My Early Researches on Fuzzy Set and Fuzzy Logic
Keywords:
fuzzy subgroup, fuzzy integral, binary numeral system, IQ test, artificial intelligenceAbstract
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
[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)
Additional Files
Published
Issue
Section
License
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.
