My Early Researches on Fuzzy Set and Fuzzy Logic

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.

Automated summary

This paper presents the author's works on fuzzy sets and fuzzy systems in early 1980's, including an isomorphic theorem on fuzzy subgroups and fuzzy series, and the convergence theorem of fuzzy integral type II contributed by Zhang Wenxiu and Zhao Ruhuai. Both types of fuzzy integrals have been important in engineering device design for the past 40 years.