Continuous parameterized families of RIM quantifiers and quasi-preference with some properties

Pu, Xingting; Jin, LeSheng; Mesiar, Radko; Yager, Ronald R.

doi:10.1016/j.ins.2018.12.068

Cited by 21 publications

(13 citation statements)

References 27 publications

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“…In general, large orness of an OWA weight vector indicates more optimistic attitude of decision maker, and vice versa. If the concerned OWA weight vectors form a continuous family of OWA weight vectors, 31 then the OWA operator with an OWA weight vector having a larger orness surely obtains a larger aggregation result than that having a smaller orness. The orness/andness is strictly defined as a mapping in the following.…”

Section: Some Reviews and Discussion About Aggregation Functions Owa Operators And Iowa Operatorsmentioning

confidence: 99%

GnIOWA operators and some weights allocation methods with their properties

et al. 2021

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This study proposes some standard and general forms of induced ordered weighted averaging (GnIOWA) operators where the inductive information is ordered weighted averaging (OWA) weight vectors instead of real numbers. It shows the usefulness of such type of generalized induced OWA in decision‐making and evaluation and many other applications. We propose three weights allocation methods that are specifically designed for the proposed GnIOWA operators. For each of the proposed weights allocation methods, a numerical example is also attached accordingly. With the use of convex/concave Regular Increasing Monotone quantifiers, we further discuss some mathematical properties of these weights allocation methods.

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Section: Some Reviews and Discussion About Aggregation Functions Owa Operators And Iowa Operatorsmentioning

confidence: 99%

GnIOWA operators and some weights allocation methods with their properties

et al. 2021

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“…Next, we review the standard definitions related to the space of parameterized OWA weight vectors (of dimension r) and a partial ordering relation on it. Definition 2.3 [13] For any OWA weight function w (r) ∈ W (r) , an associated function ⃗ w (r) ∶ {1, ..., r} → [0, 1] such that ⃗ w (r) (i) = ∑ i j=1 w (r) (j) is called the accumulation function of w (r) . Definition 2.4 [13] Given…”

Section: Some Definitions For Dealing With Heterogeneous Evaluation Informationmentioning

confidence: 99%

“…Definition 2.3 [13] For any OWA weight function w (r) ∈ W (r) , an associated function ⃗ w (r) ∶ {1, ..., r} → [0, 1] such that ⃗ w (r) (i) = ∑ i j=1 w (r) (j) is called the accumulation function of w (r) . Definition 2.4 [13] Given…”

Section: Some Definitions For Dealing With Heterogeneous Evaluation Informationmentioning

confidence: 99%

“…Recall that aggregation operators [10,11] have been widely applied in evaluation and information fusion, and the related theories have been fast developed during the last few decades [11][12][13][14][15]. A type of well-known aggregation operators used in MCDM include weighted average, geometrical weighted average, and weighted harmonic mean [10], etc.…”

Section: Introductionmentioning

confidence: 99%

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Consistent Construction of Evaluation Threshold Values and Rules for Heterogeneous Linguistic Input Information

Qian

Zhang

Chen

et al. 2021

Int J Comput Intell Syst

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This study firstly proposes a simpler method for evaluating one certain object’s quality with multiple criteria according to some preset evaluation threshold values that are real numbers. In real life, numerous individual valuations are provided with distributional linguistic input information and with multiple criteria, and thus they can become heterogeneous. Against this background, by using OWA weight functions we propose an extended setting and some methods to generate distributional evaluation threshold values which are suitable for the corresponding thresholds-based evaluation method. Some special definitions and formulations are also well provided with necessary analyses and comments. A numerical example of reservoir evaluation and effect are also illustrated.

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“…Scholars have developed extended variants of OWA aggregation, such as induced OWA (IOWA) aggregation and weighted OWA (WOWA) aggregation . Furthermore, many methods for generating weights have appeared, including regular increasing monotone (RIM)‐based weights generation and optimization‐based weight generation, further providing the feasibility of OWA aggregation for more applications. Scholars have also proposed several generalized mathematical expressions of OWA aggregation .…”

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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Continuous parameterized families of RIM quantifiers and quasi-preference with some properties

Cited by 21 publications

References 27 publications

GnIOWA operators and some weights allocation methods with their properties

GnIOWA operators and some weights allocation methods with their properties

Consistent Construction of Evaluation Threshold Values and Rules for Heterogeneous Linguistic Input Information

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

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