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