My Early Researches on Fuzzy Set and Fuzzy Logic

  • Yong Shi Chinese Academy of Sciences

Abstract

This paper presents the author’s works on fuzzy sets and fuzzy systems in early 1980’s to celebrate the 100-year birthday of Lotfi A. Zadeh. They were originally published in Chinese. The first part of the paper is about an isomorphic theorem on fuzzy subgroups and fuzzy series of invariant subgroups, which could be a theoretical basis when the multiple-valued computer system will be reconsidered or redeveloped in the future. The second part of the paper describes the convergence theorem of fuzzy integral of type II which was contributed by Wenxiu Zhang and Ruhuai Zhao. Both fuzzy integral of type I developed by M. Sugeno and the fuzzy integral of type II have been playing an important role in the design of various engineering devices for last 40 years.

References

[1] Hands, J. (2019). Cosmosapiens: Human evolution from the origin of the universe. Abrams, 2019.

[2] Huang, J.; Zheng, D. (1980). The convergence theorem of fuzzy integral of distribution function Modern Cybernetics Information, 1980. (In Chinese)

[3] Leibniz, G. (1879). Explication de I'Arithm6tique Binaire. Die Mathematische Schriften, ed, 1879.

[4] Liu, F.; Shi, Y. (2014). The search engine IQ test based on the Internet IQ evaluation algorithm. Procedia Computer Science, 31, 1066-1073, 2014.
https://doi.org/10.1016/j.procs.2014.05.361

[5] Liu, F.; Shi, Y.; Liu, Y. (2017). Intelligence quotient and intelligence grade of artificial intelligence. Annals of Data Science, 4(2), 179-191, 2017.
https://doi.org/10.1007/s40745-017-0109-0

[6] Liu, F.; Shi, Y.; Wang, B. (2015) World search engine IQ test based on the internet IQ evaluation algorithms. International Journal of Information Technology & Decision Making, 14(02), 221-237, 2015.
https://doi.org/10.1142/S0219622015500030

[7] MIT Technology Review. October 13, 2017.

[8] Rosenfeld, A. (1971). Fuzzy groups. Journal of mathematical analysis and applications, 35(3), 512-517, 1971.
https://doi.org/10.1016/0022-247X(71)90199-5

[9] Shi, Y. (1981). Another isomorphic theorem on fuzzy subgroups and fuzzy series of invariant subgroups. Journal of Southwestern Petroleum Institute, 1981. (In Chinese)

[10] Shi, Y. (1981). Convergence theorem of fuzzy integral of type II. Journal of Southwestern Petroleum Institute, 1981. (In Chinese)

[11] Sugeno, M. (1993). Fuzzy measure and fuzzy Integral. Transactions of the Society of Instrument and Control Engineers, 8, 2, 218-226, 1993.
https://doi.org/10.9746/sicetr1965.8.218

[12] Sugeno, M., Terano, T. (1975). Analytical representation of fuzzy systems. Special Interest Discussion on Fuzzy Automata and Decision Processes, 1975.

[13] Terano, T., Sugeno, M. (1975). Conditional fuzzy measures and their applications. Fuzzy Sets and Their Applications to Cognitive and Decision Processes , 1975.
https://doi.org/10.1016/B978-0-12-775260-0.50011-6

[14] Wu, W. (1981). Fuzzy normal subgroup. Fuzzy mathematics, 1, 21-30, 1981. (In Chinese).

[15] Xiong, Q. (1978) Universal algebra. Shanghai Science and Technology Press, 1978. (In Chinese)

[16] Zadeh, L. A. Fuzzy sets. Information and control, 8(3), 338-353, 1965.
https://doi.org/10.1016/S0019-9958(65)90241-X

[17] Zhang, W.; Zhao, R. (1980). Generalization of fuzzy measure and fuzzy integral Science Report of Xi'an Jiaotong University, 1980. (In Chinese)

[18] Zheng, D.; Jinli Huang, J.(1980). The neighborhood theorem of quasi-fixed points and the convergence theorem in measure of fuzzy integral Modern Cybernetics Information, 1980. (In Chinese)

[19] Zou, K. (1981). Fuzzy group theory. Collection of Graduate Papers of Mathematics Department of Beijing Normal University, 1981. (In Chinese)
Published
2020-11-30
How to Cite
SHI, Yong. My Early Researches on Fuzzy Set and Fuzzy Logic. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 16, n. 1, nov. 2020. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/4090>. Date accessed: 04 mar. 2021. doi: https://doi.org/10.15837/ijccc.2021.1.4090.