On Algebraic Properties and Linearity of Owa Operators for Fuzzy Sets

Abstract We deal with an ordered weighted averaging operator (OWA operator) on the set of all fuzzy sets. Our starting point is OWA operator on any lattice introduced in Lizasoain, I.-Moreno,C.: OWA operators defined on complete lattices, Fuzzy Sets and Systems 224 (2013), 36-52; Ochoa, G.-Lizasoain, I.- -Paternain, D.-Bustince, H.-Pal, N. R.: Some properties of lattice OWA operators and their importance in image processing, in: Proc. of the 16th World Congress of the Internat. Systems Assoc.-IFSA ’15 and the 9th Conf. of the European Soc. for Fuzzy Logic and Technology-EUSFLAT ’15 (J. M. Alonso et al., eds.), Atlantis Press, Gijón, Spain, 2015, pp. 1261-1265. We focus on a particular case of lattice, namely that of all normal convex fuzzy sets in [0,1], and study algebraic properties and linearity of the proposed OWA operator. It is shown that the operator is an extension of standard OWA operator for real numbers and it possesses similar algebraic properties as standard one, however, it is neither homogeneous nor shift-invariant, i.e., it is not linear in contrast to the standard OWA operator.

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Three Ways of Defining Owa Operator on the Set of All Normal Convex Fuzzy Sets

Tatra Mountains Mathematical Publications ◽

10.1515/tmmp-2017-0017 ◽

2017 ◽

Vol 69 (1) ◽

pp. 101-118

Author(s):

Zdenko Takáč

Keyword(s):

Fuzzy Sets ◽

Linear Order ◽

Recent Literature ◽

Weighted Averaging ◽

Owa Operator ◽

Main Obstacle ◽

Owa Operators ◽

Ordered Weighted Averaging ◽

Algebraic Properties

Abstract We deal with an extension of ordered weighted averaging (OWA, for short) operators to the set of all normal convex fuzzy sets in [0, 1]. The main obstacle to achieve this goal is the non-existence of a linear order for fuzzy sets. Three ways of dealing with the lack of a linear order on some set and defining OWA operators on the set appeared in the recent literature. We adapt the three approaches for the set of all normal convex fuzzy sets in [0, 1] and study their properties. It is shown that each of the three approaches leads to operator with desired algebraic properties, and two of them are also linear.

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Interval type 2 fuzzy sets multiple criteria decision making based on quantifier guided aggregation ordered weighted averaging operator

2017 Joint 17th World Congress of International Fuzzy Systems Association and 9th International Conference on Soft Computing and Intelligent Systems (IFSA-SCIS) ◽

10.1109/ifsa-scis.2017.8023334 ◽

2017 ◽

Author(s):

Kuo-Ping Chiao

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Multiple Criteria Decision Making ◽

Multiple Criteria ◽

Weighted Averaging ◽

Ordered Weighted Averaging ◽

Averaging Operator ◽

Ordered Weighted Averaging Operator ◽

Interval Type

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A Study of OWA Operators Learned in Convolutional Neural Networks

Applied Sciences ◽

10.3390/app11167195 ◽

2021 ◽

Vol 11 (16) ◽

pp. 7195

Author(s):

Iris Dominguez-Catena ◽

Daniel Paternain ◽

Mikel Galar

Keyword(s):

Neural Networks ◽

Convolutional Neural Networks ◽

Practical Method ◽

Local Information ◽

Weighted Averaging ◽

Global Information ◽

Owa Operator ◽

Owa Operators ◽

Ordered Weighted Averaging

Ordered Weighted Averaging (OWA) operators have been integrated in Convolutional Neural Networks (CNNs) for image classification through the OWA layer. This layer lets the CNN integrate global information about the image in the early stages, where most CNN architectures only allow for the exploitation of local information. As a side effect of this integration, the OWA layer becomes a practical method for the determination of OWA operator weights, which is usually a difficult task that complicates the integration of these operators in other fields. In this paper, we explore the weights learned for the OWA operators inside the OWA layer, characterizing them through their basic properties of orness and dispersion. We also compare them to some families of OWA operators, namely the Binomial OWA operator, the Stancu OWA operator and the exponential RIM OWA operator, finding examples that are currently impossible to generalize through these parameterizations.

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