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Algorithms to extend crisp functions and their inverse - EUSFLAT
ALGORITHMS TO EXTEND CRISP FUNCTIONS AND THEIR. INvERSE FUNCTIONS TO FUZZY NUMBERS. O.G. Duarte. Department of Electrical Engineering.

Algorithms to extend crisp functions and their inverse functions to
it is not the best way to deal with inverse functions, because there are special ... algorithm used to extend crisp functions to fuzzy numbers; in Section 4 we ...

11 Fuzzy Logic
networks directly without having to apply a learning algorithm. An expert ... The difference between crisp (i.e., classical) and fuzzy sets is established by ... A fuzzy set is completely determined by its membership function. Note ... The geometric visualization can be extended ..... 11.2.2 Fuzzy numbers and inverse operation.

Fuzzy UTASTAR: A method for discovering utility functions from
We propose Fuzzy UTASTAR, a method for inferring fuzzy utility functions from a ... this is the first attempt to extend UTASTAR method to handle both crisp and fuzzy eval- ..... The UTASTAR algorithm (Siskos & Yannacopoulos, 1985) is an .... fuzzy numbers in practical applications, due to their simplicity ... Inverse interval.

Gradual Numbers and their Application to Fuzzy Interval - IRIT
as crisp sets of entities we call gradual (real) numbers. They ... However since calculations with fuzzy intervals extend interval analysis , interval ... number of kinks in the resulting membership functions. The paper is .... This proposition is the basis of the (FWA) Algorithm  which computes .... be their inverse functions. It is.

AN EVOLUTIONARY ALGORITHM DETERMINING A - TASK-u
Dec 27, 2006 ... In most cases, the membership function of a fuzzy number, A, is assumed ... on convex fuzzy numbers increase fuzziness significantly and depend ... functions was crucial and arithmetic operations on their inverse parts needed to be defined for them to be in agreement with operations on crisp real numbers.

Iterative Inversion of Fuzzi ed Neural Networks - Programming
Next we derive the inversion algorithm of fuzzi ed neural networks by ... these reasons, the inversion yields estimate inverses which approximate the ... algorithm of crisp neural networks cannot be directly fuzzified hence, ... function extended from f. ... 1In this paper, we denote fuzzy numbers and fuzzy functions by sans serif ...

Fuzzy Logic in Insurance: The First 20 Years
... arithmetic, fuzzy inference systems, fuzzy clustering algorithms, fuzzy linear ... Fuzzy sets are implemented by extending many of the basic identities that .... functions f(y|A), j=1,2, "A" a fuzzy number, which are inverse functions ... In this case, there are two crisp inputs, x0 and yo, and two sets of membership functions, A, B.

A Fuzzy Classifier Network with Ellipsoidal Epanechnikovs
vector, then a large number of Gaussians may be required but the accuracy is high in the absence of outliers. ... We extend Epanechnikov functions to be multivariate ... The inverses of these symmetric matrices ... ellipsoidal fuzzy set membership functions for the respective classes and the maximum value (fuzzy truth).

CS660 FUZZY SET THEORY AND EVOLUTIONARY ALGORITHMS
differences between the crisp set characteristic function and the fuzzy set membership ... and applications: Zadeh extension principle, image and inverse image of fuzzy ... operations with fuzzy numbers, extended operation and its properties,.

Iterative inversion of fuzzified neural networks - Fuzzy Systems, IEEE
The inversion algorithm of crisp neural networks is based on the gradient ... the inversion yields estimate inverses which approximate the in- verse of the target to a ... extended from . 1In this paper, we denote fuzzy numbers and fuzzy functions by sans serif ... extended from a monotonically increasing real-valued function.

A New Operation on Triangular Fuzzy Number for Solving Fuzzy
Keywords: Fuzzy arithmetic, Triangular fuzzy number, Function Principle. 1. Introduction ... The usual arithmetic operation on real numbers can be extended to the ones ... 2.7 α- cut of a triangular fuzzy number: We get a crisp interval by α- cut .... (v) Inverse element: Any Fuzzy Number is its own inverse under the modified ...

Supervised Learning in Fuzzy Neural Networks
work is based on the traditional backpropagation algorithm. Therefore we ... interpreted) set A. Thus classical sets are also fuzzy sets, but their membership functions ... membership functions of triangular fuzzy numbers are triangular- shaped. ... principle is the possibility to extend crisp mathematical concepts to fuzzy sets.

Solving Fuzzy System of Equations Using Gaussian Membership
Dec 22, 2009 ... system of linear equations, extended matrix, generalized inverse, fuzzy system of ... fuzzy numbers are used rather than crisp numbers. Thus the ... Wang  presented an iterative algorithm for solving a system of fuzzy linear ... of fuzzy numbers having gaussian membership function and its implementation.

Reasoning with Very Expressive Fuzzy Description Logics - JAIR
In this paper we extend the well known fuzzy ALC (f-ALC) DL (Straccia, 2001) to the ... of the reasoning algorithm for deciding the consistency of a fuzzy-SI ABox ... function Inv which returns the inverse of a role, more precisely, ..... that there are many proposals for semantics of number restrictions in fuzzy DLs (Sánchez & .

Reasoning with Very Expressive Fuzzy Description Logics
In this paper we extend the well known fuzzy ALC (f-ALC) DL (Straccia, 2001) to the ... of the reasoning algorithm for deciding the consistency of a fuzzy-SI ABox ... function Inv which returns the inverse of a role, more precisely, ..... that there are many proposals for semantics of number restrictions in fuzzy DLs (Sánchez & .

EXACT AND APPROXIMATE SOLUTIONS OF FUZZY LR - Sid
Feb 1, 2010 ... ... a crisp square system. In their method, the inverse matrix is used to ... the FLRLS after transforming the FLRLS into a corresponding crisp linear system ... our proposed algorithm to solve an extended dual fuzzy linear system . ... A fuzzy number фА is of LR-type if there exist shape functions L. (for left) ...

A generalized fuzzy Johnson algorithm - ijteee
have used half inverse operator to compare fuzzy number as well as to find triangular longer time procedure. In the present ... time for 2 x n job shop problem there after extended to m x n job shop ... used triangular, trapezoidal membership functions to describe ... to find crisp value or mean value of LR type fuzzy number.