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Fuzzy Mathematics

An Introduction for Engineers and Scientists

  • Book
  • © 2001
  • Latest edition

Overview

Authors:
  1. John N. Mordeson

    1. Center for Research in Fuzzy Mathematics and Computer Science, Creighton University, Omaha, USA

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  2. Premchand S. Nair

    1. Department of Mathematics and Computer Science, Creighton University, Omaha, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • With numerous examples
  • Presentation of concepts of fuzzy mathematics with applications to engineering, computer science, and mathematics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 20)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Fuzzy Subsets

    • John N. Mordeson, Premchand S. Nair
    Pages 1-20

  3. Fuzzy Graphs

    • John N. Mordeson, Premchand S. Nair
    Pages 21-65

  4. Fuzzy Topological Spaces

    • John N. Mordeson, Premchand S. Nair
    Pages 67-113

  5. Fuzzy Digital Topology

    • John N. Mordeson, Premchand S. Nair
    Pages 115-136

  6. Fuzzy Geometry

    • John N. Mordeson, Premchand S. Nair
    Pages 137-217

  7. Fuzzy Abstract Algebra

    • John N. Mordeson, Premchand S. Nair
    Pages 219-290

  8. Back Matter

    Pages 291-310
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Keywords

About this book

In the mid-1960's I had the pleasure of attending a talk by Lotfi Zadeh at which he presented some of his basic (and at the time, recent) work on fuzzy sets. Lotfi's algebra of fuzzy subsets of a set struck me as very nice; in fact, as a graduate student in the mid-1950's, I had suggested similar ideas about continuous-truth-valued propositional calculus (inffor "and", sup for "or") to my advisor, but he didn't go for it (and in fact, confused it with the foundations of probability theory), so I ended up writing a thesis in a more conventional area of mathematics (differential algebra). I especially enjoyed Lotfi's discussion of fuzzy convexity; I remember talking to him about possible ways of extending this work, but I didn't pursue this at the time. I have elsewhere told the story of how, when I saw C. L. Chang's 1968 paper on fuzzy topological spaces, I was impelled to try my hand at fuzzi­ fying algebra. This led to my 1971 paper "Fuzzy groups", which became the starting point of an entire literature on fuzzy algebraic structures. In 1974 King-Sun Fu invited me to speak at a U. S. -Japan seminar on Fuzzy Sets and their Applications, which was to be held that summer in Berkeley.

Authors and Affiliations

  • Center for Research in Fuzzy Mathematics and Computer Science, Creighton University, Omaha, USA

    John N. Mordeson

  • Department of Mathematics and Computer Science, Creighton University, Omaha, USA

    Premchand S. Nair

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