OWA Operator Research Articles

Induced OWA operators in linear regression

Induced OWA operators in linear regression

On the relationships between some games associated with SUOWA and Semi-SUOWA operators

The construction of functions that simultaneously generalize weighted means and OWA operators is an interesting topic that has received special attention in recent years. Due to the properties they satisfy, one of the most interesting generalization are SUOWA operators, which have been widely studied in the literature. In a recent paper, a new generalization has been introduced, the Semi-SUOWA operators, which have a close relationship with SUOWA operators. The main aim of this paper is to analyze the games associated with Semi-SUOWA operators. In this respect, we give conditions under which we can guarantee the monotonicity of these games. Moreover, we establish some relationships between some games associated with SUOWA and Semi-SUOWA operators and show the pointwise convergence of certain games.

The Distance Induced OWA Operator with Application to Multi-criteria Group Decision Making

Some aggregation operators with distance measures have been proposed, but distance measure values play the role of argument variables. In this paper, the induced ordered weighted averaging (IOWA) operator with the Hamming distance is proposed, termed as the distance induced ordered weighted averaging (DIOWA) operator. The most distinctive characteristic of the DIOWA operator is that the distance measure values play the role of order-inducing variables. Some properties and special cases of the DIOWA operator are analyzed. This new operator is further extended to the uncertain situations represented by interval numbers. A new multi-criteria group decision-making (MCGDM) method with the proposed operators in this paper is also studied. Finally, a numerical example about how to select the best candidate is given to show how to use the DIOWA operator with interval numbers in group decision making.

A Hybrid Recommender System According to the Genre of Movies Using OWA Operator

A Hybrid Recommender System According to the Genre of Movies Using OWA Operator

(1901-4946) On the use of Heronian means in a similarity classifier

This paper introduces new similarity classi fiers using the Heronian mean, and the generalized Heronian mean operators.We examine the use of these operators at the aggregation step within the similarity classifi er. The similarity classifi er was earlier studied with other operators, in particular with an arithmetic mean, generalized mean, OWA operators, andmany more. The two classi fiers here are tested on four real world data sets, i.e., echocardiogram, fertility, horse-colic, and lung cancer. Three previously studied similarity classi fiers are used as benchmarks to the new approaches. Weobserve that the similarity classi er with a generalized Heronian mean produces good classi cation results for the tested data sets, and is therefore more suitable for use in these classi fication problems.

Predicting the future price of a commodity using the OWMA operator: An approximation of the interest rate and inflation in the brown pastusa potato price

This main aim of this paper is to propose a methodology for the prediction of the future price of the brown pastusa potato in Colombia, taking into consideration the variables of interest rate, as measured by fixed term deposits (FTDs), and inflation rate, as measured by the consumer price index (CPI). The methodology conducts linear regression analysis and assesses the results using the significance test, the Durbin-Watson statistic, analysis of the variance inflation factor (VIF) and the coefficient of determination. After that, the forecast of the independent variables has been conducted with the ordered weighted moving average (OWMA) operator and new proposed OWA operators using probabilities that are presented in the paper. Using these new methods and the proposed econometric model, it is possible to establish future prices. The results show a greater impact of the interest rate than inflation, as well as the need to include supply and demand variables that have not been included due to the absence of systematic information.

Quantile‐induced vector‐based heavy OWA operator and the application in dynamic decision making

To the incentive problems in dynamic decision making, we propose a new type of aggregation operator denoted the quantile-induced vector-based heavy ordered weighted averaging (QI-VHOWA) operator. The main characteristic of the operator is that the arguments are aggregated using the form of vector. Additionally, the decision maker's incentive expectation is integrated into the aggregation process by various segmented incentive coefficients. We calculate the quantile measures of the argument vectors based on the technique for order of preference by similarity to ideal solution method. We determine the QI-VHOWA weighting vector by considering the location position of an alternative's performance as well as the development trend. The primary properties of the operator are discussed, including commutativity, boundness, and monotonicity under certain conditions. Finally, a numerical example regarding the evaluation of employees' performances in multiple periods is provided. The results are compared with that of the vector-based OWA and vector-based weighted arithmetic averaging operators. It is found that the incentive effectiveness of the QI-VHOWA is the most significant. The use of the QI-VHOWA operator is helpful to guide the long-term development of an alternative.

On fractional continuous weighted OWA (FCWOWA) operator with applications

In order statistics, CWOWA operator in real line based on Choquet integral was recently introduced by Narukawa et al. (Ann Oper Res 244(2):571–581, 2016). Recently, the relation of Choquet integral with fractional integral on a continuous support was recently discussed by Sugeno (IEEE Trans Fuzzy Syst 23:1439–1457, 2015). As an open problem, Sugeno emphasized that “it is necessary to consider fractional Choquet integral with respect to any monotone measures”. This reason permit us to consider this problem and introduce the fractional Choquet integral with respect to any monotone measures. We also introduce the fractional CWOWA operator (FCWOWA) which includes CWOWA and WOWA operators as special cases. As an application, we also present some important inequalities for FCWOWA operator.

Scalable Approximate FRNN-OWA Classification

Fuzzy rough nearest neighbor classification with ordered weighted averaging operators (FRNN-OWA) is an algorithm that classifies unseen instances according to their membership in the fuzzy upper and lower approximations of the decision classes. Previous research has shown that the use of OWA operators increases the robustness of this model. However, calculating membership in an approximation requires a nearest neighbor search. In practice, the query time complexity of exact nearest neighbor search algorithms in more than a handful of dimensions is near linear, which limits the scalability of FRNN-OWA. Therefore, we propose approximate FRNN-OWA, a modified model that calculates upper and lower approximations of decision classes using the approximate nearest neighbors returned by hierarchical navigable small worlds (HNSW), a recent approximative nearest neighbor search algorithm with logarithmic query time complexity at constant near-100% accuracy. We demonstrate that approximate FRNN-OWA is sufficiently robust to match the classification accuracy of exact FRNN-OWA while scaling much more efficiently. We test four parameter configurations of HNSW and evaluate their performance by measuring classification accuracy and construction and query times for samples of various sizes from three large datasets. We find that with two of the parameter configurations, approximate FRNN-OWA achieves near-identical accuracy to exact FRNN-OWA for most sample sizes within query times that are up to several orders of magnitude faster.

River Water Quality Assessment Model and Application Based on OWA Operator

River Water Quality Assessment Model and Application Based on OWA Operator

Aggregation of pragmatic operators to support probabilistic linguistic multi-criteria group decision-making problems

In this paper, a multi-attribute group decision-making method based on aggregation operators is presented to solve the decision-making problems which the evaluation values take the form of probabilistic linguistic terms sets (PLTSs). Firstly, some properties of the PLTS are defined, such as the concept and the linguistic terms transformation function, the existing comparison methods and the proposed score function and distance. Secondly, some novel operators are proposed by combining the Heronian mean operator with the centered OWA operator and the power average operator under probabilistic linguistic environment, such as the probabilistic linguistic weighted centered order weighted generalized Heronian mean operator and the probabilistic linguistic weighted power generalized Heronian mean operator. Thirdly, the model of deriving the criteria weight is put forward based on the ideology of deviation maximizing and customized individual attitudinal. Furthermore, based on the proposed aggregation operators and EDAS method, a scientific group decision-making procedure is put forward under probabilistic linguistic environment. Finally, an illustrative example is also given to demonstrate the feasibility and practicality of the proposed method.

A Dynamic Decision Making Method Based on GM(1,1) Model with Pythagorean Fuzzy Numbers for Selecting Waste Disposal Enterprises

With the rapid development of society and the economy, most cities have to face a serious problem of “Garbage Siege”. The garbage classification is imperative because the traditional disposal method for household solid waste is not suitable for this situation. The Chinese government proposed a public private partnership (PPP) style to increase the efficiency of garbage disposal in 2013. An effective method to evaluate the waste disposal enterprises is essential to choose suitable ones. A reasonable evaluation method should consider enterprises’ performance not only now but also in the future. This paper aims to propose a dynamic decision making method to evaluate the enterprises’ performance based on a GM(1,1) model and regret theory with Pythagorean fuzzy numbers (PFNs). First, we proposed a GM(1,1) model for predicting score function of PFNs. Then, we put forward a method to obtain the prediction of grey degree using OWA operator. Based on the prediction of score function and grey degree, we established a novel GM(1,1) model of PFNs. Furthermore, we utilized the grey incidence method to obtain the criteria weights with Pythagorean fuzzy information. We used the regret theory to aggregate information and rank the alternatives. Finally, we applied our proposed method to solve the selecting waste disposal enterprises problem in Shanghai. By the case study we can obtain that our method is effective to solve this problem.

Orness for real m-dimensional interval-valued OWA operators and its application to determine a good partition

ABSTRACTOrdered Weighted Averaging (OWA) operators are a profusely applied class of averaging aggregation functions, i.e. operators that always yield a value between the minimum and the maximum of the inputs. The orness measure was introduced to classify the behavior of the OWA operators depending on the weight vectors. Defining a suitable orness measure is an arduous task when we deal with OWA operators defined over more intricate spaces, such us intervals or lattices. In this work we propose a suitable definition for the orness measure to classify OWA operators defined on the set of m-dimensional intervals taking real values in . The orness measure is applied to decide which is the best partition of a continuous range that should be divided into four linguistic labels. This example shows the good behavior of the proposed orness measure.

On Scatters of Probability Distributions and OWA Weights Collections

This study proposes a novel concept of Scatter for probability distribution (on [0,1]). The proposed measurement is different from famous Shannon Entropy since it considers [0,1] as a chain instead of a normal set. The measurement works easily and reasonably in practice and conforms to human intuition. Some interesting properties like symmetricity, translation invariance, weak convergence and concavity of this new measurement are also obtained. The measurement also has good potential in more theoretical studies and applications. The novel concept can also be suitably adapted for discrete OWA operators and RIM quantifiers. We then propose a new measurement, the Preference Scatter, with its normalized form, the Normalized Preference Scatter, for OWA weights collections. We analyze its reasonability as a new measurement for OWA weights collections with comparisons to some other measurements like Orness, Normalized Dispersion and Hurwicz Degree of OWA operators. In addition, the corresponding Preference Scatter for RIM quantifiers is defined.

The Interval-Valued Choquet Integral Based on Admissible Permutations

Aggregation or fusion of interval data is not a trivial task, since the necessity of arranging data arises in many aggregation functions, such as OWA operators or the Choquet integral. Some arranging procedures have been given to solve this problem, but they need certain parameters to be set. In order to solve this problem, we propose the concept of an admissible permutation of intervals. Based on this concept, which avoids any parameter selection, we propose a new approach for the interval-valued Choquet integral that takes into account every possible permutation fitting to the considered ordinal structure of data. Finally, a consensus among all the permutations is constructed.

IOWA-SVM: A Density-Based Weighting Strategy for SVM Classification via OWA Operators

A weighting strategy for handling outliers in binary classification using support vector machine (SVM) is proposed in this article. The traditional SVM model is modified by introducing an induced ordered weighted averaging (IOWA) operator, in which the hinge loss function becomes an ordered weighted sum of the SVM slack variables. These weights are defined using IOWA quantifiers, while the order is induced via fuzzy density-based methods for outlier detection. The proposal is developed for both linear and kernel-based classification using the duality theory and the kernel trick. Our experimental results on well known benchmark datasets demonstrate the virtues of the proposed IOWA-SVM, which achieved the best average performance compared to other machine learning approaches of similar complexity.

A new vector valued similarity measure for intuitionistic fuzzy sets based on OWA operators

Plenty of researches have been carried out, focusing on the measures of distance, similarity, and correlation between intuitionistic fuzzy sets (IFSs).However, most of them are single-valued measures and lack of potential for efficiency validation.In this paper, a new vector valued similarity measure for IFSs is proposed based on OWA operators.The vector is defined as a two-tuple consisting of the similarity measure and uncertainty measure, in which the latter is the uncertainty of the former.OWA operators have the ability to aggregate all values in the universe of discourse of IFSs, and to determine the weights according to specific applications.A framework is built to measure similarity between IFSs.A series of definitions and theorems are given and proved to satisfy the corresponding axioms defined for IFSs.In order to illustrate the effectiveness of the proposed vector valued similarity measure,a classification problem is used as an application.

Multi-person and multi-criteria decision making with the induced probabilistic ordered weighted average distance

This paper presents a new approach for selecting suppliers of products or services, specifically with respect to complex decisions that require evaluating different business characteristics to ensure their suitability and to meet the conditions defined in the recruitment process. To address this type of problem, this study presents the multi-person multi-criteria induced ordered weighted average distance (MP-MC-IOWAD) operator, which is an extension of the OWA operators that includes the notion of distances to multiple criteria and expert valuations. Thus, this work introduces new distance measures that can aggregate the information with probabilistic information and consider the attitudinal character of the decision maker. Further extensions are developed using probabilities to form the induced probabilistic ordered weighted average distance (IPOWAD) operator. An example in the management of insurance policies is presented, where the selection of insurance companies is very complex and requires the consideration of subjective criteria by experts in decision making.

A multidistance based on generalized OWA operator and its application in power average operator

A multidistance based on generalized OWA operator and its application in power average operator

Heavy Owa Operator of Generalized Octagonal Intuitionistic Fuzzy Numbers in Fuzzy Game

Heavy Owa Operator of Generalized Octagonal Intuitionistic Fuzzy Numbers in Fuzzy Game