Relevancy transformation operators: Construction methods

This article deals with the construction of relevancy transformation (RET) operators for fuzzy systems. The notion of pseudo‐duality is introduced to obtain new RET operators, and t‐norms, t‐conorms, nullnorms, and uninorms are used in different ways for the same purpose. Finally, several other methods to construct new RET operators from old ones are pointed out. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 155–171, 2006.     

Multicriteria decision-making using Archimedean aggregation operators in Pythagorean hesitant fuzzy environment

In multicriteria decision-making (MCDM), the existing aggregation operators are mostly based on algebraic t-conorm and t-norm. But, Archimedean t-conorms and t-norms are the generalized forms of t-conorms and t-norms which include algebraic, Einstein, Hamacher, Frank, and other types of t-conorms and t-norms. From that view point, in this paper the concepts of Archimedean t-conorm and t-norm are introduced to aggregate Pythagorean hesitant fuzzy information. Some new operational laws for Pythagorean hesitant fuzzy numbers based on Archimedean t-conorm and t-norm have been proposed. Using those operational laws, Archimedean t-conorm and t-norm-based Pythagorean hesitant fuzzy weighted averaging operator and weighted geometric operator are developed. Some of their desirable properties have also been investigated. Afterwards, these operators are applied to solve MCDM problems in Pythagorean hesitant fuzzy environment. The developed Archimedean aggregation operators are also applicable in Pythagorean fuzzy contexts also. To demonstrate the validity, practicality, and effectiveness of the proposed method, a practical problem is considered, solved, and compared with other existing method.     

The structure of decomposable indistinguishability operators

Decomposable fuzzy relations are studied.Symmetric fuzzy relations are proved to be generated by a single fuzzy subset.For Archimedean t-norms, decomposable indistinguishability operators generate special kinds of betweenness relations that characterize them.A new way to generate indistinguishability operators coherent with the underlying ordering structure of the real line is given in the sense that this structure is compatible with the betweenness relation generated by the relation is developed.     

Chamfer metrics, the medial axis and mathematical morphology

This paper describes a number of efficient algorithms for morphological operations which use discs defined by chamfer distances as structuring elements. It presents an extension to previous work on extending metrics (such as the p-q-metrics). Theoretical results and algorithms are presented for p-q-r-metrics, which are not extending. These metrics can approximate the Euclidean metric close enough for most practical situations. The algorithms are based on an analysis of the structure of shortest paths in the p-q-r-metric and of the set of values this metric can assume. Efficient algorithms are presented for the medial axis and the opening transform. The opening transform algorithm is two orders of magnitude faster than a more straightforward algorithm.This research was supported by the Foundation for Computer Science in The Netherlands (SION) with financial support from The Netherlands Organisation for Scientific Research (NWO). Part of it was performed while the author was a guest at the Technical University of Vienna in the framework of the Erasmus exchange program of the European Community.     

Generating indistinguishability operators from prototypes

Given a T‐indistinguishability operator E defined between some fuzzy subsets of a universe of discourse X, this paper studies three ways to generate an indistinguishability operator on X compatible with E inspired by the tools used in approximate reasoning and on the duality principle. Of special interest are the cases when the fuzzy subsets determine a partition and a hard‐partition of the universe X. © 2002 Wiley Periodicals, Inc.     

Maps and isometries between indistinguishability operators

 In this paper, some geometric aspects of indistinguishability operators are studied by using the concept of morphism between them. Among all possible types of morphisms, the paper is focused on the following cases: Maps that transform a T-indistinguishability operator into another of such operators with respect to the same t-norm T and maps that transform a T-indistinguishability operator into another one of such operators with respect to a different t-norm T ^′. The group of isometries of a given T-indistinguishability operator is also studied and it is determined for the case of one-dimensional operators, in particular for the natural indistinguishability operators E _T on [0, 1]. Finally, the indistinguishability operators invariant under translations on the real line are characterized.     

Interval valued (\in,\in\!\vee\,q) -fuzzy filters of pseudo BL-algebras

We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued -fuzzy filters of pseudo BL-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these generalized interval valued fuzzy filters of pseudo BL-algebras is considered. Finally, we consider the concept of implication-based interval valued fuzzy implicative filters of pseudo BL-algebras, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed.     

Influence of image‐quality degradation on accommodation mechanism in human vision: Conditions necessary for objective image‐quality evaluation metrics

This paper clarifies the relationship between image quality and accommodation in human vision through two types of experiments. One examines how image‐quality degradation influences the accommodation mechanism, and the other examines which type of information of quality‐degraded images activates the accommodation mechanism. Actually, accommodative responses are measured using an infrared optometer while subjects are subjectively evaluating sharpness, noise, and pseudo‐contours and while they are observing sine, square, and missing fundamental (MF) square waves. The following results were derived: (1) the accommodation lag increases as the degree of sharpness is degraded regardless of the tone‐reproducing methods; (2) the accommodation lag decreases considerably in the existence of noise or pseudo‐contours, whereas it increases for uniform or gently curved planes; (3) the spatial features of presented images activate the accommodation mechanism. These results suggest that accommodative responses influence human subjective judgments as well as being a human factor related closely to image quality and that the spatial features of quality‐degraded images underlie human subjective judgments. In other words, they imply that objective image‐quality evaluation metrics should satisfy the following two conditions: the incorporation of the accommodation characteristics into such metrics and the formulation of such metrics in the spatial region.     

Fuzzy interior operators

We study interior operators from the point of view of fuzzy set theory. The present approach generalizes the particular cases studied previously in the literature in two aspects. First, we use complete residuated lattices as structures of truth values thus generalizing several important cases like the classical Boolean case, (left-)continuous t-norms, MV-algebras, BL-algebras, etc. Second, and more importantly, we pay attention to graded subsethood of fuzzy sets, which turns out to play an important role. In the first part, we define, illustrate by examples and study general fuzzy interior operators. The second part is devoted to fuzzy interior operators induced by fuzzy equivalence relations (similarities).     

Aggregation operators based on indistinguishability operators

This article gives a new approach to aggregating assuming that there is an indistinguishability operator or similarity defined on the universe of discourse. The very simple idea is that when we want to aggregate two values a and b we are looking for a value λ that is as similar to a as to b or, in a more logical language, the degrees of equivalence of λ with a and b must coincide. Interesting aggregation operators on the unit interval are obtained from natural indistinguishability operators associated to t‐norms that are ordinal sums. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 857–873, 2006.     

基于投影寻踪的Web软件复杂性度量

传统的软件复杂性度量方法主要是针对C/C++、Ada等语言开发的非Web应用。以面向对象的基于Struts框架的Web软件为研究对象,提出了适合于Web-Struts软件的3个方面的复杂性度量指标,并提出了一种基于带交叉算子人工鱼群和投影寻踪(PP)算法的Web应用软件复杂性度量方法。把Web软件多个复杂性度量指标综合成一维综合投影值,利用样本数据求解最佳投影方向,确定评价等级的综合投影值区间,根据测试样本综合投影值与区间值比较,获得综合评价结果。实例评价结果表明,所提方法具有较强的适用性和应用性。     

t-norms induced by metrics on Boolean algebras

Let d _ν be the metric associated with a strictly positive submeasure ν on some Boolean algebra . If d _ν is bounded from above by 1, E _ν=1−d _ν is a (fuzzy) similarity relation on at least w.r.t. the Lstrok ukasiewicz t-norm, but possibly also w.r.t. numerous further t-norms.In this paper, we show that under certain assumptions on and ν, we may associate with ν in a natural way a continuous t-norm w.r.t. which E _ν is a similarity relation and which, in a certain sense, is the weakest such t-norm. Up to isomorphism, every continuous t-norm arises in this way     

高维数据的增量式聚类算法的距离度量选择研究

合适的距离度量函数对于聚类结果有重要的影响。针对大规模高维数据集,使用增量式聚类算法进行距离度量的选择分析。SpFCM算法是将大规模数据集分成小样本进行增量分批聚类,可在有限的计算机内存中获得较好的聚类结果。在传统的SpFCM算法的基础上,使用不同的距离度量函数来衡量样本之间的相似性,以得出不同的距离度量对SpFCM算法的影响。在不同的大规模高维数据集中,使用欧氏距离、余弦距离、相关系数距离和扩展的杰卡德距离来计算距离。实验结果表明,后3个距离度量相对于欧氏距离可以很大程度地提高聚类效果,其中相关系数距离可以得到较好的结果,余弦距离和扩展的杰卡德距离效果比较一般。     

离群点检测算法的评价指标

随着离群点检测技术的深入研究和广泛应用，越来越多的优秀算法被提出来，然而，现有的离群点检测技术的评价仍然沿用传统分类算法的测量指标，存在着评价指标单一、适应性差的问题。针对这些问题，提出了一类高真正率指标（HT_AUC）和二类低假正率指标（LF_AUC）。首先，整理常用的离群点检测评价指标，分析其优缺点和适用场景；然后，在已有的曲线下面积（AUC）方法的基础上，分别针对高真正率（TPR）要求和低假正率（FPR）要求，提出了一类高真正率指标和二类低假正率指标，为离群点检测算法的效果评价和量化集成提供了更合适的指标。在真实数据集上的实验结果表明，与传统评价指标的相比，所提出的方法更能满足一类高真正率和二类低假正率要求。     

Ranking of software engineering metrics by fuzzy‐based matrix methodology

This research paper presents a framework for ranking of software engineering metrics based on expert opinion elicitation and fuzzy‐based matrix methodology. The proposed methodology is able to accommodate the imprecise and inexact data involved in the problem of ranking of software engineering metrics, vagueness and ambiguity occurring during expert (human) decision making and to depart from the complexity of formulation of the objective and the constraint function. The matrices lend themselves to mechanical manipulations and are useful for analyzing and deriving systems functions expeditiously to meet the objectives. The current research is based on software engineering metrics identified in an earlier study conducted by Lawrence Livermore National Laboratory. A set of ranking criteria were identified. Software engineering metrics are then ranked in ascending order using experts' opinion in accordance with the value of Permanent function on their criteria matrix. The proposed methodology has also been compared with other known methodologies. Copyright © 2011 John Wiley & Sons, Ltd.     

Cohesion and coupling metrics for ontology modules

In recent years, an increasing number of ontologies and semantic web applications have been developed and used. A conscious effort has been made to develop methods to modularize ontologies. These methods contribute to building a new ontology. However, few studies have focused on the evaluative methods for ontology modules. In this study, we propose novel metrics to measure ontology modularity. To evaluate the ontology modules, we introduce cohesion and coupling based on the theory of software metrics. A cohesion metric and two coupling metrics were used to measure cohesion and coupling for ontology modules. The proposed metrics provide more detailed support in considering the different types of relationships between classes in ontology modules. In addition, the new coupling metrics contribute to checking the consistency between the ontology modules and their original ontology. The proposed metrics were validated using well-known verification frameworks and empirical experiments to complement the previous investigations. The results of this study offer ontology engineers valuable criteria with which to evaluate ontology modules and help ontology users select qualifying ontology modules.     

基于融合欧氏距离与Kendall Tau距离度量的谱聚类算法

大多数现存的谱聚类方法均使用传统距离度量计算样本之间的相似性, 这样仅仅考虑了两两样本之间的相似性而忽略了周围的近邻信息, 更没有顾及数据的全局性分布结构. 因此, 本文提出一种新的融合欧氏距离和 Kendall Tau距离的谱聚类方法. 该方法通过融合两两样本之间的直接距离以及其周围的近邻信息, 充分利用了不同的相似性度量可以从不同角度抓取数据之间结构信息的优势, 更加全面地反映数据的底层结构信息. 通过与传统聚类算法在UCI标准数据集上的实验结果作比较, 验证了本文的方法可以显著提高聚类效果.     

Aggregation of T‐transitive relations

This article studies the aggregation of transitive fuzzy relations. We first find operators that preserve transitivity and then extend the results to aggregating operators. As special cases, means and some kind of suitable ordered weighted averaging (OWAs) are used to aggregate transitive fuzzy relations with respect to an Archimedean t‐norm. Three families of transitive relations that allow us to modify the entries of a given relation R continuously towards the smallest and the greatest ones in our universe are given. Aggregation of nonfinite families of transitive relations also is studied and applied to calculate the degree of inclusion or similarity of fuzzy quantities (fuzzy subsets of an interval of the real line). © 2003 Wiley Periodicals, Inc.     

On fuzzy relational equations and the covering problem

Previous studies have shown that fuzzy relational equations (FREs) based on either the max-continuous Archimedean t-norm or the max-arithmetic mean composition can be transformed into the covering problem, which is an NP-hard problem. Exploiting the properties common to the continuous Archimedean t-norm and the arithmetic mean, this study proposes a generalization of them as the “u-norm”, enabling FREs that are based on the max-continuous u-norm composition also to be transformed into the covering problem. This study also proposes a procedure for transforming the covering problem into max-product FREs. Consequently, max-continuous u-norm FREs can be solved by extending any procedure for solving either the covering problem or max-product FREs.