Learning Weights in the Generalized OWA Operators

Beliakov, Gleb

doi:10.1007/s10700-004-5868-3

Cited by 84 publications

(33 citation statements)

References 29 publications

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“…For more information on other families, see (Ahn and Park 2008;Beliakov 2005;Beliakov et al 2007;Emrouznejad 2008;Liu 2008;Merigó 2008;Xu 2005;Yager 1993;1996;2007).…”

Section: The Owa Operatormentioning

confidence: 99%

Decision Making With Distance Measures and Induced Aggregation Operators

Merigó

Casanovas

2008

Computational Intelligence in Decision and Control

128

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Abstract:We present a new decision-making approach that uses distance measures and induced aggregation operators. We introduce the induced ordered weighted averaging distance (IOWAD) operator, a new aggregation operator that extends the OWA operator by using distance measures and a reordering of the arguments that depends on order-inducing variables. The main advantage of the IOWAD is that it provides a parameterized family of distance aggregation operators between the maximum and the minimum distance based on a complex reordering process that reflects a complex attitudinal character of the decision-maker. We study some of its main properties and particular cases. We develop an application in a decision-making problem regarding the selection of investments. We see that the main advantage of this approach in decision-making is that it is able to provide a more complete picture of the decision process, so the decision-maker is able to select the alternative most in accordance with his interests.Keywords: Decision-making, OWA operator, Hamming distance, Induced aggregation operators. JEL Classification: C44, C49, D81, D89.Resumen: Se presenta un nuevo modelo para la toma de decisiones basado en el uso de medidas de distancia y de operadores de agregación inducidos. Se introduce la distancia media ponderada ordenada inducida (IOWAD). Es un nuevo operador de agregación que extiende el operador OWA a través del uso de distancias y un proceso de reordenación de los argumentos basado en variables de ordenación inducidas. La principal ventaja el operador IOWAD es la posibilidad de utilizar una familia parametrizada de operadores de agregación entre la distancia individual máxima y la mínima. Se estudian algunas de sus principales propiedades y algunos casos particulares. Se desarrolla un ejemplo numérico en un problema de toma de decisiones sobre selección de inversiones. Se observa que la principal ventaja de este modelo en la toma de decisiones es la posibilidad de mostrar una visión más completa del proceso, de forma que el decisor está capacitado para seleccionar la alternativa que está más cerca de sus intereses.3

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“…For more information on other families, see (Ahn and Park 2008;Beliakov 2005;Beliakov et al 2007;Emrouznejad 2008;Liu 2008;Merigó 2008;Xu 2005;Yager 1993;1996;2007).…”

Section: The Owa Operatormentioning

confidence: 99%

Decision Making With Distance Measures and Induced Aggregation Operators

Merigó

Casanovas

2008

Computational Intelligence in Decision and Control

128

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“…While simple rules of thumb have been used for this purpose so far (see e.g. [7,58]), a more systematic study of their generation is mandatory, e.g., by using learning methods as proposed in [3,19,55]. This study is left for future research.…”

Section: Discussionmentioning

confidence: 99%

“…However, we adopt the terminology of [43]. 3 In [43], Mieszkowicz-Rolka and Rolka only defined the inclusion errors for a non-empty fuzzy set A. We extend their definition to include the empty set, in order to allow the use of a general binary fuzzy relation R in Definition 4.…”

Section: Definition 4 (Seementioning

confidence: 99%

A comprehensive study of implicator–conjunctor-based and noise-tolerant fuzzy rough sets: Definitions, properties and robustness analysis

D'eer

Verbiest

Cornelis

et al. 2015

Fuzzy Sets and Systems

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Both rough and fuzzy set theories offer interesting tools for dealing with imperfect data: while the former allows us to work with uncertain and incomplete information, the latter provides a formal setting for vague concepts. The two theories are highly compatible, and since the late 1980s many researchers have studied their hybridization. In this paper, we critically evaluate most relevant fuzzy rough set models proposed in the literature. To this end, we establish a formally correct and unified mathematical framework for them. Both implicator-conjunctor-based definitions and noise-tolerant models are studied. We evaluate these models on two different fronts: firstly, we discuss which properties of the original rough set model can be maintained and secondly, we examine how robust they are against both class and attribute noise. By highlighting the benefits and drawbacks of the different fuzzy rough set models, this study appears a necessary first step to propose and develop new models in future research.

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“…Its fundamental aspect is a reordering step in which the input arguments are rearranged in descending order and the weighting vector is merely associated with its ordered position. Since it was proposed in 1988, the OWA operator has been widely used in decision making under uncertainty, including expert systems, neural networks, fuzzy systems and controls [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Based on the geometric mean, Xu and Yager [15] developed the ordered weighted geometric (OWG) operator to aggregate the arguments in a similar way as the OWA operator.…”

Section: Introductionmentioning

confidence: 99%

Induced Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet integral operators and their application in decision making

Meng¹,

Cheng²,

Zhang³

2014

IJCIS

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Based on the Choquet integral and the generalized Shapley function, two new induced -valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley -valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley -valued intuitionistic fuzzy hybrid Choquet geometric mean (IGS-IVIFHCGM) operator. These operators do not only globally consider the importance of elements and their ordered positions, but also overall reflect the correlations among them and their ordered positions. Meantime, some important cases are examined, and some desirable properties are studied. Furthermore, if the information about the weighting vectors is incompletely known, the models for the optimal fuzzy measures on attribute set and ordered set are established, respectively. Moreover, an approach to multi-attribute decision making under -valued intuitionistic fuzzy environment is developed. Finally, a numerical example is provided to illustrate the proposed procedure.

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Learning Weights in the Generalized OWA Operators

Cited by 84 publications

References 29 publications

Decision Making With Distance Measures and Induced Aggregation Operators

Decision Making With Distance Measures and Induced Aggregation Operators

A comprehensive study of implicator–conjunctor-based and noise-tolerant fuzzy rough sets: Definitions, properties and robustness analysis

Induced Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet integral operators and their application in decision making

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