Some Approximation Methods in Fuzzy Logic: Some Method For Finding Approximation of Fuzzy Functions and Fuzzy Numbers

Publisher: Lambert Academic Publishing, ISBN: 978-3659137402

ABSTRACT In this book we define some new methods to approximate a fuzzy function by fuzzy polynomials. Also by introducing some new distances we define the nearest approximations of a fuzzy number. ‎In his book‎, the ‎definition of fuzzy linear programming with fuzzy variables and a‎ ‎method for solving it according to a special class of ranking which is used ‎to find the approximating polynomials as well as‎ ‎definition of the problem of approximation‎, ‎‎are discussed‎. Then the approximation problem on triangular fuzzy numbers ‎leads us to an approximating polynomial name eϕ-approximation‎ ‎and on the set of all fuzzy numbers‎, ‎the approximation problem gives ‎us the D-approximation and we present a method to find it‎, ‎ also ‎the universal and SAF-approximations which are special cases of D-approximation are found in this book‎. ‎Also two best ‎approximations of a triangular valued fuzzy function on a set of‎ ‎points are defined and are computed‎. ‎Furthermore a chapter contains an idea for ‎computing the nearest approximation of a fuzzy number out of a‎ ‎particular subset of all fuzzy numbers.

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