In this paper a class of bottleneck combinatorial optimization problems with uncertain costs is discussed. The uncertainty is modeled by specifying a discrete scenario set containing a finite number of cost vectors, called scenarios. In order to choose a solution the Ordered Weighted Averaging aggregation operator (shortly OWA) is applied. The OWA operator generalizes traditional criteria in de...

Abstract An IFS is suitable way to deal with uncertainty, but operators on it are complex in computation even though they work well. This study presents a C-OWA operator-based method to make aggregation over intuitionistic fuzzy information more easy and convenient, and then applies it to complicated decision making under uncertainty. IFNs or IIFNs are transformed into intervals which are easy ...

Recently, in (Loyer & Straccia 2005) the Any-World Assumption (AWA) has been introduced for normal logic programs as a generalization of the well-known notions of Closed World Assumption (CWA) and the Open World Assumption (OWA). The AWA allows any assignment (i.e. interpretation), over a truth space (bilattice), to be a default assumption and, thus, the CWA and OWA are just special cases. Whil...

We study different types of aggregation operators. We focus on the generalized OWA (GOWA) operator developed by Yager which represents a generalization to a wide range of aggregation operators. We distinguish between aggregations with a descending or with an ascending order. We introduce the induced generalized OWA (IGOWA) operator which represents an extension to the GOWA operator. It generali...

This paper deals with the characterization of two classes of monotonic and neutral (MN) aggregation operators . The first class corresponds to (MN) aggregators which are stable for the same positive linear transformations and present the ordered linkage property. The second class deals with (MN)-idempotent aggregators which are stable for positive linear transformations with same unit, independ...

The Minkowski distance is a distance measure that generalizes a wide range of other distances such as the Hamming and the Euclidean distance. In this paper, we develop a generalization of the Minkowski distance by using the induced ordered weighted averaging (IOWA) operator. We will call it the induced Minkowski OWA distance (IMOWAD). Then, we are able to obtain a wider range of distance measur...

We propose a least absolute deviation model for obtaining OWA operator weights: Minimize ∑i=n−1 i=1 |wi − wi−1| subject to orness(W ) = ∑n i=1 n−i n−1wi = α, 0 ≤ α ≤ 1, w1 + · · ·+ wn = 1, 0 ≤ wi, i = 1, · · · , n. Recently, the extended minimax disparity problem was proved by Hong [Fuzzy Sets and Systems, 168 (2011) 35-46]. In this paper, we investigated the equivalence of the solutions for th...

The methods for determining OWA operator weights have aroused wide attention. We first review the main existing methods for determining OWA operator weights. We next introduce the principle of maximum entropy for setting up probability distributions on the basis of partial knowledge and prove that Xu’s normal distribution-based method obeys the principle of maximum entropy. Finally, we propose ...

In this paper we propose an extension of the wellknown OWA functions introduced by Yager to interval-valued (IVFS) and Atanassov’s intuitionistic (AIFS) fuzzy set theory. We first extend the arithmetic and the quasi-arithmetic mean using the arithmetic operators in IVFS and AIFS theory and investigate under which conditions these means are idempotent. Since on the unit interval the construction...

Committee scoring voting rules are multiwinner analogues of positional scoring rules which constitute an important subclass of single-winner voting rules. We identify several natural subclasses of committee scoring rules, namely, weakly separable, representation-focused, top-$k$-counting, OWA-based, and decomposable rules. We characterize SNTV, Bloc, and $k$-Approval Chamberlin--Courant as the ...