Generalization and ranking of fuzzy numbers by relative preference relation

Koppula, Kavitha; Kedukodi, Babushri Srinivas; Kuncham, Syam Prasad

doi:10.1007/s00500-021-06616-1

Cited by 3 publications

(1 citation statement)

References 30 publications

(27 reference statements)

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“…Newer methods, e.g., [21][22][23] are limited to a comparison of (special) fuzzy numbers. Very good and promising approaches can be found in [24][25][26].…”

Section: Comparative Values From Literaturementioning

confidence: 99%

Percentage Comparison of Fuzzy Numbers Using a Newly Presented Method in the Context of Surrogate Modeling

Oberleiter,

Willner

2024

Int. J. Fuzzy Syst.

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The O-index presented here allows a statement about the percentage deviation between two fuzzy numbers. For this purpose, one fuzzy number is defined s the reference. This fuzzy number is described with the help of its core value and its support. The deviation of the other fuzzy number, which is defined as the comparison number, is then quantified via the area differences of the left and right limits of the two numbers. In addition, the case when decomposed fuzzy numbers are involved, which are given as $$\alpha $$ α -cuts is taken into account. Thus, the O-index-$$\alpha $$ α can be used to calculate a separate percentage deviation for each $$\alpha $$ α -cut and thus generate additional knowledge. The O-index then allows a very detailed description of the deviation between two fuzzy numbers. One application of the O-index is the estimation of the accuracy of a surrogate model in relation to a reference model in the context of uncertainty quantification. This is illustrated by a mechanical example, a bending beam.

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“…Newer methods, e.g., [21][22][23] are limited to a comparison of (special) fuzzy numbers. Very good and promising approaches can be found in [24][25][26].…”

Section: Comparative Values From Literaturementioning

confidence: 99%

Percentage Comparison of Fuzzy Numbers Using a Newly Presented Method in the Context of Surrogate Modeling

Oberleiter,

Willner

2024

Int. J. Fuzzy Syst.

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Polygonal Types of Lift Fuzzy Real Numbers

Jayalakshmi,

Shanmugapriya

2024

Fudan J. Hum. Soc. Sci.

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Some new types of generalized fuzzy real numbers

Jayalakshmi,

Shanmugapriya

2024

IFS

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This study provides the generalization of fuzzy real numbers by imposing the elevator’s condition upon it’s legs. Our aim is to construct three types of Lift Fuzzy Real Numbers, an extension of h-generalized fuzzy real numbers, to indicate medical signals, stock market values, and commercial establishment profits over time. It explores concepts like ɛ-cut, strong ɛ-cut, β-level set, and convexity, and presents a graphical representation based on profit earned by three industries. Appropriate numerical examples are provided to support the new ideas. It’s interesting to note that Lift Fuzzy Real Numbers are also used to represent real numbers. Additionally, the connections between the Lift Fuzzy real numbers have been established. The new fuzzy real numbers offer an advantage in representing data sets not represented by existing fuzzy numbers.

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Generalization and ranking of fuzzy numbers by relative preference relation

Abstract: We define $$2n+1$$ 2 n + 1 and 2n fuzzy numbers, which generalize triangular and trapezoidal fuzzy numbers, respectively. Then, we extend the fuzzy preference relation and relative preference relation to rank $$2n+1$$ 2 n + 1 and 2n fuzzy numbers. When the data is represen… Show more

Cited by 3 publications

References 30 publications

Percentage Comparison of Fuzzy Numbers Using a Newly Presented Method in the Context of Surrogate Modeling

Percentage Comparison of Fuzzy Numbers Using a Newly Presented Method in the Context of Surrogate Modeling

Polygonal Types of Lift Fuzzy Real Numbers

Some new types of generalized fuzzy real numbers

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