1. Full name:     Roan Thi Ngan                                      2. Sex: Female

3. Date of birth: October 12, 1990                                  4. Place of birth: Thaibinh Province

5. Admission decision number: 3035/QĐ-ĐHKHTN, dated on August 22, 2016 by Rector of VNU University of Science.

6. Changes in academic process: Decision No 567/QĐ-ĐHKHTN, dated on February 14, 2020, by Rector of VNU University of Science.

7. Official thesis title: Some new measures and representations of intuitionistic fuzzy systems and applications.

8. Major: Applied Mathematics                                       9. Code: 9460112.01

10. Supervisors:            1) Assoc. Prof. D.Sc. Bui Cong Cuong

                                 2) Assoc. Prof. Dr. Le Hoang Son

11. Summary of the new findings of the thesis

i) Intuitionistic fuzzy measures:  The δ−equality measure and the H-max distance measure.

ii) Intuitionistic fuzzy representations:

- A new representation of intuitionistic fuzzy systems based on complex numbers and a new measure named P−distance.

- A new representation of intuitionistic fuzzy systems based on quaternion numbers and a quaternion measure via this representation.

iii) Applications to Medical Diagnosis:

- An intuitionistic fuzzy decision-making systems based on the δ−equality.

- Two medical diagnosis models from numeric data and image data based on the H-max measure.5

- A complex intuitionistic fuzzy decision-making.

- A quaternion measure method for decision-making problems.

12. Paratical applicability, if any: The research issue aims to contribute to perfecting intuitionistic fuzzy theory and applying to decision-making problems, is a topical topic, which is significant in both science and application practice.

13. Further research directions, if any

• New notions of sub δ−equalities such as the weighted δ−equalities will be investigated.

• We will extend the distance measures in other types of advanced fuzzy sets such as the picture fuzzy set, the neutrosophic set and others.

• The other logical operations and measures based on the proposed representation such as implication operation and equality measure will be studied.

• Constructing algebraic operations and building topological structures on , laying the foundation for analytic research on intuition fuzzy sets.

• Expanding the uses of quaternion number representation to represent complex intuitionistic fuzzy set theory and logic can be considered.

14. Thesis-related publications:

Ngan R.T., Ali M., Son L.H. (2018), “δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis”, Applied Intelligence 48(2), pp. 499-525. (SCI. IF 3.325, Q2, Hindex 58)

Ngan R.T., Son L.H., Cuong B.C., Ali M. (2018), “H-max distance measure of intuitionistic fuzzy sets in decision making”, Applied Soft Computing 69, pp. 393-425. (SCIE, IF 5.472, Q1, H-index 124)

Son L.H., Ngan R.T., Ali M., Fujita H., Giang N.L., Manogaran G., Priyan M.K. (2019), “A New Representation of Intuitionistic Fuzzy Systems and Their Applications in Critical Decision Making”, IEEE Intelligent Systems 35(1), pp. 6-17. (SCI, IF 5.010, Q1, H-index 115, IEEE)

Ngan R.T., Son L.H., Ali M., Tamir D.E., Rishe N.D., Kandel A. (2019), “Representing Complex Intuitionistic Fuzzy Set by Quaternion Numbers and Applications to Decision Making”, Applied Soft Computing 87, 105961, pp. 1-15. (SCIE, IF 5.472, Q1, H-index 124)

Ngan R.T., Cuong B.C., Tuan T.M., Son L.H. (2018), “Medical Diagnosis from Images with Intuitionistic Fuzzy Distance Measures”, Lecture Notes in Artificial Intelligence, Rough Sets, Inter. Joint Conf., pp. 479-490. (Springer, Cham)