<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

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

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Three Ways of Defining Owa Operator on the Set of All Normal Convex Fuzzy Sets"}

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...

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

Published Online: Mar 23, 2018

Page range: 101 - 118

Received: Apr 13, 2017

DOI: https://doi.org/10.1515/tmmp-2017-0017

Keywords
OWA operator, ordered weighted averaging operator, linear order, total order, fuzzy interval, normal, convex, gradual number, gradual interval

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Mar 23, 2018

Page range: 101 - 118

Received: Apr 13, 2017

DOI: https://doi.org/10.1515/tmmp-2017-0017

KeywordsOWA operator, ordered weighted averaging operator, linear order, total order, fuzzy interval, normal, convex, gradual number, gradual interval

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
OWA operator, ordered weighted averaging operator, linear order, total order, fuzzy interval, normal, convex, gradual number, gradual interval