a trustworthy decision, it is necessary to know the risk of the given system or procedure correctly [4]. Fuzzy logic is the most popular risk assessment and is a risk analysis method that can be deployed in almost any field [5; 6]. Fuzzy logic is a type of logic with many values, in which the range of truth values lies between 0 and 1. Fuzzy logic is opposed to Boolean logic in which the truth values of variables may only be the numerical values 0 or 1. Fuzzy logic has been deployed to deal with incomplete truth, where the true value may be totally true or totally untrue [7]. Many research efforts have also been done for designing fuzzy logic with a special structure to solve the curse of dimensionality. Hierarchical fuzzy systems have been designed in order to solve the exponential increase of rules based on the number of inputs entered into the system. The size of hierarchical fuzzy logic can be characterized by different modules that are carried out as a computational contribution to the final solution. Low-level modules have some input variables and the output of the same can be used as input variables to the high-level module for the last solution. The key benefit of the construction of hierarchical fuzzy systems is the obligation of fewer rules as compared to the monolithic fuzzy system. In conventional fuzzy logic, the number of rules may increase exponentially as the number of system variables increases; hence, the conventional fuzzy logic is not applicable in the case of a large number of input variables [8; 9; 10]. The objective of this paper is to design a fuzzy logic with a special structure to handle the curse of dimensionality. Underground risk assessment is very complex due to several parameters. In order to accurately assess the risk of a location, the maximum number of parameters should be taken into account.