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Three ways of defining OWA operator on the set of all normal convex fuzzy sets

In: Tatra Mountains Mathematical Publications, vol. 69, no. 2
Zdenko Takáč
Detaily:
Rok, strany: 2017, 101 - 118
Kľúčové slová:
$\operatorname{OWA}$ operator, ordered weighted averaging operator, linear order, total order, fuzzy interval, normal, convex, gradual number, gradual interval.
O článku:
We deal with an extension of ordered weighted averaging ($\operatorname{OWA}$, 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 $\operatorname{OWA}$ 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.
Ako citovať:
ISO 690:
Takáč, Z. 2017. Three ways of defining OWA operator on the set of all normal convex fuzzy sets. In Tatra Mountains Mathematical Publications, vol. 69, no.2, pp. 101-118. 1210-3195.

APA:
Takáč, Z. (2017). Three ways of defining OWA operator on the set of all normal convex fuzzy sets. Tatra Mountains Mathematical Publications, 69(2), 101-118. 1210-3195.