GENERALIZED MOVING AVERAGES, DISTANCE MEASURES AND OWA OPERATORS

2013 ◽  
Vol 21 (04) ◽  
pp. 533-559 ◽  
Author(s):  
JOSÉ M. MERIGÓ ◽  
RONALD R. YAGER
Keyword(s):  
Moving Average ◽  
Aggregation Operators ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Wide Range ◽  
Moving Averaging ◽  
Generalized Distance ◽  
Weighted Moving Average

The concept of moving average is studied. We analyze several extensions by using generalized aggregation operators, obtaining the generalized moving average. The main advantage is that it provides a general framework that includes a wide range of specific cases including the geometric and the quadratic moving average. This analysis is extended by using the generalized ordered weighted averaging (GOWA) and the induced GOWA (IGOWA) operator. Thus, we get the generalized ordered weighted moving average (GOWMA) and the induced GOWMA (IGOWMA) operator. Some of their main properties are studied. We further extend this approach by using distance measures suggesting the concept of distance moving average and generalized distance moving average. We also consider the case with the OWA and the IOWA operator, obtaining the generalized ordered weighted moving averaging distance (GOWMAD) and the induced GOWMAD (IGOWMAD) operator. The paper ends with an application in multi-period decision making.

scholarly journals A method for decision making with the OWA operator

2012 ◽  
Vol 9 (1) ◽  
pp. 357-380 ◽  
Author(s):  
José Merigó ◽  
Anna Gil-Lafuente
Keyword(s):  
Decision Making ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Minimum Level ◽  
Ordered Weighted Averaging ◽  
Special Cases ◽  
Wide Range ◽  
Decision Making Problem ◽  
Parameterized Family

A new method for decision making that uses the ordered weighted averaging (OWA) operator in the aggregation of the information is presented. It is used a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index is based on distance measures and other techniques that are useful for decision making. By using the OWA operator in the IMAM, we form a new aggregation operator that we call the ordered weighted averaging index of maximum and minimum level (OWAIMAM) operator. The main advantage is that it provides a parameterized family of aggregation operators between the minimum and the maximum and a wide range of special cases. Then, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. A further extension of this approach is presented by using hybrid averages and Choquet integrals. We also develop an application of the new approach in a multi-person decision-making problem regarding the selection of strategies.

OWA aggregation with dual preferences for basic uncertain information

2021 ◽  
pp. 1-10
Author(s):  
LeSheng Jin ◽  
Ronald R. Yager ◽  
Jana Špirková ◽  
Radko Mesiar ◽  
Daniel Paternain ◽  
...  
Keyword(s):  
Decision Makers ◽  
Input Vector ◽  
Weighted Averaging ◽  
Preference Aggregation ◽  
Uncertain Information ◽  
Interval Vector ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Wide Range ◽  
Original Information

Basic Uncertain Information (BUI) as a newly introduced concept generalized a wide range of uncertain information. The well-known Ordered Weighted Averaging (OWA) operators can flexibly and effectively model bipolar preferences of decision makers over given real valued input vector. However, there are no extant methods for OWA operators to be carried out over given BUI vectors. Against this background, this study firstly discusses the interval transformation for BUI and elaborately explains the reasonability within it. Then, we propose the corresponding preference aggregations for BUI in two different decisional scenarios, the aggregation for BUI vector without original information influencing and the aggregation for BUI vector with original information influencing after interval transformation. For each decisional scenario, we also discuss two different orderings of preference aggregation, namely, interval-vector and vector-interval orderings, respectively. Hence, we will propose four different aggregation procedures of preference aggregation for BUI vector. Some illustrative examples are provided immediately after the corresponding aggregation procedures.

scholarly journals Linguistic Weighted Aggregation under Confidence Levels

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Chonghui Zhang ◽  
Weihua Su ◽  
Shouzhen Zeng ◽  
Linyun Zhang
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
New Approach ◽  
Confidence Levels ◽  
Ordered Weighted Averaging ◽  
Special Cases ◽  
Wide Range ◽  
Information Providers

We develop some new linguistic aggregation operators based on confidence levels. Firstly, we introduce the confidence linguistic weighted averaging (CLWA) operator and the confidence linguistic ordered weighted averaging (CLOWA) operator. These two new linguistic aggregation operators are able to consider the confidence level of the aggregated arguments provided by the information providers. We also study some of their properties. Then, based on the generalized means, we introduce the confidence generalized linguistic ordered weighted averaging (CGLOWA) operator. The main advantage of the CGLOWA operator is that it includes a wide range of special cases such as the CLOWA operator, the confidence linguistic ordered weighted quadratic averaging (CLOWQA) operator, and the confidence linguistic ordered weighted geometric (CLOWG) operator. Finally, we develop an application of the new approach in a multicriteria decision-making under linguistic environment and illustrate it with a numerical example.

scholarly journals Some Generalized Dependent Aggregation Operators with Interval-Valued Intuitionistic Fuzzy Information and Their Application to Exploitation Investment Evaluation

2013 ◽  
Vol 2013 ◽  
pp. 1-24 ◽  
Author(s):  
Xiao-wen Qi ◽  
Chang-yong Liang ◽  
Junling Zhang
Keyword(s):  
Aggregation Operators ◽  
Weighted Averaging ◽  
Weighting Method ◽  
Intuitionistic Fuzzy Numbers ◽  
Investment Evaluation ◽  
Ordered Weighted Averaging ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Wide Range ◽  
Interval Valued

We investigate multiple attribute group decision making (MAGDM) problems with arguments taking the form of interval-valued intuitionistic fuzzy numbers. In order to relieve influence of unfair arguments, a Gaussian distribution-based argument-dependent weighting method and a hybrid support-function-based argument-dependent weighting method are devised by, respectively, measuring support degrees of arguments indirectly and directly, based on which the Gaussian generalized interval-valued intuitionistic fuzzy ordered weighted averaging operator (Gaussian-GIIFOWA) and geometric operator (Gaussian-GIIFOWG), the power generalized interval-valued intuitionistic fuzzy ordered weighted averaging (P-GIIFOWA) operator and geometric (P-GIIFOWA) operator are proposed to generalize a wide range of aggregation operators for decision makers to flexibly choose in decision modelling. And some desirable properties of the proposed operators are also analyzed. Further, application of an approach integrating proposed operators to exploitation investment evaluation of tourist spots has shown the effectiveness and practicality of developed methods; experimental results also verify the properties of proposed operators.

The OWA distance operator and its application in business failure

Kybernetes ◽  
2017 ◽  
Vol 46 (1) ◽  
pp. 114-130 ◽  
Author(s):  
Valeria Scherger ◽  
Antonio Terceño ◽  
Hernán Vigier
Keyword(s):  
Decision Making ◽  
Hamming Distance ◽  
Decision Rules ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Business Failure ◽  
Content Type ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Alternative Measures

Purpose The purpose of this paper is to develop a goodness index based on Hamming distance and ordered weighted averaging distance (OWAD), which is useful to make decisions. These alternative measures enrich the results of diagnostic fuzzy models and facilitate the experts’ task in decision-making. An application to a set of firms to verify the results is also presented. Design/methodology/approach The paper follows the basis of OWA operators to design a methodology to reduce the map of causes of business failure into monitoring key areas. Findings The present paper introduces two alternative measures to test the proposal of grouping. In the empirical application, the superiority of the minimum T-norm over other decision rules is verified. The ordered weighted averaging distance (OWAD) goodness index predicts a better adjustment over the index built using OWA and Hamming distance measures. Practical implications A useful mechanism to reduce the map of causes or diseases detected in key areas is added through this analysis. At the same time, these key areas can be disaggregated once some alert indicator is identified; this allows knowing the causes that require special attention. This application of OWA can encourage the development of suitable computer systems for monitoring the firm’s problems, alerting regarding failures and easing decision-making. Originality/value A comparison of grouping causes into key areas through a goodness index based on Hamming distance and OWAD is proposed. These contributions enrich the Vigier and Terceño (2008) model and could be applied to any model of fuzzy diagnosis to test the results.

scholarly journals DECISION MAKING IN THE ASSIGNMENT PROCESS BY USING THE HUNGARIAN ALGORITHM WITH OWA OPERATORS

2015 ◽  
Vol 21 (5) ◽  
pp. 684-704 ◽  
Author(s):  
Emili VIZUETE-LUCIANO ◽  
José M. MERIGÓ ◽  
Anna M. GIL-LAFUENTE ◽  
Sefa BORIA-REVERTER
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Arithmetic Means ◽  
Owa Operators ◽  
Hungarian Algorithm ◽  
Assignment Algorithm ◽  
Wide Range ◽  
Decision Making Problem ◽  
Parameterized Family

Assignment processes permit to coordinate two set of variables so each variable of the first set is connected to another variable of the second set. This paper develops a new assignment algorithm by using a wide range of aggregation operators in the Hungarian algorithm. A new process based on the use of the ordered weighted averaging distance (OWAD) operator and the induced OWAD (IOWAD) operator in the Hungarian algorithm is introduced. We refer to it as the Hungarian algorithm with the OWAD operator (HAOWAD) and the Hungarian algorithm with the IOWAD operator (HAIOWAD). The main advantage of this approach is that we can provide a parameterized family of aggregation operators between the minimum and the maximum. Thus, the information can be represented in a more complete way. Furthermore, we also present a general framework by using generalized and quasi-arithmetic means. Therefore, we can consider a wide range of particular cases including the Euclidean and the Minkowski distance. The paper ends with a practical application of the new approach in a financial decision making problem regarding the assignment of investments.

scholarly journals A Study of OWA Operators Learned in Convolutional Neural Networks

2021 ◽  
Vol 11 (16) ◽  
pp. 7195
Author(s):  
Iris Dominguez-Catena ◽  
Daniel Paternain ◽  
Mikel Galar
Keyword(s):  
Neural Networks ◽  
Convolutional Neural Networks ◽  
Practical Method ◽  
Local Information ◽  
Weighted Averaging ◽  
Global Information ◽  
Owa Operator ◽  
Owa Operators ◽  
Ordered Weighted Averaging

Ordered Weighted Averaging (OWA) operators have been integrated in Convolutional Neural Networks (CNNs) for image classification through the OWA layer. This layer lets the CNN integrate global information about the image in the early stages, where most CNN architectures only allow for the exploitation of local information. As a side effect of this integration, the OWA layer becomes a practical method for the determination of OWA operator weights, which is usually a difficult task that complicates the integration of these operators in other fields. In this paper, we explore the weights learned for the OWA operators inside the OWA layer, characterizing them through their basic properties of orness and dispersion. We also compare them to some families of OWA operators, namely the Binomial OWA operator, the Stancu OWA operator and the exponential RIM OWA operator, finding examples that are currently impossible to generalize through these parameterizations.

scholarly journals Triangular Cubic Hesitant Fuzzy Einstein Hybrid Weighted Averaging Operator and Its Application to Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 658 ◽  
Author(s):  
Aliya Fahmi ◽  
Fazli Amin ◽  
Florentin Smarandache ◽  
Madad Khan ◽  
Nasruddin Hassan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Linguistic Information ◽  
Ordered Weighted Averaging ◽  
Averaging Operator ◽  
Multiple Attribute ◽  
The Relationship

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making with linguistic information is developed based on the TCHFEWA and the TCHFEHWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the existing aggregation operators. Finally, a numerical example is provided to demonstrate the application of the established approach.

scholarly journals Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators With New Distance Measures

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 280 ◽  
Author(s):  
Harish Garg ◽  
Gagandeep Kaur
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Weight Vector ◽  
Aggregation Operators ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Maximum Deviation ◽  
Dual Hesitant Fuzzy Set ◽  
Deviation Method

Probabilistic dual hesitant fuzzy set (PDHFS) is an enhanced version of a dual hesitant fuzzy set (DHFS) in which each membership and non-membership hesitant value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. By emphasizing the advantages of the PDHFS and the aggregation operators, in this manuscript, we have proposed several weighted and ordered weighted averaging and geometric aggregation operators by using Einstein norm operations, where the preferences related to each object is taken in terms of probabilistic dual hesitant fuzzy elements. Several desirable properties and relations are also investigated in details. Also, we have proposed two distance measures and its based maximum deviation method to compute the weight vector of the different criteria. Finally, a multi-criteria group decision-making approach is constructed based on proposed operators and the presented algorithm is explained with the help of the numerical example. The reliability of the presented decision-making method is explored with the help of testing criteria and by comparing the results of the example with several prevailing studies.

scholarly journals Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information

2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Muhammad Akram ◽  
Naveed Yaqoob ◽  
Ghous Ali ◽  
Wathek Chammam
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Ordered Weighted Averaging ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Electre I ◽  
Geometric Operator

An m-polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The m-polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under the m-polar fuzzy environment with the help of Dombi norm operations. In this article, we develop some averaging and geometric aggregation operators using Dombi t-norm and t-conorm to handle uncertainty in m-polar fuzzy (mF, henceforth) information, which are mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid averaging (mFDHA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi weighted ordered geometric operator, and mF Dombi hybrid geometric (mFDHG) operator. We investigate properties, namely, idempotency, monotonicity, and boundedness, for the proposed operators. Moreover, we give an algorithm to solve multicriteria decision-making issues which involve mF information with mFDWA and mFDWG operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with mF-ELECTRE-I approach (Akram et al. 2019) and mF Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test.

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