Fitting Generated Aggregation Operators to Empirical Data (original) (raw)

Aggregation-based extensions of fuzzy measures

Fuzzy Sets and Systems, 2012

We present a method extending fuzzy measures on N = {1, ... , n} (represented as Boolean utility functions) to n-ary aggregation functions (utility functions) by means of a suitable n-ary aggregation function and the Möbius transform of the considered fuzzy measure. The method generalizes the well-known Lovász and Owen extensions of nondecreasing pseudo-Boolean functions linked to fuzzy measures. All n-ary aggregation functions suitable for the proposed construction are completely characterized, including, among others, all n-ary copulas. Associative extended aggregation functions applicable in the case of an arbitrary arity are also completely characterized.

On Some Properties of Aggregation-Based Extensions of Fuzzy Measures

Tatra Mountains Mathematical Publications, 2018

In this paper, we analyse properties of aggregation-based extensions of fuzzy measures depending on properties of aggregation functions which they are based on. We mainly focus on properties possessed by the well-known Lovász and Owen extensions. Moreover, we characterize aggregation functions suitable for extension of particular subclasses of fuzzy measures.

Extensions of fuzzy aggregation

Fuzzy Sets and Systems, 1997

We discuss the equivalence between aggregation of fuzzy sets and integration with respect to a special class of nonadditive set functions. Both fuzzy integral and Choquet integral are considered. First, we study aggregation of a finite family of fuzzy sets and then we extend our results to aggregation of an infinite family. The concepts of comonotonic maxitivity and additivity play a central role. We argue that, for the purpose of aggregating fuzzy sets, comonotonic maxitivity is a more desirable requirement than comonotonic additivity. In the absence of any such requirement we explore a wider class of aggregation procedures.

Aggregation of sequence of fuzzy measures

Iranian Journal of Fuzzy Systems, 2020

In this paper we present construction of new fuzzy measures by applying extended aggregation function on a sequence of fuzzy measures. According to properties of applied aggregation function and properties of initial fuzzy measures, some properties of constructed fuzzy measure are proved. Additionally, one new extended aggregation function named extended weighted arithmetic mean of distorted arguments is introduced, and its relevant properties are proved. It is shown that this extended aggregation function, with appropriated parameters, can be suitable for construction of new fuzzy measures. Other types of non-additive measures can be constructed in the same way, by applying aggregation function on the initial sequence of non-additive measures.

On extension of fuzzy measures to aggregation functions

Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011), 2011

In the paper we study a method extending fuzzy measures on the set N = {1, . . . , n} to n-ary aggregation functions on the interval [0, 1]. The method is based on a fixed suitable n-ary aggregation function and the Möbius transform of the considered fuzzy measure. This approach generalizes the wellknown Lovász and Owen extensions of fuzzy measures. We focus our attention on the special class of n-dimensional Archimedean quasi-copulas and prove characterization of all suitable n-dimensional Archimedean quasi-copulas. We also present a special universal extension method based on a suitable associative binary aggregation function. Several examples are included.

New Fuzzy Aggregations . Part II : Associated Probabilities in the Aggregations of the POWA operator

2016

The Ordered Weighted Averaging (OWA) operator was introduced by R.R. Yager [58] to provide a method for aggregating inputs that lie between the max and min operators. In this article several variants of the generalizations of the fuzzy-probabilistic OWA operator POWA (introduced by J.M. Merigo [27,28]) are presented in the environment of fuzzy uncertainty, where different monotone measures (fuzzy measure) are used as an uncertainty measure. The considered monotone measures are: possibility measure, Sugeno − λ additive measure, monotone measure associated with Belief Structure and capacity of order two. New aggregation operators are introduced: AsPOWA and SA-AsPOWA. Some properties of new aggregation operators are proved. Concrete faces of new operators are presented with respect to different monotone measures and mean operators. Concrete operators are induced by the Monotone Expectation (Choquet integral) or Fuzzy Expected Value (Sugeno integral) and the Associated Probability Class...

A New Aggregation Operator Based on Intuitionistic Fuzzy Choquet Integral

Journal of Computer Science & Computational Mathematics

There are many aggregation techniques have been introduced to intuitionistic fuzzy sets (IFS). Most of the existing aggregation techniques are considered all the elements are independent. Usually, in some situation, these methods cannot be used to deal with it as in the real situation involves interdependent among the criteria. For this reason, traditional aggregation is not suitable to apply to aggregate since there have not considered the interaction between criteria when making decisions. Thus, the appropriate method to exhibit the interdependence between criteria is Choquet integral. The Choquet integral is relies on its fuzzy measure. The established fuzzy measure is lambda-measure. However, lambda-meausre has a single solution. In this paper, we have evaluated the Choquet integral by considering maximized Lmeasure and Delta-measure that based on intuitionistic fuzzy sets. An illustrative example is provided by showing step by step of the proposed model. It show that it is effective and applicable in the decision-making environment.

Properties of the aggregation operators related with fuzzy relations

Fuzzy Sets and Systems, 2003

The problem of information generalization in multicriteria decision making is considered in this paper. The information is uniÿed by fuzzy relations and the generalization is realized with the help of aggregation operators. Some of the most oftenly used operators are presented and their properties depending on the properties of the fuzzy relations, which they aggregate, are proved. The sensitivity of the operators with respect to variations in their arguments is investigated. The numerical example deciding the problem of alternatives' ranking is given as well.

Some Induced Averaging Aggregation Operators Based on Pythagorean Fuzzy Numbers

Mathematics Letters

In this paper we present two new types aggregation operators such as, induced Pythagorean fuzzy ordered weighted averaging aggregation operator and induced Pythagorean fuzzy hybrid averaging aggregation operator. We also discuss of important properties of these proposed operators and construct some examples to develop these operators.

Aggregation Functions in Theory and in Practise

Advances in Intelligent Systems and Computing, 2013

In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator, one from a fuzzy operator and a fuzzy relation and the other one from two fuzzy operators. The first one is an extension of the well-known fuzzy operator induced by a fuzzy relation through Zadeh's compositional rule. Finally, we aggregate these operators through the quasi-arithmetic mean associated to a continuous Archimedean t-norm in order to compare the operator obtained by aggregating the generators with the operator obtained by the aggregation of the generated ones.