S-H OWA Operators with Moment Measure

Wang, Jian; Merigó, José M.; Jin, LeSheng

doi:10.1002/int.21829

Cited by 25 publications

(33 citation statements)

References 36 publications

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“…However, only entropy itself cannot reflect all the properties of an OWA weighting vector, because we remember that OWA weights are scattered on a linearly ordered domain. The recently introduced concepts of Moment, HD/SD, and RHD/RSD help us to recognize the OWA weights from another side. On the other hand, the OWA distance is another very important characteristic of OWA operators.…”

Section: Review Of Three Major Characteristics Of Owa Operatorsmentioning

confidence: 99%

“…A useful normalization of this measure is:

D (w) = disp (w) / ln (n)

and then

D (w) \in [0, 1]

. Definition (Moment) For any OWA operator of dimension n ,

w = (w_{1}, w_{2}, \dots, w_{n})

with its andness degree α, its Moment (M) is defined as follows:

0true M (w) = \sum_{i = 1}^{n} ((), w_{i} \cdot (||, \frac{i - 1}{n - 1} - α))

Remark An equivalent definition using orness degree can be written as: For any OWA operator of dimension n ,

w = (w_{1}, w_{2}, \dots, w_{n})

with orness degree

α^{'} = 1 - α

, its Moment is defined as follows:

0true M^{'} (w) = \sum_{i = 1}^{n} ((), w_{i} \cdot (||, \frac{n - i}{n - 1} - α^{'}))

Definition For any OWA operator of dimension n ,

w = (w_{1}, w_{2}, \dots, w_{n})

with its andness degree α, the Left Moment (LM) is defined as follows:

0true L M

…”

Section: Review Of Three Major Characteristics Of Owa Operatorsmentioning

confidence: 99%

“…such that

\frac{t - 1}{n - 1} \leq α

and

\frac{t}{n - 1} > α

. Definition For any OWA operator of dimension n ,

w = (w_{1}, w_{2}, \dots, w_{n})

with its andness degree α, the Right Moment (RM) is defined by:

0true R M (w) = \sum_{i = t + 1}^{n} ((), w_{i} \cdot (||, \frac{i - 1}{n - 1} - α))

…”

Section: Review Of Three Major Characteristics Of Owa Operatorsmentioning

confidence: 99%

“…such that

\frac{t - 1}{n - 1} \leq α

and

\frac{t}{n - 1} > α

. Proposition For any OWA operators of dimension n,

w = (w_{1}, w_{2}, \dots, w_{n})

with andness degree α, we have

M (w) = L M (w) + R M (w)

. Example Given OWA operator

w = (0.15, 0.3, 0.15, 0.4)

with andness degree 0.6, its Moment, LM and RM are, respectively, as follow:

\begin{matrix} true \\ right M false(boldw false) = \sum_{i = 1}^{4} (w_{i} \cdot |\frac{i - 1}{n - 1} - 0.6|) & = & left (0.15) \cdot 0.6 + (0.3) \cdot ((), 0.6 - \frac{1}{3}) + (0.15) \cdot ((), \frac{2}{3} - 0.6) \\ left + false(0.4 false) \cdot false(1 - 0.6 false) \\ = & left 0.09 + 0.08 + 0.01 + 0.16 = 0.34 . \end{matrix}

…”

Section: Review Of Three Major Characteristics Of Owa Operatorsmentioning

confidence: 99%

See 3 more Smart Citations

On some characteristics and related properties for OWF and RIM quantifier

Wang

Kalina

Mesiar

et al. 2018

Int. J. Intell. Syst.

Self Cite

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Regular Increasing Monotone (RIM) quantifier and Ordered Weighted Function are important counterparts of discrete ordered weighted averaging operators. Some important characteristics such as entropy, Moment, and Step/Hurwicz degree have already been proposed and studied by several researchers. The main propose of this paper is to put the concepts of entropy, Moment, and Step/Hurwicz degree for RIM quantifier into a continuous environment. Some well‐defined representative families of RIM quantifiers are also presented. The metric spaces of RIM quantifiers are discussed.

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Section: Review Of Three Major Characteristics Of Owa Operatorsmentioning

confidence: 99%

“…A useful normalization of this measure is:

D (w) = disp (w) / ln (n)

and then

D (w) \in [0, 1]

. Definition (Moment) For any OWA operator of dimension n ,

w = (w_{1}, w_{2}, \dots, w_{n})

with its andness degree α, its Moment (M) is defined as follows:

0true M (w) = \sum_{i = 1}^{n} ((), w_{i} \cdot (||, \frac{i - 1}{n - 1} - α))

Remark An equivalent definition using orness degree can be written as: For any OWA operator of dimension n ,

w = (w_{1}, w_{2}, \dots, w_{n})

with orness degree

α^{'} = 1 - α

, its Moment is defined as follows:

0true M^{'} (w) = \sum_{i = 1}^{n} ((), w_{i} \cdot (||, \frac{n - i}{n - 1} - α^{'}))

Definition For any OWA operator of dimension n ,

w = (w_{1}, w_{2}, \dots, w_{n})

with its andness degree α, the Left Moment (LM) is defined as follows:

0true L M

…”

Section: Review Of Three Major Characteristics Of Owa Operatorsmentioning

confidence: 99%

“…such that

\frac{t - 1}{n - 1} \leq α

and

\frac{t}{n - 1} > α

. Definition For any OWA operator of dimension n ,

w = (w_{1}, w_{2}, \dots, w_{n})

with its andness degree α, the Right Moment (RM) is defined by:

0true R M (w) = \sum_{i = t + 1}^{n} ((), w_{i} \cdot (||, \frac{i - 1}{n - 1} - α))

…”

Section: Review Of Three Major Characteristics Of Owa Operatorsmentioning

confidence: 99%

“…such that

\frac{t - 1}{n - 1} \leq α

and

\frac{t}{n - 1} > α

. Proposition For any OWA operators of dimension n,

w = (w_{1}, w_{2}, \dots, w_{n})

with andness degree α, we have

M (w) = L M (w) + R M (w)

. Example Given OWA operator

w = (0.15, 0.3, 0.15, 0.4)

with andness degree 0.6, its Moment, LM and RM are, respectively, as follow:

\begin{matrix} true \\ right M false(boldw false) = \sum_{i = 1}^{4} (w_{i} \cdot |\frac{i - 1}{n - 1} - 0.6|) & = & left (0.15) \cdot 0.6 + (0.3) \cdot ((), 0.6 - \frac{1}{3}) + (0.15) \cdot ((), \frac{2}{3} - 0.6) \\ left + false(0.4 false) \cdot false(1 - 0.6 false) \\ = & left 0.09 + 0.08 + 0.01 + 0.16 = 0.34 . \end{matrix}

…”

Section: Review Of Three Major Characteristics Of Owa Operatorsmentioning

confidence: 99%

See 2 more Smart Citations

On some characteristics and related properties for OWF and RIM quantifier

Wang

Kalina

Mesiar

et al. 2018

Int. J. Intell. Syst.

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is worth noting that the choice of the weight distribution has generated a large literature (in the case of OWA operators, see, for instance, Llamazares, Liu, Wang, and Bai).…”

mentioning

confidence: 99%

SUOWA operators: A review of the state of the art

Llamazares

2018

Int J Intell Syst

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SUOWA operators are a particular case of Choquet integral that simultaneously generalize weighted means and OWA operators. Because they are constructed by using normalized capacities, they possess properties such as continuity, monotonicity, idempotency, compensativeness, and homogeneity of degree 1. Besides these ones, some articles published in recent years have shown that SUOWA operators also exhibit other interesting properties. So, we think that the time has come to summarize existing knowledge of these operators. The aim of this paper is to collect the main results obtained so far on SUOWA operators. Moreover, we also introduce some new results and illustrate the usefulness of SUOWA operators by using an example given by Beliakov (2018).

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A Review on Piezoelectric, Magnetostrictive, and Magnetoelectric Materials and Device Technologies for Energy Harvesting Applications

2017

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In the coming era of the internet of things (IoT), wireless sensor networks that monitor, detect, and gather data will play a crucial role in advancements in public safety, human healthcare, industrial automation, and energy management. Batteries are currently the power source of choice for operating wireless network devices due to their ease of installation; however, they require periodic replacement due to capacity limitations. Within the scope of the IoT, battery maintenance of the trillion sensor nodes that may be implemented will be practically infeasible from environmental, resource, and labor cost perspectives. In considering individual self-powered sensor nodes, the idea of harvesting energy from ambient vibrations, heat, and electromagnetic waves has recently triggered noticeable research interest in the academic community. This paper gives an overview of energy harvesting materials and systems. Three main categories are presented: piezoelectric ceramics/polymers, magnetostrictive alloys, and magnetoelectric (ME) multiferroic composites. State-of-the-art harvesting materials and structures are presented with a focus on characterization, fabrication, modeling and simulation, and durability and reliability. Some perspectives and challenges for the future development of energy harvesting materials are also highlighted.

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S-H OWA Operators with Moment Measure

Cited by 25 publications

References 36 publications

On some characteristics and related properties for OWF and RIM quantifier

On some characteristics and related properties for OWF and RIM quantifier

SUOWA operators: A review of the state of the art

A Review on Piezoelectric, Magnetostrictive, and Magnetoelectric Materials and Device Technologies for Energy Harvesting Applications

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