-measures are special fuzzy measures decomposable with respect to some fixed t-conorm . We investigate the relationship of -measures with some distinguished properties of fuzzy measures, such as subadditivity, submodularity, belief, etc. We show, for example, that each -measure is a plausibility measure, and that each -measure is submodular whenever is 1-Lipschitz.
-rings are commutative rings whose factor rings modulo prime ideals are valuation rings. -rings occur most naturally in connection with partially ordered rings (= porings) and have been studied only in this context so far. The present note first develops the theory of -rings systematically, without assuming the presence of a partial order. Particular attention is paid to the question of axiomatizability (in the sense of model theory). Partially ordered -rings (-porings) are introduced, and...
We shall prove that Sacks algebra is nowhere -distributive, which implies that Sacks forcing collapses to .
We provide upper and lower bounds in consistency strength for the theories “ZF + + All successor cardinals except successors of uncountable limit cardinals are regular + Every uncountable limit cardinal is singular + The successor of every uncountable limit cardinal is singular of cofinality ω” and “ZF + + All successor cardinals except successors of uncountable limit cardinals are regular + Every uncountable limit cardinal is singular + The successor of every uncountable limit cardinal is singular...
The cardinality of a finite fuzzy set can be defined as a scalar or a fuzzy quantity. The fuzzy cardinalities are represented by means the generalized natural numbers, where it is possible to define arithmetical operations, in particular the division by a natural number. The main result obtained in this paper is that, if determined conditions are assured, the scalar cardinality of a finite fuzzy set, B, whose fuzzy cardinality is a rational part of the fuzzy cardinality of another fuzzy set, A,...
We characterize the unsolvable exponential polynomials over the exponential fields introduced by Zilber, and deduce Picard's Little Theorem for such fields.
In [11] and [12] Trillas et al. introduced the study of contradiction in the framework of Fuzzy Logic because of the significance to avoid contradictory outputs in the processes of inference. Later, the study of contradiction in the framework of intuitionistic or Atanassov s fuzzy sets was initiated in [6] and [5]. The aim of this work is to go into the problem of measuring the self-contradiction in the case of intuitionistc fuzzy sets, since it is interesting to know not only if a set is contradictory,...