Similarity classifier with ordered weighted averaging operators

In this article we extend the similarity classifier to cover also ordered weighted averaging (OWA) operators. Earlier, similarity classifier was mainly used with generalized mean operator, but in this article we extend this aggregation process to cover more general OWA operators. With OWA operators we concentrate on linguistic quantifier guided aggregation where several different quantifiers are studied and on how they best suite for the similarity classifier. Our proposed method is applied to real world medical data sets which are new thyroid, hypothyroid, lymphography and hepatitis data sets. Results are very promising and show improvement compared to the earlier used generalized mean operator. In this article we will show that by using OWA operators instead of generalized mean, we can improve classification accuracy with chosen data sets.     

Maximum Bayesian entropy method for determining ordered weighted averaging operator weights

Determination of the ordered weighted averaging (OWA) operators is an important issue in the theory of the OWA operator weights. In this paper, the main existing models for determining the OWA operator weights are outlined and the concept of the Bayesian entropy is introduced. Based upon the Bayesian entropy the maximum Bayesian entropy approach for obtaining the OWA operator weights is proposed. In this model it is assumed, according to previous experiences or from theoretical considerations that a decision maker may have reasons to consider a given prior OWA vector. Finally the new model is solved according to the prior OWA vector with specific level of orness comparing the results with other methods. The results demonstrate the efficiency of our model in generating the OWA operator weights. An applied example is also presented to illustrate the applications of the proposed model.     

A New Family of Induced OWA Operators

A new family of induced ordered weighted averaging (OWA) operators is proposed by invoking the order‐inducing variables at the aggregation step. The objective is to consider the variations in the magnitudes of the order‐inducing variables. The new family of operators include weighted induced OWA, weighted generalized induced OWA, and weighted induced ordered weighted geometric operators. These are further extended to the intuitionistic fuzzy domain. The usefulness of these operators is shown in a supplier selection problem.     

基于改进属性加权的朴素贝叶斯分类模型

构造了一种新的属性间相关性度量方法,提出了改进属性加权的朴素贝叶斯分类模型。经实验证明,提出的朴素贝叶斯分类模型明显优于张舜仲等人提出的分类模型。     

A class of aggregation functions encompassing two-dimensional OWA operators

In this paper we prove that, under suitable conditions, Atanassov’s K_α operators, which act on intervals, provide the same numerical results as OWA operators of dimension two. On one hand, this allows us to recover OWA operators from K_α operators. On the other hand, by analyzing the properties of Atanassov’s operators, we can generalize them. In this way, we introduce a class of aggregation functions - the generalized Atanassov operators - that, in particular, include two-dimensional OWA operators. We investigate under which conditions these generalized Atanassov operators satisfy some properties usually required for aggregation functions, such as bisymmetry, strictness, monotonicity, etc. We also show that if we apply these aggregation functions to interval-valued fuzzy sets, we obtain an ordered family of fuzzy sets.     

Constructing Choquet integral-based operators that generalize weighted means and OWA operators

In this paper we introduce the semi-uninorm based ordered weighted averaging (SUOWA) operators, a new class of aggregation functions that, as WOWA operators, simultaneously generalize weighted means and OWA operators. To do this we take into account that weighted means and OWA operators are particular cases of Choquet integral. So, SUOWA operators are Choquet integral-based operators where their capacities are constructed by using semi-uninorms and the values of the capacities associated to the weighted means and the OWA operators. We also show some interesting properties of these new operators and provide examples showing that SUOWA and WOWA operators are different classes of aggregation operators.     

On Obtaining Piled OWA Operators

In this study, we propose the concept of piled ordered weighted averaging (OWA) operators, which generalize the centered OWA operators and also connect the step OWA operators with the Hurwicz OWA operators with given the orness degree. We propose a controllable algorithm to generate the family of piled OWA operators depending on their predefined three parameters: orness degree, step‐like or Hurwicz‐like degree, and the numbers of “supporting” vectors. By these preferences, we can generate infinite more piled OWA operators with miscellaneous forms, and each of them is similar to the well‐known binomial OWA operator, which is very useful but only has one form corresponding to one given orness degree.     

Bonferroni Distances and Their Application in Group Decision Making

Abstract

The aim of the paper is to develop new aggregation operators using Bonferroni means, ordered weighted averaging (OWA) operators and some distance measures. We introduce the Bonferroni-Hamming weighted distance (BON-HWD), Bonferroni OWA distance (BON-OWAD), Bonferroni OWA adequacy coefficient (BON-OWAAC) and Bonferroni distances with OWA operators and weighted averages (BON-IWOWAD). The main advantages of using these operators are that they allow the consideration of different aggregations contexts to be considered and multiple comparison between each argument and distance measures in the same formulation. An application is developed using these new algorithms in combination with Pichat algorithm to solve a group decision-making problem. Creative personality is taken as an example for forming creative groups. The results show fuzzy dissimilarity relations in order to establish the maximum similarity subrelations and find groups according to each individual’s creative personality similarities.     

基于高斯核函数的朴素贝叶斯分类器依赖扩展

朴素贝叶斯分类器不能有效地利用属性之间的依赖信息, 而目前所进行的依赖扩展更强调效率, 使扩展后分类器的分类准确性还有待提高. 针对以上问题, 在使用具有平滑参数的高斯核函数估计属性密度的基础上, 结合分类器的分类准确性标准和属性父结点的贪婪选择, 进行朴素贝叶斯分类器的网络依赖扩展. 使用UCI 中的连续属性分类数据进行实验, 结果显示网络依赖扩展后的分类器具有良好的分类准确性.

     

The Metric Space of Ordered Weighted Average Operators with Distance Based on Accumulated Entries

Ordered weighted average (OWA) operators with their weighting vectors are very important in many applications. We show that directly taking Minkowski distances (including Manhattan distance and Euclidean distance) as the distances for any two OWA operator is not reasonable. In this study, we propose the standard distance measures for any two OWA operators and then propose a standard metric space for the set of all n‐dimension OWA operators. We analyze and discuss some properties of the introduced OWA metric and further propose a metric space of Choquet integrals represented by the underlying fuzzy measures. Some applications in decision making of OWA distances are also presented in this study.     

Bayesian network classifiers for mineral potential mapping

In this paper, we describe three Bayesian classifiers for mineral potential mapping: (a) a naive Bayesian classifier that assumes complete conditional independence of input predictor patterns, (b) an augmented naive Bayesian classifier that recognizes and accounts for conditional dependencies amongst input predictor patterns and (c) a selective naive classifier that uses only conditionally independent predictor patterns. We also describe methods for training the classifiers, which involves determining dependencies amongst predictor patterns and estimating conditional probability of each predictor pattern given the target deposit-type. The output of a trained classifier determines the extent to which an input feature vector belongs to either the mineralized class or the barren class and can be mapped to generate a favorability map. The procedures are demonstrated by an application to base metal potential mapping in the proterozoic Aravalli Province (western India). The results indicate that although the naive Bayesian classifier performs well and shows significant tolerance for the violation of the conditional independence assumption, the augmented naive Bayesian classifier performs better and exhibits finer generalization capability. The results also indicate that the rejection of conditionally dependent predictor patterns degrades the performance of a naive classifier.     

A Study of AdaBoost with Naive Bayesian Classifiers: Weakness and Improvement

This article investigates boosting naive Bayesian classification. It first shows that boosting does not improve the accuracy of the naive Bayesian classifier as much as we expected in a set of natural domains. By analyzing the reason for boosting's weakness, we propose to introduce tree structures into naive Bayesian classification to improve the performance of boosting when working with naive Bayesian classification. The experimental results show that although introducing tree structures into naive Bayesian classification increases the average error of the naive Bayesian classification for individual models, boosting naive Bayesian classifiers with tree structures can achieve significantly lower average error than both the naive Bayesian classifier and boosting the naive Bayesian classifier, providing a method of successfully applying the boosting technique to naive Bayesian classification. A bias and variance analysis confirms our expectation that the naive Bayesian classifier is a stable classifier with low variance and high bias. We show that the boosted naive Bayesian classifier has a strong bias on a linear form, exactly the same as its base learner. Introducing tree structures reduces the bias and increases the variance, and this allows boosting to gain advantage.     

The uncertain induced quasi‐arithmetic OWA operator

We present the uncertain induced quasi‐arithmetic OWA (Quasi‐UIOWA) operator. It is an extension of the OWA operator that uses the main characteristics of the induced OWA (IOWA), the quasi‐arithmetic OWA (Quasi‐OWA) and the uncertain OWA (UOWA) operator. Thus, this generalization uses quasi‐arithmetic means, order inducing variables in the reordering process and uncertain information represented by interval numbers. A key feature of the Quasi‐UIOWA operator is that it generalizes a wide range of aggregation operators such as the uncertain quasi‐arithmetic mean, the uncertain weighted quasi‐arithmetic mean, the UOWA, the uncertain weighted generalized mean, the uncertain induced generalized OWA (UIGOWA), the Quasi‐UOWA, the uncertain IOWA, the uncertain induced ordered weighted geometric (UIOWG), and the uncertain induced ordered weighted quadratic averaging (UIOWQA) operator. We study some of the main properties of this approach including how to obtain a wide range of particular cases. We further generalize the Quasi‐UIOWA operator by using discrete Choquet integrals. We end the article with an application of the new approach in a decision making problem about investment selection. © 2010 Wiley Periodicals, Inc.     

Learning and Revising User Profiles: The Identification of Interesting Web Sites

We discuss algorithms for learning and revising user profiles that can determine which World Wide Web sites on a given topic would be interesting to a user. We describe the use of a naive Bayesian classifier for this task, and demonstrate that it can incrementally learn profiles from user feedback on the interestingness of Web sites. Furthermore, the Bayesian classifier may easily be extended to revise user provided profiles. In an experimental evaluation we compare the Bayesian classifier to computationally more intensive alternatives, and show that it performs at least as well as these approaches throughout a range of different domains. In addition, we empirically analyze the effects of providing the classifier with background knowledge in form of user defined profiles and examine the use of lexical knowledge for feature selection. We find that both approaches can substantially increase the prediction accuracy.     

From quantitative to qualitative orness for lattice OWA operators

This paper deals with OWA (ordered weighted average) operators defined on an arbitrary finite lattice endowed with a t-norm and a t-conorm. A qualitative orness measure for any OWA operator is suggested, based on its proximity to the OR operator that yields the maximum of the given data. In the particular case of a finite distributive lattice, considering the t-norm given by the meet and the t-conorm given by the join, this qualitative measure agrees with the value that some discrete Sugeno integral takes on the vector consisting of all the members of the lattice. Some applications of the qualitative orness of OWA operators to decision-making problems are shown. In addition, OWA operators defined on a finite product lattice are also applied in image processing. We analyze the effect of several OWA operators with respect to their orness.     

Fuzzy induced generalized aggregation operators and its application in multi-person decision making

We present a wide range of fuzzy induced generalized aggregation operators such as the fuzzy induced generalized ordered weighted averaging (FIGOWA) and the fuzzy induced quasi-arithmetic OWA (Quasi-FIOWA) operator. They are aggregation operators that use the main characteristics of the fuzzy OWA (FOWA) operator, the induced OWA (IOWA) operator and the generalized (or quasi-arithmetic) OWA operator. Therefore, they use uncertain information represented in the form of fuzzy numbers, generalized (or quasi-arithmetic) means and order inducing variables. The main advantage of these operators is that they include a wide range of mean operators such as the FOWA, the IOWA, the induced Quasi-OWA, the fuzzy IOWA, the fuzzy generalized mean and the fuzzy weighted quasi-arithmetic average (Quasi-FWA). We further generalize this approach by using Choquet integrals, obtaining the fuzzy induced quasi-arithmetic Choquet integral aggregation (Quasi-FICIA) operator. We also develop an application of the new approach in a strategic multi-person decision making problem.     

Generalized prioritized aggregation operators

This paper deals with multicriteria decision‐making problems in which the criteria are partitioned into q categories, and a prioritization relationship exists over categories. We aggregate the criteria in the same priority category by a weighted OWA (ordered weighted averaging) operator and introduce two averaging operators, a generalized prioritized averaging operator and a generalized prioritized OWA operator. In the case with one criterion in each priority category, the two operators reduce to the prioritized averaging operator and the prioritized OWA operator as proposed by Yager. © 2012 Wiley Periodicals, Inc.     

Heavy Moving Averages and Their Application in Econometric Forecasting

This paper presents the heavy ordered weighted moving average (HOWMA) operator. It is an aggregation operator that uses the main characteristics of two well-known techniques: the heavy ordered weighted averaging (OWA) and the moving averages. Therefore, this operator provides a parameterized family of aggregation operators from the minimum to the total operator and includes the OWA operator as a special case. It uses a heavy weighting vector in the moving average formulation and it represents the information available and the knowledge of the decision maker about the future scenarios of the phenomenon, according to his attitudinal character. Some of the main properties of this operator are studied, including a wide range of families of HOWMA operators such as the heavy moving average and heavy weighted moving average operators. The HOWMA operator is also extended using generalized and quasi-arithmetic means. An example concerning the foreign exchange rate between US dollars and Mexican pesos is also presented.     

基于语言型混合算子的模糊信息聚合方法

在多属性决策过程中经常会用到聚合算子,有序加权平均聚合(OWA)算子是最常用的聚合算子之一,通常用于聚合确切的数值.然而,现实世界部分信息的不确定性以及决策者对一些信息的模糊性,使得部分信息不能用确切的数值表示,从而导致OWA算子及其扩展算子向着多元化发展.对此,给出一种语言型混合有序加权平均聚合(LHOWA)算子,同时研究该算子所应具备的一些基本性质,并给出一种基于该算子的语言型信息聚合方法,用于多属性决策过程中模糊信息的聚合.最后,通过一个煤矿安全评价的算例对所提出方法的优越性进行了验证.     

Modeling zero-inflated explanatory variables in hybrid Bayesian network classifiers for species occurrence prediction

Datasets with an excessive number of zeros are fairly common in several disciplines. The aim of this paper is to improve the predictive power of hybrid Bayesian network classifiers when some of the explanatory variables show a high concentration of values at zero. We develop a new hybrid Bayesian network classifier called zero-inflated tree augmented naive Bayes (Zi-TAN) and compare it with the already known tree augmented naive bayes (TAN) model. The comparison is carried out through a case study involving the prediction of the probability of presence of two species, the fire salamander (Salamandra salamandra) and the Spanish Imperial Eagle (Aquila adalberti), in Andalusia, Spain. The experimental results suggest that modeling the explanatory variables containing many zeros following our proposal boosts the performance of the classifier, as far as species distribution modeling is concerned.