A Letter of a Historical Remark on Fuzzy Topology

Professor Lotfi A Zadeh

Subject: Fuzzy Topology
Date: Tue, 05 Feb 2013 15:58:37 -0800
From: Lotfi A. Zadeh
Reply-To: zadeh@eecs.berkeley.edu, bisc-group@lists.EECS.Berkeley.EDU
Organization: Department of EECS, UC Berkeley
To: lchen@udc.edu, Michelle Quirk
CC: bisc-group@lists.EECS.Berkeley.EDU

Dear Li and Mihaela,

Thank you for your constructive questions and comments. You may be interested in a bit of history.

In 1967, two years after the publication of my first paper on fuzzy sets, a well known professor of mathematics in Israel, M. ..., (I do not recall his full name) sent a letter to Richard Hamming in which he said that he found my paper to be quite interesting. In particular, he told Hamming that he felt that the concept of a fuzzy set may suggest new directions in topology. He sketched a few ideas of how this could be done. Hamming forwarded the letter to me. I showed the letter to a very smart student of mine, C.L. Chang, who had a strong background in mathematics, and suggested to C.L. to take a look at M. ...'s ideas. C.L. did that and a few weeks later brought me a short paper which he wrote on the subject of fuzzy topology. I communicated his paper to the Journal of Mathematical Analysis and Applications. The paper was published in 1968 under the title of "Fuzzy topological spaces." This was the beginning of fuzzy topology. C.L.'s paper attracted the attention of Robert Lowen, a mathematician in Belgian, and Y. Liu, a leading mathematician in China, among others. The ball began to roll. Here is what we see today. The 24 papers on fuzzy topology which were listed in my first message came from just one journal entitled "Journal of Advanced Studies of Topology." Google Scholar lists 337 papers with "fuzzy topology" in title and 848 with "fuzzy topological spaces" in title. Google Books lists 34 books with "fuzzy topology" in title and 56 books with "fuzzy topological spaces" in title. These numbers speak for themselves. Attached are samples of titles. Historians of science may find it of interest to take a closer look of how a short paper authored by a student in computer science blossomed into an extensive literature in pure mathematics.

Regards to all,


Lotfi A. Zadeh
Professor Emeritus
Director, Berkeley Initiative in Soft Computing (BISC)

729 Soda Hall #1776
Computer Science Division
Department of Electrical Engineering and Computer Sciences
University of California
Berkeley, CA 94720-1776
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URL: http://www.cs.berkeley.edu/~zadeh/

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fuzzy topology in title- Google Scholar
fuzzy topological spaces in title- Google Scholar
fuzzy topology in title- Google Books Search
fuzzy topological spaces in title- Google Books Search