Fuzzy Mathematics: An Introduction for Engineers and Scientists

✍ Scribed by Professor John N. Mordeson, Associate Professor Premchand S. Nair (auth.)

• Publisher: Physica-Verlag Heidelberg
• Year: 2001
• Tongue: English
• Leaves: 318
• Series: Studies in Fuzziness and Soft Computing 20
• Edition: 2
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiii
Fuzzy Subsets....Pages 1-20
Fuzzy Graphs....Pages 21-65
Fuzzy Topological Spaces....Pages 67-113
Fuzzy Digital Topology....Pages 115-136
Fuzzy Geometry....Pages 137-217
Fuzzy Abstract Algebra....Pages 219-290
Back Matter....Pages 291-310

✦ Subjects

Mathematics, general; Math Applications in Computer Science; Computational Intelligence; Game Theory/Mathematical Methods