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On fuzzy number-valued fuzzy measures defined by fuzzy number-valued fuzzy integrals I
Fuzzy Sets and Systems, 1992The author generalizes some concepts on fuzzy measure and fuzzy integral to the case where the fuzzy measure can take fuzzy numbers and both of fuzzy measure and fuzzy integral are defined on fuzzy sets, particularly, he discusses when such a fuzzy integral could determine a fuzzy number- valued fuzzy measure.
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Fuzzy Sets and Systems, 1999
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Congxin Wu +3 more
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Congxin Wu +3 more
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Information Sciences, 1989
By Zadeh's extension principle a binary operation * on the real numbers \({\mathbb{R}}\) is extended to fuzzy numbers \(f_ i: {\mathbb{R}}\to [0,1]\), \(i=1,2\), as follows \((f_ 1*f_ 2)(z)=\bigvee \{f_ 1(x_ 1)\wedge f_ 2(x_ 2):\) \(x_ 1*x_ 2=z\}\). Then the equation \(f*x=g\) is considered.
Loredana Biacino, Ada Lettieri
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By Zadeh's extension principle a binary operation * on the real numbers \({\mathbb{R}}\) is extended to fuzzy numbers \(f_ i: {\mathbb{R}}\to [0,1]\), \(i=1,2\), as follows \((f_ 1*f_ 2)(z)=\bigvee \{f_ 1(x_ 1)\wedge f_ 2(x_ 2):\) \(x_ 1*x_ 2=z\}\). Then the equation \(f*x=g\) is considered.
Loredana Biacino, Ada Lettieri
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Fuzzy Sets and Systems, 2004
The authors introduce some kind of covariance between marginal possibility distributions and use it as a measure of interactivity between these marginal distributions. Some examples illustrate the usefulness of this notion. The general mathematical background seems to be the theory of copulas.
Robert Fullér, Péter Majlender
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The authors introduce some kind of covariance between marginal possibility distributions and use it as a measure of interactivity between these marginal distributions. Some examples illustrate the usefulness of this notion. The general mathematical background seems to be the theory of copulas.
Robert Fullér, Péter Majlender
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2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2013
In this paper we build the concept of fuzzy quaternion numbers as a natural extension of fuzzy real numbers. We discuss some important concepts such as their arithmetic properties, distance, supremum, infimum and limit of sequences.
Ronildo P. A. Moura +3 more
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In this paper we build the concept of fuzzy quaternion numbers as a natural extension of fuzzy real numbers. We discuss some important concepts such as their arithmetic properties, distance, supremum, infimum and limit of sequences.
Ronildo P. A. Moura +3 more
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Fuzzy Numbers and Fuzzy Arithmetic
2008The arithmetical and topological structures of fuzzy numbers have been developed in the 1980s and this enabled to design the elements of fuzzy calculus (see [6, 7]); Dubois and Prade stated the exact analytical fuzzy mathematics and introduced the well-known LR model and the corresponding formulas for the fuzzy operations. For the basic concepts see, e.
STEFANINI LUCIANO +2 more
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International Journal of Intelligent Systems, 2000
Summary: At the heart of many statistical processing algorithms lies the concept of ordering a set of crisp numbers, either according to their own values (``direct'' sorting), or according to the values of a second set of numbers (``indirect'' sorting).
H. B. Mitchell, P. A. Schaefer
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Summary: At the heart of many statistical processing algorithms lies the concept of ordering a set of crisp numbers, either according to their own values (``direct'' sorting), or according to the values of a second set of numbers (``indirect'' sorting).
H. B. Mitchell, P. A. Schaefer
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A representation of fuzzy numbers
Fuzzy Sets and Systems, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yingming Chai, Dexue Zhang
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On the centroids of fuzzy numbers
Fuzzy Sets and Systems, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ying-Ming Wang 0001 +3 more
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Fuzzy number-valued fuzzy measure and fuzzy number-valued fuzzy integral on the fuzzy set
Fuzzy Sets and Systems, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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