Desirable Axioms Research Articles

Uncertainty measures for evidential reasoning I: A review

This paper is divided into two parts. Part I discusses limitations of the measures of global uncertainty of Lamata and Moral and total uncertainty of Klir and Ramer. We prove several properties of different nonspecificity measures. The computational complexity of different total uncertainty measures is discussed. The need for a new measure of total uncertainty is established in Part I. In Part II, we propose a set of intuitively desirable axioms for a measure of total uncertainty and then derive an expression for the same. Several theorems are proved about the new measure. The proposed measure is additive, and unlike other measures, has a unique maximum. This new measure reduces to Shannon's probabilistic entropy when the basic probability assignment focuses only on singletons. On the other hand, complete ignorance—basic assignment focusing only on the entire set, as a whole—reduces it to Hartley's measure of information. The computational complexity of the proposed measure is O(N), whereas the previous measures are O(N 2).

Is there a convenient category of spectra?

The construction of the smash product of two spectra is one of the most unsatisfactory aspects of every available treatment of the stable category. Increased interest in enriched ring and module spectra has made the misbehavior of smash products a source of growing frustration. This paper conveys the unhappy message that this frustration is unavoidable. Five simple, obviously desirable axioms for a good category of spectra with a well-behaved smash product are listed. Then it is shown that no category can satisfy all five of these minimal axioms.