Stancu OWA Operator

Singh, Amit Kumar; Kishor, Arun; Pal, Nikhil R.

doi:10.1109/tfuzz.2014.2336696

Cited by 16 publications

(14 citation statements)

References 45 publications

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“…As the generalization form of binomial OWA operators and even Hurwicz OWA operators, Stancu OWA operators can have more variation in the possible Hurwicz‐like extent, though with much more complex mathematical structures.…”

Section: The S‐h Owa Operators Derived By Some Known Mathematical Resmentioning

confidence: 99%

“…The Stancu OWA operators are defined as follows: For an OWA operator of dimension i ,

u^{(i)} = (u_{i 1}, u_{i 2}, ..., u_{i i})

( i = 1, 2, …), if its weights satisfy the condition (an empty product denotes 1)

u_{i j} = \frac{(\begin{matrix} left i - 1 \\ left i - j \end{matrix}) \prod_{s = 0}^{i - j - 1} (t + s α) \prod_{s = 0}^{j - 2} (1 - t + s α)}{\prod_{s = 0}^{i - 2} (1 + s α)}

with

t \in [0, 1]

α \geq 0

being two parameters, then it is called a Stancu OWA operator .…”

Section: The S‐h Owa Operators Derived By Some Known Mathematical Resmentioning

confidence: 99%

“…It is important that the orness of Stancu OWA operators is just the parameter t irrespective of α(

α \geq 0

) and dimension i ( i = 1, 2, …). It is also very significant that average OWA operators, binomial OWA operators, and Hurwicz OWA operators are special cases of Stancu OWA operators with parameters

(t = 0, 5; α = 0.5)

(t = o r n e s s; α = 0)

and

(t = o r n e s s; α = + \infty)

, respectively …”

Section: The S‐h Owa Operators Derived By Some Known Mathematical Resmentioning

confidence: 99%

“…There are many theories about this type that can be found in some part of Yager's decision theory involving preferences and some aggregation functions studies . For example, the well‐known ordered weighted averaging (OWA) operator has been widely used in a large variety of areas and applications . We have known that OWA operators can effectively model and generalize many cognitive concepts such as maximum, minimum, and average of an input arguments set.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: The S‐h Owa Operators Derived By Some Known Mathematical Resmentioning

confidence: 99%

“…The Stancu OWA operators are defined as follows: For an OWA operator of dimension i ,

u^{(i)} = (u_{i 1}, u_{i 2}, ..., u_{i i})

( i = 1, 2, …), if its weights satisfy the condition (an empty product denotes 1)

u_{i j} = \frac{(\begin{matrix} left i - 1 \\ left i - j \end{matrix}) \prod_{s = 0}^{i - j - 1} (t + s α) \prod_{s = 0}^{j - 2} (1 - t + s α)}{\prod_{s = 0}^{i - 2} (1 + s α)}

with

t \in [0, 1]

α \geq 0

being two parameters, then it is called a Stancu OWA operator .…”

Section: The S‐h Owa Operators Derived By Some Known Mathematical Resmentioning

confidence: 99%

“…It is important that the orness of Stancu OWA operators is just the parameter t irrespective of α(

α \geq 0

) and dimension i ( i = 1, 2, …). It is also very significant that average OWA operators, binomial OWA operators, and Hurwicz OWA operators are special cases of Stancu OWA operators with parameters

(t = 0, 5; α = 0.5)

(t = o r n e s s; α = 0)

and

(t = o r n e s s; α = + \infty)

, respectively …”

Section: The S‐h Owa Operators Derived By Some Known Mathematical Resmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

S-H OWA Operators with Moment Measure

Wang

Merigó

Jin

2016

Int. J. Intell. Syst.

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show abstract

“…Researchers have separately extended OWA aggregation to work in particular environments with inputs that are nonreal numbers . Other recent OWA aggregation developments include the significant Crescent method and the Stancu OWA operator . With the continuous theoretical innovations, widespread application of OWA aggregation techniques has been witnessed in recent years …”

Section: Introductionmentioning

confidence: 99%

Nested formulation paradigms for induced ordered weighted averaging aggregation for decision‐making and evaluation

et al. 2019

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Existing extensions to Yager's ordered weighted averaging (OWA) operators enlarge the application range and to encompass more principles and properties related to OWA aggregation. However, these extensions do not provide a strict and convenient way to model evaluation scenarios with complex or grouped preferences. Based on earlier studies and recent evolutionary changes in OWA operators, we propose formulation paradigms for induced OWA aggregation and a related weight function with self-contained properties that make it possible to model such complex preference-involved evaluation problems in a systematic way. The new formulations have some recursive forms that provide more ways to apply OWA aggregation and deserve further study from a mathematical perspective. In addition, the new proposal generalizes almost all of the well-known extensions to the original OWA operators. We provide an example showing the representative use of such paradigms in decision-making and evaluation problems. K E Y W O R D S aggregation function, decision aiding model, decision-making, evaluation, induced ordered weighted averaging operator, ordered weighted averaging operator

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A Framework for Triangular Fuzzy Random Multiple-Criteria Decision Making

Chen

Chin

2015

Int. J. Fuzzy Syst.

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Stancu OWA Operator

Cited by 16 publications

References 45 publications

S-H OWA Operators with Moment Measure

S-H OWA Operators with Moment Measure

Nested formulation paradigms for induced ordered weighted averaging aggregation for decision‐making and evaluation

A Framework for Triangular Fuzzy Random Multiple-Criteria Decision Making

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