Medical diagnosis is considered as an important step in dentistry treatment which assists clinicians to give their decision about diseases of a patient. It has been affirmed that the accuracy of medical diagnosis, which is much influenced by the clinicians' experience and knowledge, plays an important role to effective treatment therapies. In this paper, we propose a novel decision making method based on fuzzy aggregation operators for medical diagnosis from dental X-Ray images. It firstly divides a dental X-Ray image into some segments and identified equivalent diseases by a classification method called Affinity Propagation Clustering (APC+). Lastly, the most potential disease is found using fuzzy aggregation operators. The experimental validation on real dental datasets of Hanoi Medical University Hospital, Vietnam showed the superiority of the proposed method against the relevant ones in terms of accuracy.

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Context and background: Complex fuzzy theory has a strong practical implication in many real-world applications. Complex Fuzzy Inference System (CFIS) is a powerful technique to overcome the challenges of uncertain, periodic data. However, a question is raised for CFIS: How can we deduce and predict the result in case there is little knowledge about data information and rule base? This is significance because many real applications do not have enough knowledge of rule base for inference so that the performance of systems may be low. Thus, it is necessary to have an approximate reasoning method to represent and derive final results. Motivation: Recently, the Mamdani Complex Fuzzy Inference System (M-CFIS) has been proposed with a specific inference mechanism according to the Mamdani type. A new improvement so-called the Mamdani Complex Fuzzy Inference System with Rule Reduction (M-CFIS-R) has been designed to utilize granular computing with complex similarity measures to reduce the rule base so as to gain better performance in decision-making problems. However in M-CFIS-R, testing data are checked by matching with each rule in the rule base, which leads to a high cost of computational time. Besides, if the testing data contain records that are not inferred by the rule base, the output cannot be generated. This happens in real commerce systems in which the rule base is small at the time of creation and needs to feed with new rules. Methodology: In order to handle those issues, this paper first time proposes the Fuzzy Knowledge Graph to represent the rule base in terms of linguistic labels and their relationships according to the rule set. An adjacent matrix of Fuzzy Knowledge Graph is generated for inference. When a record in the Testing dataset is given, it would be fuzzified and labelled. Each component in the record is checked with the Fuzzy Knowledge Graph by the inference mechanism in approximate reasoning called Fast Inference Search Algorithm. Then, we derive the label of the new record by the Max-Min operator. Besides, we also propose four extensions of

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