Summary of Computer doctoral thesis: Some extensions of the complex fuzzy inference system for decision support problem

Research objectives of the thesis: Research the theories of complex fuzzy sets, complex fuzzy logic and measures based on complex fuzzy sets; research and development of fuzzy inference system based on complex fuzzy sets; research applied techniques to reduce rules, optimize fuzzy rules in complex fuzzy inference system; research on how to represent rules based on fuzzy knowledge graphs to reduce inference computation time for the test set and deal with the cases where the new dataset is not present in the training data set.
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Summary of Computer doctoral thesis: Some extensions of the complex fuzzy inference system for decision support problem MINISTRY OF EDUCATION VIETNAM ACADEMY AND TRAINING OF SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY OF SCIENCE AND TECHNOLOGY ------------------------------- LUONG THI HONG LAN SOME EXTENSIONS OF THE COMPLEX FUZZY INFERENCE SYSTEM FOR DECISION SUPPORT PROBLEM Major: Computer science Code: 9 48 01 01 SUMMARY OF COMPUTER DOCTORAL THESIS Ha Noi - 2021 The doctoral thesis was completed at Graduate University of Science and Technology – Vietnam Academy of Science and Technology Supervisor 1: Assoc. Prof. Dr. Le Hoang Son Supervisor 2: Assoc. Prof. Dr. Nguyen Long Giang Reviewer 1: Reviewer 2: Reviewer 3: This doctoral thesis will be defended at the Board of Examiners of Graduate University of Science and Technology, Vienam Academy of Science and Technology on hour….., date….. month….. 2021 This doctoral thesis can be explored at: - Library of the Graduate University of Science and Technology - National Library of Vietnam 1 PREFACE Fuzzy set (FS) [1] proposed by Zadeh in 1965 is considered as an effective tool to solve the problems with uncertain properties. Various extensions and operations of FS have been presented in recent years [2-6]. One of the most important techniques in FS is Fuzzy Inference System (FIS), which is widely applied in many decision-making and classification/prediction problems such as green supplier selection, personnel selection, company strategy, etc. In these applications, FIS was used to generate a set of fuzzy rules to detect, predict or classify objects such as lung cancer detection, detection of diabetes mellitus, heart disease prediction, evaluation of green supply chain management performance, penetration index estimation in rock mass [7-13]. An extended version of FIS embedded with neural network and gradient-based learning is the Adaptive Neuro Fuzzy Inference System (ANFIS) [14], which also demonstrated good performance in coronary artery disease prognosis, estimating thermal conductivity enhancement of metal and metal oxide, flood prediction, etc. [15- 21]. Recently, with the boost up of various decision-making problems inspired by time variants or phase changes, an extension of the Fuzzy Set namely the Complex Fuzzy Set (CFS) with new membership functions including both the amplitude and the phase terms has been proposed [37]. CFS has been applied with much concentration by new fuzzy aggregation operators, complex fuzzy soft information, distance measures, and complex fuzzy concept lattice [37]–[43]. The advantage of CFS is the capability to model phenomena and events by the phase term to show their overall progress within a given context. For an example, in order to validate whether blood pressure of a patient is ‘High’ or ‘Low’, a sample of 30 measured times is recorded, and the mean and variance are computed. Using the fuzzification of FIS in the CFS, the blood pressure of the patient can be easily measured within the recorded period as ‘Low’ amplitude with ‘Low’ phase (i.e. small mean and variance values). If the blood pressure is measured in a specific time stamp, a wrong decision may be given out. Another example of the problem of disease diagnosis: if only based on the disease attribute values without considering other attributes, the diagnosis result will be inaccurate, because the disease conclusion depends not only on each disease attribute value, but also need to consider factors related to that disease. Moreover, there are also many scenarios that involves a phase term, which is encountered in data with a periodic trend, such as rainfall recorded in a region, or the sound waves produced by a musical instrument. It is therefore evident, that complex numbers must be given a place in the literature of fuzzy inference system as well. This is therefore the main motive of this thesis. The ordinary fuzzy inference systems such as the Mamdani, Sugeno and Tsukamoto systems and various versions of the ANFIS architectures are only able to handle phenomena that are not periodic or seasonal. In order to handle time-series data in time-periodic phenomena, FISs and ANFISs employ two general strategies: 1) ignore the information related to the phase term; 2) represent the amplitude and phase terms separately using two fuzzy sets. This would cause loss of information and produce unreliable results (if information related to the phase terms are ignored), distortion of information, and a reduction in computational efficiency (if information related to the amplitude and phase are represented separately) as it becomes more time-consuming due to the increased number of sets that need to be dealt with. Complex fuzzy inference systems are considered to be an effective tool for solving problems with periodicity and uncertainty. The first system introduced by Ramot [44] is called Complex Fuzzy Logic System, which is developed from the usual fuzzy logic system but replaces the fuzzy set and the implication rule by its version in complex plane. Another study by Man et al. [45] is based on the combination of inductive learning 2 with inference systems in complex fuzzy sets. Another version of embedded learning with neural fuzzy network on CFS set called Adaptive Neural Complex Fuzzy Inference System (ANCFIS) was introduced by Chen et al. [46]. Then two improvements of ANCFIS with the aim of increasing the computational speed are also given in [47-48]. In the other words, most of the so-called CFISs that have been prop ...