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1.
The fusion of transitive fuzzy relations preserving the transitivity is linked to the domination of the involved aggregation operator. The aim of this contribution is to investigate the domination of OWA operators over t-norms whereas the main emphasis is on the domination over the ukasiewicz t-norm. The domination of OWA operators and related operators over continuous Archimedean t-norms will also be discussed.This work was partly supported by network CEEPUS SK-42, COST Action 274 TARSKI and project APVT 20-023402. 相似文献
2.
The employment of a decision support system for optimizing fund raising strategies is crucial to the management of non‐profit organizations. Commonly considered methodologies utilize the organization's donor database in order to gather and analyse information. However, many organizations, especially small‐ and medium‐sized ones, do not own or efficiently manage a database, and consequently, the usual methods are inapplicable. In this paper, a decision support system is developed that is able to identify the most promising fund raising strategies on the basis of the organization's profile. The profile factors of a non‐profit organization are analysed and hierarchically organized in a decision tree in order to effectively employ the Choquet integral methodology, which is recommended in these kinds of multi‐criteria decision problems. The results obtained in the real operational context show the effectiveness of the proposed system. 相似文献
3.
ABSTRACTThe paper offers an extension and generalization of the definitions of the weighted arithmetic mean WAM, the ordered weighted averaging function OWA and the discrete Choquet integral using not only positive but also negative weights. Negative weights are important in various contexts, including statistics and robust aggregation, and they directly affect the monotonicity of the mentioned functions. The paper offers insights into the extended WAM, OWA and Choquet integral-based averaging functions with respect to their directional monotonicity, and establish the systems of linear inequalities which define the cone of monotonicity of these functions. 相似文献
4.
Ronald R. Yager 《国际通用系统杂志》2020,49(2):222-233
ABSTRACTWe first describe an approach to multi-criteria making which makes use of a fuzzy measure over the set of criteria to model the user expressed relationship between the criteria. Under this approach we use the Choquet integral, guided by this fuzzy measure, to aggregate an alternative’s satisfactions to the individual criteria. Our focus in this paper is to look at the formulation, in terms of fuzzy measures, of some interesting and novel relationships between the criteria. After noting that the OWA aggregation can be modeled using a cardinality measure we look at the measure formulation of a rule-based expression of a collection of OWA aggregations. We then focus on the measure representation of a user provided well-formed formula in the language of propositional logic expressed relationship between the criteria. 相似文献
5.
We develop a new decision making approach for dealing with uncertain information and apply it in tourism management. We use a new aggregation operator that uses the uncertain weighted average (UWA) and the uncertain induced ordered weighted averaging (UIOWA) operator in the same formulation. We call it the uncertain induced ordered weighted averaging - weighted averaging (UIOWAWA) operator. We study some of the main advantages and properties of the new aggregation such as the uncertain arithmetic UIOWA (UA-UIOWA) and the uncertain arithmetic UWA (UAUWA). We study its applicability in a multi-person decision making problem concerning the selection of holiday trips. We see that depending on the particular type of UIOWAWA operator used, the results may lead to different decisions. 相似文献
6.
We are interested in the study of L-fuzzy contexts taking into account different criteria. These contexts arise when we want to analyze the relationship between objects and attributes from different points of view. Furthermore, in some occasions, these L-fuzzy contexts have several values for every pair object attribute. We will see how both the WOWA operators and the Choquet integrals will be interesting tools for the aggregation processes that we are going to carry out. 相似文献
7.
This study first revamps Yager prioritized ordered weighted averaging operators, and condenses them into a conceptual frame with putting aside one realization from Yager's original proposal. Then, based on elicited conceptual frame called Yager prioritized preference conceptual frame, this article proposes three distinct realizations to the conceptual frame with corresponding different instances, in which some evaluation models with weights determination methods are provided. Numerical examples are also presented immediately after every instance. Lastly, this study proposes the concepts of outer monotonic, inner monotonic, and global monotonic weights functions, and discusses some related properties, which are often embodied in preferences of decision makers. 相似文献
8.
Ronald R. Yager 《Information Sciences》2009,179(22):3908-42
We describe some basic features of the OWA operator. We turn to the problem of determining the weights associated with this operator and particularly the maximal dispersion (entropy) approach. We consider the possibility of using minimization of dispersion. After discussing concerns with both maximization and minimization of dispersion we investigate the possibility of finding an optimal solution intermediate to these extremes. We next consider alternative measures of dispersion. We introduce a fundamental requirement for a measure of dispersion called the Preference for Equal Division. A number of general classes of dispersion measures are provided notable among these are those based on t-norm and t-conorm operators. 相似文献
9.
R. R. Yager 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》1999,3(3):187-196
The basic properties of the Ordered Weighted Averaging (OWA) operator are recalled. The role of these operators in the formulation
of multi-criteria decision functions, using the concept of quantifier guided aggregation, is discussed. An extended class
of OWA operators, one based upon a relaxation of the requirements on the OWA operators, is introduced. This relaxation allows
us to consider a new branch of OWA operators, NOMOWA operators, which have negative weights and which exhibit nonmonotonicity.
Some special cases of these operators are discussed and then we investigate the role of these nonmonotonic operators in the
formulation of multi-criteria decision functions. 相似文献
10.
Ronald R. Yager 《国际通用系统杂志》2013,42(6):617-641
We recall the concept of an intuitionistic fuzzy subset (IFS). Fundamental to an IFS is the fact that it is defined using two values, a degree of membership and degree of non-membership. The ordered weighted averaging (OWA) operator is introduced and several of its features are described. Particularly notable is the idea of the dual of an OWA operator. We next discuss the aggregation of a collection of IFS using a prescribed OWA operator. It is shown that while the aggregation of the degrees of membership is performed using the prescribed OWA operator, the aggregation of the degrees of non-membership requires use of the dual of the prescribed OWA operator. The Choquet integral aggregation operator is introduced and applied to the aggregation of IFSs. Here again the concept of the dual is needed to perform the aggregation of the degrees of non-membership. We also discuss the aggregation of IFSs using the Sugeno integral. Fundamental to this work is our realisation of the importance of the concept of the dual operators in dealing with the aggregation of IFS. 相似文献
11.
P. Struk 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2006,10(6):502-505
Fuzzy integral is a monotone idempotent functional on a fuzzy measure. The extremal fuzzy integrals are introduced. Regular
fuzzy integrals do not distinguish functions not distinguishable by the underlying fuzzy measures. These integrals include
Choquet, Sugeno, Shilkret and several other well known integrals. 相似文献
12.
One of the most common techniques to find the adequate weights in ordered weighted averaging (OWA) operators is based on the orness concept, where the weights are determined by maximizing the entropy (variation) for a fixed orness value. But such an entropy represents a dispersion measure for nominal variables, while weights in an OWA operator are essentially ordinal rather than nominal. Hence, in this paper, we propose a novel way to determine OWA weights based upon ordinal dispersion measures instead of an standard entropy measure. From this approach, we find an explicit formula for the weights, and we illustrate differences by means some multicriteria decision-making examples. 相似文献
13.
This two-part state-of-the-art overview on aggregation theory summarizes the essential information concerning aggregation issues. An overview of aggregation properties is given, including the basic classification on aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with multiple arities (extended means). 相似文献
14.
In view of the recent interests in random sets in information technology, such as models for imprecise data in intelligent systems, morphological analysis in image processing, we present, in this paper, some contributions to the foundation of random set theory, namely, a complete study of topological properties of capacity functionals of random sets, generalizing weak convergence of probability measures. These results are useful for investigating the concept of Choquet weak convergence of capacity functionals leading to tractable criteria for convergence in distribution of random sets. The weak topology is defined on the space of all capacity functionals on Rd. We show that this topological space is separable and metrizable. 相似文献
15.
Radko Mesiar 《Information Sciences》2008,178(18):3557-3564
Infinitary aggregation functions acting on sequences and possessing some a priori given properties as additivity, comonotone additivity, symmetry, etc., are investigated. On the other side, we discuss infinitary aggregation functions related to given extended aggregation functions, where special attention is given to triangular norms, triangular conorms and weighted means. 相似文献
16.
The decision to choose a reinsurance program has many complexities because it is difficult to simultaneously achieve high levels in different optimal criteria including maximum gain, minimum variance, and probability of ruin. This article suggests a new method by which, through membership functions, we can measure the distance of each alternative to an optimal result and aggregate it by using different types of aggregations. In this article, particular attention is given to the induced Minkowski ordered weighted averaging distance operator and the induced Minkowski probabilistic ordered weighted averaging distance operator. The main advantage of these operators is that they include a wide range of special cases. Thus, they can adapt efficiently to the specific needs of the calculation processes. By doing so, the reinsurance system can make better decisions by using different scenarios in the uncertain environment considered. 相似文献
17.
The key property of monotone classifiers is that increasing (decreasing) input values lead to increasing (decreasing) the output value. Preserving monotonicity for a classifier typically requires many constraints to be respected by modelling approaches such as artificial intelligence techniques. The type of constraints strongly depends on the modelling assumptions. Of course, for sophisticated models, such conditions might be very complex. In this study, we present a new family of kernels that we call it Choquet kernels. Henceforth, it allows for employing popular kernel-based methods, such as support vector machines. Instead of a naïve approach with exponential computational complexity, we propose an equivalent formulation with quadratic time in the number of attributes. Furthermore, because coefficients derived from kernel solutions are not necessarily monotone in the dual form, different approaches are proposed to monotonize coefficients. Finally, experiments illustrate beneficial properties of the Choquet kernels. 相似文献
18.
Thaddeus Shannon 《国际通用系统杂志》2013,42(1):89-102
It is known that for basic linear fuzzy measures the Aumann and the Choquet integrals defined on a special class of fuzzy subsets of some Banach space commute. We characterize basic linear fuzzy measures by means of appropriate linear functionals, and consequently the relevant integral representation (by means of the Lebesgue integral) is introduced. As a corollary the well-known additivity of perimeters of convex subsets in the real plane is obtained. 相似文献
19.
Ronald R. Yager 《Applied Intelligence》2004,21(3):277-288
Our goal is to provide some tools, based on soft computing aggregation methods, useful in the two fundamental steps in case base reasoning, matching the target and the cases and fusing the information provided by the relevant cases. To aid in the first step we introduce a methodology for matching the target and cases which uses a hierarchical representation of the target object. We also introduce a method for fusing the information provided by relevant retrieved cases. This approach is based upon the nearest neighbor principle and uses the induced ordered weighted averaging operator as the basic aggregation operator. A procedure for learning the weights is described. 相似文献
20.
在数据挖掘、模糊专家系统和多Agent协同决策过程中,要经常面对信息聚集技术和对多个模糊数据来源进行聚集运算,一般用得最多的是合取、析取及加权平均等算子,但是不同的领域有着不同的需求,本文着重对加权聚集算子进行研究。首先,提出了加权平均关系与析取关系结合后的析取-加权平均算子,该算子解决了加权平均算子不能区分析取与合取的关系。然后,提出了一种最大加权平均算子和最小加权平均算子,该算子将最大最小值算子与加权平均算子进行了泛化,解决了同时考虑信息局部性特征与信息整体性特征的问题。理论分析表明,本文提出的加权模糊聚集算子对于模糊信息源的聚集运算起到了很好的补充和完善的功能。 相似文献