In this article we present a proposal for the descomposition of large uncertainties associated with a fuzzy set u and the multilinearization of a function f to be used in the approximation of the fuzzy set f̂(u) obtained by extension principle. Also, we present conditions on f assuring that f̂ preserves differentiability.

Spline wavelet tight frames of [20] have been used widely in frame based image analysis and restorations (see, e.g. survey articles [15, 22]). However, except for the tight frame property and the approximation order of the truncated series (see [13,20]), there are few other properties of this family of spline wavelet tight frames to be known. This paper is to present a few new properties of thi...

Jaccard index similarity measure which applies the extension principle approach to obtain fuzzy maximum and fuzzy minimum has been proposed in ranking fuzzy numbers. However, the extension principle used is only applicable to normal fuzzy numbers and, therefore, fails to rank non-normal ones. Apart from that, the extension principle does not preserve the type of membership function of fuzzy num...

The unitary extension principle (UEP) by Ron and Shen yields conditions for the construction of a multi-generated tight wavelet frame for L2(Rs) based on a given refinable function. In this paper we show that the UEP can be generalized to locally compact abelian groups. In the general setting, the resulting frames are generated by modulates of a collection of functions; via the Fourier transfor...

Over the past two decades, naturalistically minded philosophers have expended a fair amount of ______________________________ This paper presents the leading idea of my doctoral dissertation and thus has been shaped by the reactions of all the members of my thesis committee: Charles Chastain, Walter Edelberg, W. Kent Wilson, Dorothy Grover, and Charles Marks. I am especially grateful for the he...

This paper addresses invariance principles for a certain class of switched nonlinear systems. We provide an extension of LaSalle’s Invariance Principle for these systems and state asymptotic stability criteria. We also present some related results that deal with the compactness of the trajectories of these switched systems and that are interesting by their own.

Transportation models play an important role in logistics and supply chain management for reducing cost and improving service. This paper develops a procedure to derive the fuzzy objective value of the fuzzy transportation problem, in that the cost coefficients and the supply and demand quantities are fuzzy numbers. The idea is based on the extension principle. A pair of mathematical programs i...

This paper studies the problem of providing multiple public goods for agents with single-peaked preferences. A decision rule selects m points for the m identical public goods for every pro le of reported preferences. In Miyagawa (1998c) these multiple public goods are options, i.e., alternatives are compared by the most preferred goods according to the agents' preferences. In this paper agents ...

The increasing variety of semantics proposed in the context of Dung’s theory of argumentation makes more and more inadequate the example-based approach commonly adopted for evaluating and comparing different semantics. To fill this gap, this paper provides two main contributions. First, a set of general criteria for semantics evaluation is introduced by proposing a formal counterpart to several...