On methods of defuzzification of parametrically represented fuzzy numbers

Nasıbov, Efendi; Mert, Ali

doi:10.3103/s0146411607050057

Cited by 20 publications

(21 citation statements)

References 6 publications

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“…Linguistic variables use fuzzy variables as their values. Fuzzy variable is characterized by a triple ( X , U , R ( X )) in which X is the name of the variable, U is a universe of discourse, and R ( X ) is a fuzzy subset of U , which represents a fuzzy restriction imposed by X Definition A fuzzy number with membership function in the form

μ_{A} (x) = \{\begin{matrix} left {((), \frac{x - a}{b - a})}^{1 / s}, x \in ([, a, b false),) \\ left {((), \frac{c - x}{c - b})}^{1 / s}, x \in ([, b, c false),) \\ left 0, otherwise \end{matrix}

where

s > 0

is a parameter (Figure ), will be termed as a parametric triangular fuzzy number

A = (s; a, b, c)

.…”

Section: Preliminariesmentioning

confidence: 99%

“…The WABL method is defined in Refs. . It is a kind of defuzzification methods such as mean of maxima, centroid, etc.…”

Section: Preliminariesmentioning

confidence: 99%

“…A way to determine the

p (α)

function is given in Ref. by using the following formula (Equation ):

p (α) = (k + 1) α^{k}

where

k > 0

is a parameter.…”

Section: Preliminariesmentioning

confidence: 99%

“…It is valid for the theorem given below and proven in the study: Theorem Let

A = (s; a, b, c)

will be termed as a parametric triangular fuzzy number with a parameter

s > 0

and suppose that the distribution function of the importance of the degrees has the form (Equation ). Then the following formula for WABL is valid:

WABL (A) = c_{R} (c - \frac{k + 1}{k + s + 1} (c - b)) + c_{L} (c - \frac{k + 1}{k + s + 1} (b - a))

…”

Section: Preliminariesmentioning

confidence: 99%

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A fuzzy ID3 induction for linguistic data sets

Savaş

Nasıbov

2018

Int. J. Intell. Syst.

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In real life, humans communicate by means of words. Computing with words enables flexibility via fuzzy logic to reach more informative results for the classification and decision-making. Fuzzy logic handles the imprecise information. In our paper, we propose a novel fuzzy ID3 algorithm for the classification on linguistic data set, where data can be given as linguistic variables. Linguistic variables are defined by using triangular fuzzy numbers given as LR (left-right) fuzzy numbers. And weighted averaging based on levels (WABL) method is used as the defuzzification method for each data. Then, fuzzy c-means algorithm is performed to handle the membership degrees for each variable given in each data set used in an experimental study. At last, the fuzzy ID3 algorithm is applied. The rules are generated, and the reasoning is done by different T-operators.Our study is encouraged by (using) statistical analysis. In conclusion, it is seen that our algorithm proposed for linguistic data is as good as the proposed approach for numeric data. Also, it is shown that the proposed linguistic approach by using different T-operators on linguistic data gives better results than numerical approach on some data sets. K E Y W O R D Sfuzzy classification, fuzzy ID3 algorithm, linguistic data, weighted averaging based on levels (WABL) method INTRODUCTIONClassification is one of the important topics in machine learning and data mining. Humans use words for communication. Words provide us more information than numbers in decision making. Fuzzy logic includes flexibility to handle the imprecise information for computing with words. 858

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μ_{A} (x) = \{\begin{matrix} left {((), \frac{x - a}{b - a})}^{1 / s}, x \in ([, a, b false),) \\ left {((), \frac{c - x}{c - b})}^{1 / s}, x \in ([, b, c false),) \\ left 0, otherwise \end{matrix}

where

s > 0

is a parameter (Figure ), will be termed as a parametric triangular fuzzy number

A = (s; a, b, c)

.…”

Section: Preliminariesmentioning

confidence: 99%

“…The WABL method is defined in Refs. . It is a kind of defuzzification methods such as mean of maxima, centroid, etc.…”

Section: Preliminariesmentioning

confidence: 99%

“…A way to determine the

p (α)

function is given in Ref. by using the following formula (Equation ):

p (α) = (k + 1) α^{k}

where

k > 0

is a parameter.…”

Section: Preliminariesmentioning

confidence: 99%

“…It is valid for the theorem given below and proven in the study: Theorem Let

A = (s; a, b, c)

will be termed as a parametric triangular fuzzy number with a parameter

s > 0

and suppose that the distribution function of the importance of the degrees has the form (Equation ). Then the following formula for WABL is valid:

WABL (A) = c_{R} (c - \frac{k + 1}{k + s + 1} (c - b)) + c_{L} (c - \frac{k + 1}{k + s + 1} (b - a))

…”

Section: Preliminariesmentioning

confidence: 99%

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A fuzzy ID3 induction for linguistic data sets

Savaş

Nasıbov

2018

Int. J. Intell. Syst.

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show abstract

“…Some aggregation methods with importance or weights information have been proposed for OWA operators, quasi-arithmetic means, and other aggregation operators [6,[9][10][11]14,16,21,33,[35][36][37][38]47]. These weighted aggregation methods have been used for the fuzzy number estimation or defuzzification in recent years [14,22,23,[25][26][27][28]31,39,47,51]. If the membership function of a fuzzy set is replaced with the probability density function, these methods can also be used to estimate the random variables.…”

Section: Introductionmentioning

confidence: 99%