## 1 Introduction  
When faced with a new problem, it is always helpful to consider the solution to a similar problem from the past. From increasing historical experience, it is possible to identify useful solutions. Case-based reasoning (CBR), a knowledge-based system, is an experience-based method [1]. It solves new problems by retrieving the most similar case from a member of cases [2], which is also the core process of the CBR cycle [3]. CBR is demonstrably suitable for solving problems in fault diagnosis. [PERSON] et al. (2004) added a Petri net to a CBR system to improve the revision function, and successfully applied it to electronic motor diagnosis [4]. Owing to the complexity and uncertainty of the operating environment, [PERSON] et al. (2017) proposed an optimized hybrid model combining CBR and a Bayesian network for embedded software fault diagnosis [5]. A CBR system for the intelligent fault diagnosis of power equipment was proposed by [PERSON] [6]. Decision makers often need to weigh different criteria when making decisions as the factors involved in decision making become more complex. In addition, the importance of different criteria should be considered. Multi-attribute decision making (MADM), or multi-criteria decision making (MCDM), is a decision making methodological framework based on multiple criteria or multiple attributes [7]. MADM provides decision makers with a set of recommendations for alternatives, goals, or solutions [8]. The main task of MADM is to assess a member of the alternatives and then rank them [9, 10]. MCDM has been applied in many fields such as supplier [11], material [12], and flotation machine selections [13]. Evidently, MADM and CBR have some commonalities. Both can solve the problem of choosing the best solution from among numerous alternatives [14]. On the one hand, CBR is good at dealing with knowledge-intensive and multidisciplinary complex problems,such as medical diagnosis and aviation fault diagnosis. In general, fault diagnosis in these domains cannot be achieved simply by searching for a few keywords. In most cases, a detailed description of the fault is required. Therefore, it may be more reasonable to consider the semantics of fault descriptions rather than strings. In addition, there are several complex unstructured problems in these domains. Some similarity retrieval methods used in CBR can solve these problems. On the other hand, MADM can provide decision makers with a ranking of alternatives and suggest the best solution. To select the optimal solution among multiple solutions, the trade-offs between different attributes and the weight of each attribute must be considered in the MADM. Thus, integrating CBR with MADM can not only deal with complex problems in some fields, but also consider the weights of multiple attributes, thus improving the accuracy of CBR. In view of this, [PERSON] and [PERSON] (2011) combined AHP with CBR to build an intelligent tourism system ([PERSON] and [PERSON], 2014), [PERSON] et al. (2018) proposed a TOPSIS-CBR approach for cancer therapy and successfully tested it using real datasets ([PERSON] and [PERSON], 2015), and [PERSON] et al. (2015) proposed a hybrid approach to select construction materials in mechanical engineering ([PERSON] and [PERSON], 2015). However, two defects exist in the aforementioned studies. First, in most cases, the interactions among decision attributes were ignored; that is, different attributes were assumed to be noninteractive or independent of each other. In fact, there are positive or negative interactions between certain attributes that cannot be ignored ([PERSON] et al., 2017). Therefore, nonadditive measures should be introduced to remedy this defect. In addition, when synthesizing the importance and interaction of attributes, few studies have considered the influence of decision makers' attitudes on the decision making process.