An analytic approach to obtain the least square deviation OWA operator weights

Sang, Xiuzhi; Liu, Xinwang

doi:10.1016/j.fss.2013.08.007

Cited by 37 publications

(18 citation statements)

References 32 publications

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“…It is an important issue to the application and theory of OWA operators to determine the weights of the operators. Previous studies have proposed a number of approaches for obtaining the associated weights in different areas such as date mining, decision making, neural networks, approximate reasoning, expert systems, fuzzy system and control [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. A number of approaches have been proposed for the identification of associated weights, including exponential smoothing [6], quantifier guided aggregation [19,20] and learning [20].…”

Section: Introductionmentioning

confidence: 99%

The General Least Square Deviation OWA Operator Problem

Hong

Han

2019

Mathematics

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A crucial issue in applying the ordered weighted averaging (OWA) operator for decision making is the determination of the associated weights. This paper proposes a general least convex deviation model for OWA operators which attempts to obtain the desired OWA weight vector under a given orness level to minimize the least convex deviation after monotone convex function transformation of absolute deviation. The model includes the least square deviation (LSD) OWA operators model suggested by Wang, Luo and Liu in Computers & Industrial Engineering, 2007, as a special class. We completely prove this constrained optimization problem analytically. Using this result, we also give solution of LSD model suggested by Wang, Luo and Liu as a function of n and α completely. We reconsider two numerical examples that Wang, Luo and Liu, 2007 and Sang and Liu, Fuzzy Sets and Systems, 2014, showed and consider another different type of the model to illustrate our results.

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Section: Introductionmentioning

confidence: 99%

The General Least Square Deviation OWA Operator Problem

Hong

Han

2019

Mathematics

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“…Merigó presented the probabilistic weighted average operator and the probabilistic OWA (POWA) operator, respectively. The method of Lagrange multipliers to determine the optimal weighting vector was proposed by Sang and Liu . Note also that there are several generalizations of the OWA operators, such as weighted OWA (WOWA) operator, induced OWA operator, generalized OWA operator, POWA operator, and so on.…”

Section: Introductionmentioning

confidence: 99%

Elliptical distribution-based weight-determining method for ordered weighted averaging operators

2018

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The ordered weighted averaging (OWA) operators play a crucial role in aggregating multiple criteria evaluations into an overall assessment supporting the decision makers’ choice. One key point steps is to determine the associated weights. In this paper, we first briefly review some main methods for determining the weights by using distribution functions. Then we propose a new approach for determining OWA weights by using the regular increasing monotone quantifier. Motivated by the idea of normal distribution‐based method to determine the OWA weights, we develop a method based on elliptical distributions for determining the OWA weights, and some of its desirable properties have been investigated.

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“…Ahn presented four analytic forms of OWA operator weighting functions to generate the OWA weights. Sang and Liu discussed the analytic approach to determine the least‐square deviation OWA operator weights. The most popular method is to obtain the desired weights under a given

italicorness

level, which is usually formulated as a constrained optimization problem .…”

Section: Introductionmentioning

confidence: 99%

Monotonic argument-dependent OWA operators

Zeng

2018

Int. J. Intell. Syst.

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The ordered weighted averaging (OWA) operator introduced by Yager is one of the most popular aggregation technique. In this paper, we develop two kinds of argument‐dependent OWA (DOWA) operators including the pessimistic‐dependent OWA (PE‐DOWA) operator and optimistic‐dependent OWA (OP‐DOWA) operator, that point out that the PE‐DOWA operator is decreasing and the OP‐DOWA operator is increasing, and investigate some properties of our proposed monotonic DOWA operators in detail. Furthermore, we introduce the concept of original function in which a gradient vector generates the weights of the PE‐DOWA and OP‐DOWA operators. Meanwhile, we propose two classes of original functions including summing‐type original function and multiplying‐type original function and investigate the sufficient monotonic conditions for the DOWA operators generated by the original functions. Finally, we discuss the characteristics and properties of our proposed DOWA operators in detail and use a numerical example to illustrate the flexibility of our proposed operators.

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An analytic approach to obtain the least square deviation OWA operator weights

Cited by 37 publications

References 32 publications

The General Least Square Deviation OWA Operator Problem

The General Least Square Deviation OWA Operator Problem

Elliptical distribution-based weight-determining method for ordered weighted averaging operators

Monotonic argument-dependent OWA operators

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