### A partial comparison of two conditions on the intersections of regressive sets.

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Les arguments de Maddy avancés en 1990 contre la théorie des agrégats se trouvent affaiblis par le retournement qu’elle opère en 1997. La présente communication examine cette théorie à la lumière de ce retournement ainsi que des récentes recherches sur les “Nouveaux axiomes pour les mathématiques”. Si la théorie des ensembles est la théorie de la partie–tout des singletons, identifier les singletons à leurs membres singuliers ramène la théorie des ensembles à la théorie des agrégats. Toutefois si...

An axiomatization of fuzzy classes more general than usual fuzzy sets is proposed. Connections and interpretations with other axiomatizations of set theory and fuzzy set theory are investigated.

In the 1960s Professor Hu Guoding proposed a method of measuring information based on the idea that connotation and denotation of a concept satisfies inverse ratio rule. According to this information measure, firstly we put forward the information quantity for information systems and decision systems; then, we discuss the updating mechanism of information quantity for decision systems; finally, we give an attribute reduction algorithm for decision tables with dynamically varying attribute values....

Some of the covering properties of spaces as defined in Parts I and II are here characterized by games. These results, applied to function spaces ${C}_{p}\left(X\right)$ of countable tightness, give new characterizations of countable fan tightness and countable strong fan tightness. In particular, each of these properties is characterized by a Ramseyan theorem.

In [Fund. Math. 210 (2010), 1-46] we claimed the truth of two statements, one now known to be false and a second lacking a proof. In this "Errata" we report these matters in the interest of setting the record straight on the status of these claims.

Total orderings in the range of fuzzy sets can serve as choice criteria for fuzzy sets, a wide class of orderings based on functions is proposed (section 2). Decomposable measures are taken to measure the items on which the fuzzy sets are given (section 3). Combining the two levels of measurement by means of the integral introduced by the second author we obtain evaluations of fuzzy sets as functionals with appropriate properties, the concepts of energy and fuzziness are included (section 4).

This paper follows a companion paper (Stochastica 8 (1984), 99-145) in which we gave the state of the art of the theory of fuzzy relation equations under a special class of triangular norms. Here we continue this theory establishing new results under lower and upper semicontinuous triangular norms and surveying on the main theoretical results appeared in foregoing papers. Max-t fuzzy equations with Boolean solutions are recalled and studied. Many examples clarify the results established.