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Along with the development of Information Technology, Online Social Networks (OSN) are constantly developing and have become popular media in the world. Besides communication enhancement benefits, OSN have such limitations on rapid spread of false information as rumors, fake news, and contradictory news. False information spread is collectively referred to as misinformation which has significant on social communities. The more sources and topics of misinformation are, the greater the number of users are affected. Therefore, it is necessary to prevent the spread of misinformation with multiple topics within a given period of time. In this paper, we propose a Multiple Topics Linear Threshold model for misinformation diffusion, and define a misinformation blocking problem based on this model that takes account of multiple topics and budget constraint. The problem is to find a set of nodes that minimizes the impact of misinformation at an allowed cost when blocking them from the network. We prove that the problem is NP-hard and the time complexity of the objective function calculation is #P-hard. We also prove that the objective function is monotone and submodular. We propose an approximation algorithm with approximation ratio (1 − 1/ √ e) based on these attributes. For large networks, we propose an extended algorithm by using a tree data structure for quickly updating and calculating the objective function. Experiments conducted on real-world datasets show efficiency and effectiveness of our proposed algorithms in comparison with other state-of-the-art algorithms.

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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Attribute reduction from decision tables is one of the crucial topics in data mining. This problem belongs to NP-hard and many approximation algorithms based on the filter or the filter-wrapper approaches have been designed to find the reducts. Intuitionistic fuzzy set (IFS) has been regarded as the effective tool to deal with such the problem by adding two degrees, namely the membership and non-membership for each data element. The separation of attributes in the view of two counterparts as in the IFS set would increase the quality of classification and reduce the reducts. From this motivation, this paper proposes a new filter-wrapper algorithm based on the IFS for attribute reduction from decision tables. The contributions include a new instituitionistics fuzzy distance between partitions accompanied with theoretical analysis. The filter-wrapper algorithm is designed based on that distance with the new stopping condition based on the concept of delta-equality. Experiments are conducted on the benchmark UCI machine learning repository datasets.

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