Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we study difference bounds and octagonal relations and prove that their transitive closure is a PTIMEcomputable formula in the existential fragment of Presburger arithmetic. This result marks a significant complexity improvement, as the known algorithms have EXPTIME wo...

In practice, some special LR fuzzy numbers, like the triangular fuzzy number, the Gaussian fuzzy number and the Cauchy fuzzy number, are widely used in many areas to deal with various vague information. With regard to these special LR fuzzy numbers, called regular LR fuzzy numbers in this paper, an operational law is proposed for fuzzy arithmetic, providing a novel approach to analytically and ...

Well-defined carbon polyhedrons with faceted morphologies and hollow internal structures made of self-organized multi-walled carbon nanotubes have been fabricated by gas phase catalytic CVD inside microchannels, of which the confined space is critical for the formation of polyhedral structures with hexagonal, heptagonal and octagonal cross-sections that show superhydrophobic properties, with th...

Vagueness is a common human knowledge and linguistic phenomenon, typically manifested by predicates that lack clear applicability conditions and boundaries such as High, Expert or Bad. In the context of ontologies and semantic data, the usage of such predicates within ontology element definitions (classes, relations etc.) can hamper the latter’s quality, primarily in terms of shareability and m...

Soft set theory, proposed by Molodtsov has been regarded as an effective mathematical tool to deal with uncertainties. Vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of [0, 1]. Such a set is characterized by a truth-membership function and a falsemembership function. Thus, a vague set is actually a form of fuzzy set, albeit a more ...

Internet users face large numbers of security warnings, which they mostly ignore. To improve risk communication, warnings must be fewer but better. We report an experiment on whether compliance can be increased by using some of the social-psychological techniques the scammers themselves use, namely appeal to authority, social compliance, concrete threats and vague threats. We also investigated ...

This paper studies organizations in which participants have common preferences but communication is costly. In this model, use words to describe similar information, but need not use precise words for frequent events and vague words for unusual ones. The model identifies a source of communication failure across units. It provides an argument for giving the best-informed agents decision-making a...