Free Downloads

Fuzzy Sets And Fuzzy Logic: Theory And Applications Paperback: 592 pages

Publisher: Prentice Hall; 1st edition (May 21, 1995)

Language: English

ISBN-10: 0131011715

ISBN-13: 978-0131011717

Product Dimensions: 6.9 x 1.5 x 9 inches

Shipping Weight: 2 pounds (View shipping rates and policies)

Average Customer Review: 4.6 out of 5 stars See all reviews (8 customer reviews)

Best Sellers Rank: #588,147 in Books (See Top 100 in Books) #55 in Books > Science & Math > Mathematics > Pure Mathematics > Set Theory #70 in Books > Computers & Technology > Hardware & DIY > Microprocessors & System Design > Computer Design #178 in Books > Textbooks > Computer Science > Artificial Intelligence

I would hesistate to give anything less than a 5 star review to anything on fuzzy set theory in the wide sense. Make no mistake reading this book is worth your time. Yet, some significant problems do exist with this text. First off, read the proofs in this carefully and figure out if they do work. Klir and Yuan know that appealing to contradiction in theorem proving doesn't often work out in fuzzy theory. Yet, they go ahead and use it almost recklessly. One example is their proof on fuzzy numbers that says that they are all continuous on pages 99 to 100. After about a full, condensed page of mathematical reasoning they say that left fuzzy numbers are continuous from the left and that right fuzzy numbers are continuous from the right. After their supposed "proof" they claim that "The implication of Theorem 4.1 is that every fuzzy number be represented in the form of (4.1)." 4.1 shows a discontinuous fuzzy number. A jump discontinuity to speak more specifically. Consequently, their supposed "theorem" doesn't exactly work as a "theorem". Perhaps I misunderstand and they have some different idea of continuity. I don't get it though and neither does any other mathematician, as any break in a function whatsoever means discontinuity. More interestingly, some of their axioms for fuzzy set don't hold. For instance, on page 62 Axiom i1 (i for intersection) says that i(a, 1)=a, which they label as the "boundary conidition." This does hold for drastic products. However, it doesn't hold for all fuzzy intersections. As Buckley and Eslami point out the axioms or necessary conditions for fuzzy intersections work out as "(1) 0

Fuzzy Sets and Fuzzy Logic: Theory and Applications Fuzzy Logic: Intelligence, Control, and Information Fuzzy Logic for the Management of Uncertainty Classic Sports Card Sets: Best Sport Cards Sets From the 1950s and 1960s Set Theory (Studies in Logic: Mathematical Logic and Foundations) Ones and Zeros: Understanding Boolean Algebra, Digital Circuits, and the Logic of Sets Introductory Logic and Sets for Computer Scientists (International Computer Science Series) Fundamentals of Mathematics: An Introduction to Proofs, Logic, Sets, and Numbers Logic and set theory: With applications Introduction to the Theory of Sets (Dover Books on Mathematics) The Joy of Sets: Fundamentals of Contemporary Set Theory (Undergraduate Texts in Mathematics) Trading on the Edge: Neural, Genetic, and Fuzzy Systems for Chaotic Financial Markets Neuro-Fuzzy Pattern Recognition: Methods in Soft Computing Apple Pro Training Series: Logic Pro 8 and Logic Express 8 Critical Thinking: Decision Making with Smarter Intuition and Logic! (Critical Thinking, Decision Making, Logic, Intuition) Logic: Propositional Logic (Quickstudy: Academic) Introduction to Logic: Propositional Logic, Revised Edition (3rd Edition) Fluid Flow in the Subsurface: History, Generalization and Applications of Physical Laws (Theory and Applications of Transport in Porous Media) Ergonomics: Foundational Principles, Applications, and Technologies (Ergonomics Design & Management Theory & Applications) Stochastic Integration in Banach Spaces: Theory and Applications (Probability Theory and Stochastic Modelling)