## 1 Introduction  
The fire damage levels of reinforced concrete (RC) structures significantly depend on the size and duration of the fire [1; 2]. If the fire is small and short, the damage is likely to be small in a limited range of the concrete members. If the concrete structure is exposed to high temperatures for a long time, however, the damage is likely to be severe in a large number of the concrete members, resulting in significant reductions in their strength and durability performances, which thus threatens the safety of the whole structure [3; 4; 5]. In particular, if spalling occurs to high-strength concrete columns exposed to high temperatures, their reduced cross-section can lead to the stiffness and strength degradations of the whole structure and can even cause the collapse of the structure. To determine the appropriate repairing or strengthening method for the RC structures after fire accidents, it is very important to accurately and rapidly diagnose their fire damage levels. According to the fire damage diagnosis methods presented in the Korea Concrete Institute (KCI) [1] and the Architectural Institute of Japan (AIJ) [2], the fire damage levels of RC structures are evaluated by five grades, as shown in Table 1, based on the simple visual inspection or the detailed investigations on the fire-damaged concrete members. The diagnosis results, however, highly depend on the experience and knowledge of the inspector; it is hard to ensure their objectiveness and reliability.  
Fuzzy theory has been widely adopted in various modern engineering fields to solve many complex problems [6; 7], where many influencing factors need to be considered with large uncertainties, and theoretical or numerical solutions are not available or at least difficult to find. Fuzzy theory has been also utilized for many decision-making procedures in the civil engineering fields [8; 9; 10; 11; 12; 13]. For instance, [PERSON] et al. [8] and [PERSON] et al. [9] applied fuzzy theory for the optimization of their structural or engineering design. [PERSON] et al. [10; 11] introduced a fuzzy-based assessment method to estimate the durability and serviceability performances of reinforced concrete buildings and also developed the crack diagnosis system that can identify the primary causes of cracks. [PERSON] et al. [12] developed the remaining service life evaluation method of concrete buildings by utilizing fuzzy theory, which can consider the effects of multiple influencing factors on the deterioration of durability. [PERSON] et al. [13] also estimated the carbonation depth of a reinforced concrete member using the adaptive neuro-fuzzy inference system, in which the field inspection data had been trained to consider the combined deterioration by multiple influencing factors. All of these systems aid us to diagnose or solve the various engineering problems at the level of an expert. There has been, however, yet no study that utilizes fuzzy theory for the fire damage assessment. In this study, therefore, fuzzy theory was utilized to establish the fire damage diagnosis system (FDDS) that can comprehensively consider the various influencing factors and also objectively evaluate the fire damage levels of RC members.