scholarly journals The General Model for Least Convex Disparity RIM Quantifier Problems

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 576
Author(s):  
Dug Hun Hong
Keyword(s):  
Least Squares ◽  
General Model ◽  
Least Square ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Ordered Weighted Averaging ◽  
Full Solution

Hong (Mathematics 2019, 7, 326) recently introduced the general least squares deviation (LSD) model for ordered weighted averaging (OWA) operator weights. In this paper, we propose the corresponding generalized least square disparity model for regular increasing monotone (RIM) quantifier determination under a given orness level. We prove this problem mathematically. Using this result, we provide the full solution of the least square disparity RIM quantifier model as an illustrative example.

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 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.

scholarly journals Three Ways of Defining Owa Operator on the Set of All Normal Convex Fuzzy Sets

2017 ◽  
Vol 69 (1) ◽  
pp. 101-118
Author(s):  
Zdenko Takáč
Keyword(s):  
Fuzzy Sets ◽  
Linear Order ◽  
Recent Literature ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Main Obstacle ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Algebraic Properties

Abstract We deal with an extension of ordered weighted averaging (OWA, for short) operators to the set of all normal convex fuzzy sets in [0, 1]. The main obstacle to achieve this goal is the non-existence of a linear order for fuzzy sets. Three ways of dealing with the lack of a linear order on some set and defining OWA operators on the set appeared in the recent literature. We adapt the three approaches for the set of all normal convex fuzzy sets in [0, 1] and study their properties. It is shown that each of the three approaches leads to operator with desired algebraic properties, and two of them are also linear.

scholarly journals The General Least Square Deviation OWA Operator Problem

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 326 ◽  
Author(s):  
Dug Hong ◽  
Sangheon Han
Keyword(s):  
Optimization Problem ◽  
Weight Vector ◽  
Least Square ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Crucial Issue ◽  
Absolute Deviation ◽  
Owa Operators ◽  
Operator Problem

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.

scholarly journals Enhancing Edge Attack Strategy via an OWA Operator-Based Ensemble Design in Real-World Networks

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 830
Author(s):  
Yuan Feng ◽  
Baoan Ren ◽  
Chengyi Zeng ◽  
Yuyuan Yang ◽  
Hongfu Liu
Keyword(s):  
Real World ◽  
Similarity Index ◽  
Structural Similarity ◽  
Experimental Results ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Structural Similarity Index ◽  
Ordered Weighted Averaging ◽  
Long Time ◽  
Attack Strategy

Network disintegration has been an important research hotspot in complex networks for a long time. From the perspective of node attack, researchers have devoted to this field and carried out numerous works. In contrast, the research on edge attack strategy is insufficient. This paper comprehensively evaluates the disintegration effect of each structural similarity index when they are applied to the weighted-edge attacks model. Experimental results show that the edge attack strategy based on a single similarity index will appear limited stability and adaptability. Thus, motivated by obtaining a stable disintegration effect, this paper designs an edge attack strategy based on the ordered weighted averaging (OWA) operator. Through final experimental results, we found that the edge attack strategy proposed in this paper not only achieves a more stable disintegration effect on eight real-world networks, but also significantly improves the disintegration effect when applied on a single network in comparison with the original similarity index.

On the OWA Aggregation with Probabilistic Inputs

2015 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 143-162 ◽  
Author(s):  
Ronald R. Yager
Keyword(s):  
Stochastic Dominance ◽  
Probability Distributions ◽  
Decision Problems ◽  
Weighted Averaging ◽  
Linear Ordering ◽  
Owa Operator ◽  
Dominance Relationship ◽  
Ordered Weighted Averaging ◽  
The Individual ◽  
The Relationship

We discuss the use of the ordered weighted averaging (OWA) operator in multi-criteria decision problems as a means of aggregating the individual criteria satisfactions. We emphasize the need for ordering the arguments, the criteria satisfactions, when using the OWA operator. We consider the situation where the criteria satisfactions have some uncertainty, are finite probability distributions and note the requirement of having to order probability distributions. We introduce the idea of using pairwise stochastic dominance to provide the necessary ordering relationship over the probability distributions. We note that while this approach is appropriate, it is often not possible, since the presence of a stochastic dominance relationship between all pairs of probability distributions is not always the case, the relationship is not complete. To circumvent this problem we introduce an approach called the probabilistic exceedance method (PEM), which allows us to provide a surrogate for the OWA aggregation of probability distributions that doesn't require a linear ordering over the probability distributions. We look at this in both the cases in which the criteria have equal and unequal importances.

scholarly journals An approach to obtain the generalized mixed linear stress function for known owa weights with artificial bee colony algorithm

2017 ◽  
Vol 6 (3) ◽  
pp. 150-157
Author(s):  
Efsun Coşkun ◽  
Resmiye Nasiboglu ◽  
Baris Tekin Tezel
Keyword(s):  
Stress Function ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Piecewise Linear ◽  
Decision Function ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Ordered Weighted Averaging ◽  
Bee Colony

Abstract OWA (Ordered Weighted Averaging) is a flexible aggregation operator which is come up with Yager to create a decision function in multi-criteria decision making. It is possible to determine how optimistic or pessimistic the decision maker's opinion with the value obtained from the weights of this operator. The determination of OWA weights cannot provide characterization by itself. If it is desired to aggregate various sized objects in terms of generalization and reusability of OWA weights, a more general form is needed. In this study, we propose the parameterized piecewise linear stress function and the approach to characterize OWA weights. The stress function is expressed by parameters which are obtained by artificial bee colony algorithm. Also the weights are approximately found by using parameters. Keywords – OWA operator, aggregation, artificial bee colony algorithm.

scholarly journals Model Sistem Pendukung Keputusan Kelompok untuk Penilaian Gangguan Depresii, Kecemasan dan Stress Berdasarkan DASS-42

2020 ◽  
Vol 7 (2) ◽  
pp. 219
Author(s):  
Sri Kusumadewi ◽  
Hepi Wahyuningsih
Keyword(s):  
Decision Maker ◽  
Preference Relation ◽  
Decision Makers ◽  
Stress Disorders ◽  
Weighted Averaging ◽  
Group Decision Support System ◽  
Owa Operator ◽  
Depression And Anxiety ◽  
Test Results ◽  
Ordered Weighted Averaging

<p>Depresi, kecemasan dan stress merupakan tiga gangguan yang sering dijumpai di masyarakat. Ketiga gangguan tersebut memiliki gejala yang hampir mirip. <em>Depression, Anxiety and Stress Scales</em> (DASS) merupakan salah satu alat ukur yang dapat digunakan untuk mengukur tingkat keparahan ketiga gangguan tersebut. DASS dengan jumlah item/gejala sebanyak 42 item dikenal dengan nama DASS-42. Alat ukut ini membedakan dengan jelas item/gejala dari setiap gangguan. Setiap gangguan memiliki item yang mempengaruhi sebanyak 14 item. Pada penelitian ini dibangun model Sistem Pendukung Keputusan Kelompok (SPKK) yang memungkinkan para psikolog untuk berkolaborasi memberikan preferensi terkait prioritas gangguan yang akan terjadi apabila diketahui item/gejala tertentu menurut DASS-42. Preferensi diberikan dengan format <em>ordered vectors</em>. Untuk memudahkan proses agregasi/komposisi, selanjutnya dilakukan transformasi preferensi ke relasi preferensi fuzzy. Operator <em>Ordered Weighted Averaging</em> (OWA) digunakan untuk melakukan agregasi peferensi menjadi satu matriks. Proses seleksi alternatif terbaik dilakukan dengan menggunakan <em>Quantifier Guided Dominance Degree</em> (QGDD). Hasil pengujian menunjukkan bahwa ketepatan hasil SPKK terhadap DASS-42 adalah sebesar 71,43% (30 dari 42 item/gejala). Item/gejala yang beririsan secara signifikan antara gangguan kecemasan dan stress sebesar 16,67%. (7 dari 42), antara depresi dan kecemasan sebesar 9,52% (4 dari 42). Secara umum SPKK ini mampu mengakomodasi preferensi para pengambil keputusan dalam memberikan bobot pengaruh. Gangguan kecemasan dan gangguan stress memiliki gejala yang sangat mirip sehingga untuk beberapa item.gejala pada DASS-42 ada perbedaan yang cukup signifikan.</p><p> </p><p><em><strong>Abstract</strong></em></p><p class="Abstract"><em>Depression, anxiety and stress are three disorders that are often found in the community. These three disorders have almost identical symptoms. Depression, Anxiety and Stress Scales (DASS) is an psychological instrument that can be used to measure the severity of these disorders. DASS with a total of 42 items known as DASS-42. This instrument distinguishes clearly the symptoms of each disorder. Each disorder has 14 items affect. The three disorders have a number of symptoms that are similar, even a symptom may affect two or three disorders with different levels of influence. In this study, a Group Decision Support System (GDSS) model was developed so that psychologists can collaborate to give preference regarding priority of disorders that would occur if certain items / symptoms were identified by  DASS-42. Preferences are given in ordered vectors format. The preferences given by each decision maker aggregated to get a single preference. These preferences will be transformed to the fuzzy preference relation format. Ordered Weighted Averaging (OWA) operator used to aggregation process for all decision maker preference. The OWA operator are used to aggregate into one matrix. The best alternative selected by using Quantifier Guided Dominance Degree (QGDD). The test results show that the accuracy of the GDSS results on DASS-42 is 71.43% (30 of 42 items / symptoms). Symptoms that overlap significantly between anxiety and stress disorders are 16.67%. (7 of 42), between depression and anxiety by 9.52% (4 of 42). The GDSS is able to accommodate the preferences of decision makers in giving influence weight. Anxiety and stress disorder have very similar symptoms so that for some symptoms in the DASS-42 there are significant differences.</em></p><p><em><strong><br /></strong></em></p>

Human Focused Summarizing Statistics Using OWA Operators

2010 ◽  
pp. 238-253
Author(s):  
Ronald R. Yager
Keyword(s):  
Generating Functions ◽  
Large Data ◽  
Large Data Sets ◽  
Weighted Averaging ◽  
Data Sets ◽  
Owa Operator ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Data Analyst ◽  
Computer Aided

The ordered weighted averaging (OWA) operator is introduced and the author discusses how it can provide a basis for generating summarizing statistics over large data sets. The author further notes how different forms of OWA operators, and hence different summarizing statistics, can be induced using weight-generating functions. The author shows how these weight-generating functions can provide a vehicle with which a data analyst can express desired summarizing statistics. Modern data analysis requires the use of more human focused summarizing statistics then those classically used. The author’s goal here is to develop to ideas to enable a human focused approach to summarizing statistics. Using these ideas we can envision a computer aided construction of the weight generating functions based upon a combination of graphical and linguistic specifications provided by a data analyst describing his desired summarization.

A Modified OWA Operator and its Use in Lossless DPCM Image Compression

1997 ◽  
Vol 05 (04) ◽  
pp. 429-436 ◽  
Author(s):  
H. B. Mitchell ◽  
D. D. Estrakh
Keyword(s):  
Image Compression ◽  
Weighted Averaging ◽  
Fundamental Aspect ◽  
Owa Operator ◽  
Lossless Image Compression ◽  
Ordered Weighted Averaging ◽  
Relative Value

The ordered weighted averaging (OWA) operator of Yager was introduced to provide a method for aggregating several inputs which lies between the Max and Min operators. The fundamental aspect of the OWA operator is a reordering step in which the input arguments are re-arranged according to their actual relative value. In this paper we describe a modified OWA operator in which the input arguments are not re-arranged according to their actual relative values but rather according to their estimated relative values. We describe an unusual application of this operator to lossless image compression.

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