Some properties and representation methods for Ordered Weighted Averaging operators

Jin, LeSheng

doi:10.1016/j.fss.2014.04.019

Cited by 31 publications

(39 citation statements)

References 33 publications

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“… Function generation methods : Generally speaking, this method is based on a predefined discrete function such as Gaussian distribution or based on the use of the centering function Figuratively generation methods : These miscellaneous methods include the decaying generation method, tray and mirror generation methods, etc. The advantage of these methods is that we can predefine the desired centering degree (or generally the fuzzy Centering degree) …”

Section: Preliminariesmentioning

confidence: 99%

“… Figuratively generation methods : These miscellaneous methods include the decaying generation method, tray and mirror generation methods, etc. The advantage of these methods is that we can predefine the desired centering degree (or generally the fuzzy Centering degree) …”

Section: Preliminariesmentioning

confidence: 99%

“…And “ the pillars we use to support this bridge ” are the “ pairs ” of special OWA operators called pair‐like vectors . And these special OWA operators are none other than the step OWA operators or generalized step OWA operators …”

Section: On Obtaining Piled Owa Operatorsmentioning

confidence: 99%

“…Step 1 : To determine

p_{i}

, we need

2 \cdot 4 - 1 = 7

generalized step OWA operators as components. In this example, we need

\begin{matrix} true \\ right \begin{matrix} {bolds}_{1} = (1, 0, 0, 0, 0); & {bolds}_{11 / 12} = (2 / 3, 1 / 3, 0, 0, 0); & {bolds}_{5 / 6} = (1 / 3, 2 / 3, 0, 0, 0); \\ {bolds}_{3 / 4} = (0, 1, 0, 0, 0); & {bolds}_{1 / 2} = (0, 0, 1, 0, 0); & {bolds}_{1 / 4} = (0, 0, 0, 1, 0); \\ and {bolds}_{0} = (0, 0, 0, 0, 1) \end{matrix} \end{matrix}

…”

Section: On Obtaining Piled Owa Operatorsmentioning

confidence: 99%

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On Obtaining Piled OWA Operators

Jin

Qian

2015

Int. J. Intell. Syst.

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In this study, we propose the concept of piled ordered weighted averaging (OWA) operators, which generalize the centered OWA operators and also connect the step OWA operators with the Hurwicz OWA operators with given the orness degree. We propose a controllable algorithm to generate the family of piled OWA operators depending on their predefined three parameters: orness degree, step‐like or Hurwicz‐like degree, and the numbers of “supporting” vectors. By these preferences, we can generate infinite more piled OWA operators with miscellaneous forms, and each of them is similar to the well‐known binomial OWA operator, which is very useful but only has one form corresponding to one given orness degree.

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Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: On Obtaining Piled Owa Operatorsmentioning

confidence: 99%

“…Step 1 : To determine

p_{i}

, we need

2 \cdot 4 - 1 = 7

generalized step OWA operators as components. In this example, we need

\begin{matrix} true \\ right \begin{matrix} {bolds}_{1} = (1, 0, 0, 0, 0); & {bolds}_{11 / 12} = (2 / 3, 1 / 3, 0, 0, 0); & {bolds}_{5 / 6} = (1 / 3, 2 / 3, 0, 0, 0); \\ {bolds}_{3 / 4} = (0, 1, 0, 0, 0); & {bolds}_{1 / 2} = (0, 0, 1, 0, 0); & {bolds}_{1 / 4} = (0, 0, 0, 1, 0); \\ and {bolds}_{0} = (0, 0, 0, 0, 1) \end{matrix} \end{matrix}

…”

Section: On Obtaining Piled Owa Operatorsmentioning

confidence: 99%

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On Obtaining Piled OWA Operators

Jin

Qian

2015

Int. J. Intell. Syst.

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“…The corresponding orness measure plays an important role in studies of OWA operators [2,3,4,8,9,11,12,13,14,15,21,22,24,25,26,27,28,29,30,31,32,33,34,35,36,37]. The orness measure reflects the or-like or and-like aggregation result of an aggregation function.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy orness measure and new orness axioms

Jin¹,

Kalina²,

Qian³

2015

Kybernetika

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S-H OWA Operators with Moment Measure

Wang

Merigó

Jin

2016

Int. J. Intell. Syst.

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Step‐like or Hurwicz‐like ordered weighted averaging (OWA) (S‐H OWA) operators connect two fundamental OWA operators, step OWA operators and Hurwicz OWA operators. S‐H OWA operators also generalize them and some other well‐know OWA operators such as median and centered OWA operators. Generally, there are two types of determination methods for S‐H OWA operators: One is from the motivation of some existed mathematical results; the other is by a set of “nonstrict” definitions and often via some intermediate elements. For the second type, in this study we define two sets of strict definitions for Hurwitz/step degree, which are more effective and necessary for theoretical studies and practical usages. Both sets of definitions are useful in different situations. In addition, they are based on the same concept moment of OWA operators proposed in this study, and therefore they become identical in limit forms. However, the Hurwicz/step degree (HD/SD) puts more concerns on its numerical measure and physical meaning, whereas the relative Hurwicz/step degree (rHD/rSD), still being accurate numerically, sometimes is more reasonable intuitively and has larger potential in further studies and practical applications.

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Some properties and representation methods for Ordered Weighted Averaging operators

Cited by 31 publications

References 33 publications

On Obtaining Piled OWA Operators

On Obtaining Piled OWA Operators

Fuzzy orness measure and new orness axioms

S-H OWA Operators with Moment Measure

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