OWA operators with maximal Rényi entropy

doi:10.1016/j.fss.2005.04.006

Fuzzy Sets and Systems

Volume 155, Issue 3, 1 November 2005, Pages 340-360

https://doi.org/10.1016/j.fss.2005.04.006 Get rights and content

Abstract

This paper lays bare a parametric class of ordered weighted averaging (OWA) operators with maximal Rényi entropy OWA weights for any level of orness. In particular, we shall formulate an extended approach to decision making with OWA operators by introducing considerations of maximizing information content in the aggregation according to a general parametric class of dispersion measures.

References (18)

D.E. Boekee et al.
The R-norm information measure
Inform. Control
(1980)
Z. Daróczy
Generalized information measures
Inform. Control
(1970)
D. Filev et al.
On the issue of obtaining OWA operator weights
Fuzzy Sets and Systems
(1998)
R. Fullér et al.
An analytic approach for obtaining maximal entropy OWA operator weights
Fuzzy Sets and Systems
(2001)
R. Fullér et al.
On obtaining minimal variability OWA operator weights
Fuzzy Sets and Systems
(2003)
R.R. Yager
Families of OWA operators
Fuzzy Sets and Systems
(1993)
J. Aczél et al.
On Measures of Information and their Characterizations
(1975)
M. Carbonell, M. Mas, G. Mayor, On a class of monotonic extended OWA operators, in: Proc. 6th IEEE Internat. Conf. on...
V. Chankong et al.
Multiobjective Decision Making: Theory and Methodology
(1983)

There are more references available in the full text version of this article.

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In multiple attribute group decision-making (MAGDM), a consensus exists that the psychological factors of decision makers (DMs) generally influence their choice of optimal alternatives. To quantify well the influence of DMs’ risk attitudes on the group decision-making process, this paper develops a new approach to MAGDM by introducing DMs’ utility functions into the aggregation process. First, the ordered weighted utility distance (OWUD) operator is constructed by introducing DMs’ utility functions into the distance operator. As a novel operator, the OWUD operator not only satisfies both the basic features of distance measures and the desirable properties of aggregation operators, but also has some unique characteristics. Then, the linear risk tolerance (LRT) utility function is further used in the OWUD operator as the basic utility function, and a specific form of the OWUD operator, which is named as the ordered weighted-linear risk tolerance utility distance (OW-LRTUD) operator, is proposed. The OW-LRTUD operator can quantify well the influence of DMs’ risk attitudes on the group decision-making process. It also has an analytically tractable form and includes many well-known distance measures and aggregation operators, and thus can be applied to many different kinds of decision-making problems. Subsequently, to determine the weights of the OW-LRTUD operator, an extension of the maximum Bayesian entropy method is proposed by incorporating the prior known weight information and different risk attitudes of all individual DMs. An approach to MAGDM based on the OW-LRTUD operator and the proposed weight determination method is developed. An application for determining the optimal alternative in the investment selection is provided to show the feasibility, effectiveness and robustness of our approach in practice, and the corresponding sensitive analysis illustrates the influence of DMs’ risk attitudes on the group decision-making process.
Novel optimistic and pessimistic family of OWA operator with constant orness
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In this paper, we present a novel representative of the existing family of ordered weighted aggregation (OWA) operators with constant orness (optimism/pessimism level). In other words, orness value of weight vectors generated using the proposed operator is independent of the total number of arguments. The proposed OWA operator is the operator that is based on the beta function. Two different types of operators have been proposed with respect to the level of optimism (“or-like”) and pessimism (“and-like”) each. In addition to that the proposed operators discussed here are bi-parametric and real-valued in nature in terms of their parameters. Hence, for a given orness value (optimism or pessimism), it provides an infinite number of weight vectors as the proposed operator's orness depends on the value of one of its parameters. These properties lead to lots of flexibility for the Decision-Maker (DM). Its comparison and advantages over other existing members of the OWA family with constant orness such as S-OWA operators have been elaborated. Also, the maximum Rényi entropy of the OWA (MRE-OWA) operator and the maximum Rényi entropy of the proposed OWA operator are compared and evaluated for a specified orness level. Several other important properties and applications of the family of the proposed operators have also been analyzed in detail.
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An ideal type of OWA aggregation operator is the one constructed on the so-called Olympic weights. The orness of this operator is 1/2. Therefore, sometimes we need a trade-off between the desire of having an OWA aggregation operator with weights as close as possible to the Olympic ones and the desire of having a predefined level of orness. In this paper, we choose these optimal weights by minimizing the Euclidean distance to the Olympic weights vector under the constraint of preserving a given level of orness. First, in the case $n = 4$ , we propose an iterative algorithm where the optimal solution is given for all possible values of the orness, values that are grouped along a partition of the unit interval. This iterative algorithm will inspire us to deduce the optimal weights in the general case. Consequently, we will obtain the analytical solution of the optimal weights as a function depending on the orness level.

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OWA operators with maximal Rényi entropy

Abstract

Inform. Control

Inform. Control

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

On Measures of Information and their Characterizations

Multiobjective Decision Making: Theory and Methodology