Summary of Computer and Information technology doctoral thesis: Research on developing method of mining fuzzy association rules based on linguistic information and its application

Study methods of semantically expressing fuzzy concepts based the MF or other mathematical methods providing that they express the semantics of the most suitable concepts; studying methods of knowledge exploitation in general and fuzzy rules in particular; sesearch different data representations of information so that it can be exploited in ARs in a diverse and meaningful way.
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Summary of Computer and Information technology doctoral thesis: Research on developing method of mining fuzzy association rules based on linguistic information and its application MINISTRY OF EDUCATION VIETNAM ACADEMY OF AND TRAINING SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY OF SCIENCE AND TECHNOLOGY ------------------------------- NGUYEN TUAN ANH RESEARCH ON DEVELOPING METHOD OF MINING FUZZY ASSOCIATION RULES BASED ON LINGUISTIC INFORMATION AND ITS APPLICATION Major: Mathematical Foundation for informatics Code: 62 46 01 10 SUMMARY OF COMPUTER AND INFORMATION TECHNOLOGY DOCTORAL THESIS HA NOI, 2020 List of works of author Trần Thái Sơn, Nguyễn Tuấn Anh, “Nâng cao hiệu quả khai phá luật kết hợp mờ theo hướng tiếp cận đại số gia tử, Kỷ yếu hội nghị quốc gia lần VI 1 về nghiên cứu cơ bản và ứng dụng công nghệ thông tin (Fair) - Huế, 6/2013. Tran Thai Son, Nguyen Tuan Anh, “Improve efficiency fuzzy association 2 rule using hedge algebra approach, Journal of Computer Science and Cybernetics, Vol 30, No 4, 2014. Tran Thai Son, Nguyen Tuan Anh, Hedges Algebras and fuzzy partition 3 problem for qualitative attributes, Journal of Computer Science and Cybernetics, V.32, N.4, 2016. Tran Thai Son, Nguyen Tuan Anh, Partition fuzzy domain with multi- 4 granularity representation of data based on Hedge Algebra approach, Journal of Computer Science and Cybernetics, vol. 33, pp. 63-76, 2017. 1 INTRODUCTION Nowadays, there is an important research direction on which the problem of mining association rules (AR) is concerned and is soon developed in the direction of data mining. Specially, many algorithms have been developed in different directions but mainly focused on two main directions: (i) Improve the average speed of rule mining algorithms because this is an exponentially complex problem due to repeated database (DB) scans. (ii) Further research on the meaning of mining rules means as not all mining rules have implications for users. Fuzzy AR take the form: If X is A, then Y is B. X is A is called Premise, Y is B is called the conclusion of the rule. ???? = {????1 , ????2 , … , ???????? }, Y= {????1 , ????2 , … , ???????? } is a subsection of a set of attributes I of the DB. ???? = {????????1 , ????????2 , … , ???????????? }, B= {????????1 , ????????2 , … , ???????????? } are the corresponding fuzzy sets of attributes X and Y. Dividing the domain of the attribute is an important first step for an information processing process. Recently, researchers have paid attention to the construction of such membership functions (MF) because of the obvious influence of this step on the next step. The thesis studies the methods of exploiting legal knowledge in fuzzy combination with linguistic information (linguistic rule) from DB or digital data stores. Hedge algebras are used (HA) instead of fuzzy set theory to study some problems of AR mining: (i) The fuzzy AR is studied and there are some disadvantages, including in constructing algorithms to increase processing speed as well as in the problem of fuzzy partition planning of the attributes in order to find out the meaningful ARs. (ii) With different data representations, HA gives a simple unified approach that is highly effective in processing. Research purposes: - Study methods of semantically expressing fuzzy concepts based the MF or other mathematical methods providing that they express the semantics of the most suitable concepts. - Studying methods of knowledge exploitation in general and fuzzy rules in particular. - Research different data representations of information so that it can be exploited in ARs in a diverse and meaningful way. The thesis uses single-granular and multi-granular data representation, consistent with the increasing attention of this research direction. CHAPTER 1. SOME BASIC KNOWLEDGE 1.1. Fuzzy set and operations on fuzzy sets 1.1.1. Fuzzy set Definition 0.1: Let U be the universe of objects. The fuzzy set A on U is a set of ordered pairs (????, ???????? (????)), where ???????? (????) is a function from U to [0, 1] assigned to each x of U a value ???????? (????) reflects degree of dependence x to the fuzzy set A. 1.1.2. Linguistic variable 1.1.3. Fuzzy partition There are several methods for partitioning domain values using fuzzy logic as follows: 1) Definition 1.3: Given m fixed items ????1 , ????2 , … , ???????? that belongs to ???? = [????, ????] ⊂ ???? . It is the reference space of the basic variable ???? of the llinguistic variable ????. Then a set ???? of m fuzzy sets ????1 , ????2 , … , ???????? defined on ???? (with corresponding MFs ????????1 , ????????2 ,..., ???????????? are 2 called a fuzzy partition of ???? if the following conditions are met. complacent, ∀???? = 1, … , ????:???????????? (???????? ) (???????? belongs to the part called core of ???????? ); 2) If x ∉ [????????−1 , ????????+1 ] then ???????????? (????) = 0 3) ???????????? (????) consecutively; 4) ???????????? (????) monotonous rose on[????????−1 , ???????? ]; 5) ∀???? ∈ ????, ∃????, so that ???????????? (????) > 0; If the fuzzy partition satisfies the following conditions 6), it is called a strong fuzzy partition. 6) ∀????????????, ∑???? ????=1 ???????????? (????) = 1; If a fuzzy partition satisfies the following conditions 7), 8), 9), it is called a uniform partition. 7) If ???? ≠ ???? then ℎ???? = ????????+1 − ???????? = a constant 8) The fuzzy set ???????????? (????) is the symmetric function. 1.2. The fuzzy sets ???????????? (????) have the same geometry - Hedge algebra 1.3. The concept of hedge algebra 1.3.1. The concept of hedge algebra Definition 1.4: A HA is denoted as a set of 4 components denoted ???????? = (X, G, H, ≤) in which G is a set of generating elements, H is a set of hedges, and ≤ is a semantically inductant relationship on X. Suppose that there are constant elements 0, W, 1 in G correspondi ...