The aim of this paper is to provide a different, somewhat more general, approach to the axiomatic ranking of opportunity sets in terms of freedom of choice. The opportunity ranking is defined axiomatically relative to some standard of freedom or theory of freedom. The paper then provides a general characterization result of the opportunity ranking in terms of the family of freedom standards.

To unify the motivating principles behind Max-Sum and Single-Linkage clustering, we consider an axiomatic approach to the theory of Clustering. We discuss abstract properties of clustering functions, following the framework of Kleinberg, [7]. By relaxing one of Kleinberg’s clustering axioms, we sidestep his impossibility result and arrive at a consistent set of axioms. We suggest to extend thes...

In [She82], it is shown that four of its basic functional properties are enough to characterize plain Kolmogorov complexity, hence obtaining an axiomatic characterization of this notion. In this paper, we try to extend this work, both by looking at alternative axiomatic systems for plain complexity and by considering potential axiomatic systems for other types of complexity. First we show that ...

ur aim of this  paper  is  to introduce the concept of $L$-double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$-double fuzzy lower (resp. upper) approximation operators is defined  and the basic properties of them  are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L...

In this paper, we adopt supreme-utilities among fuzzy level (decision) vectors to propose a power allocation rule, its efficient extension and normalization in the framework of multicriteria fuzzy transferable-utility (TU) games. We also provide several axiomatic results to present the rationality for these rules. Based on different viewpoints, we introduce different formulations and dynamic re...

In this paper we apply the theory of the quantum groups Uq(g), and of the small quantum groups uq(g) for q a root of unity, g a semisimple complex Lie algebra, to obtain a classification result for an abstractly defined class of Hopf algebras. Since these Hopf algebras turn out to be deformations of a natural class of generalized small quantum groups, our result can be read as an axiomatic desc...