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S -measures, T -measures and distinguished classes of fuzzy measures

Peter Struk, Andrea Stupňanová (2006)

Kybernetika

S -measures are special fuzzy measures decomposable with respect to some fixed t-conorm S . We investigate the relationship of S -measures with some distinguished properties of fuzzy measures, such as subadditivity, submodularity, belief, etc. We show, for example, that each S P -measure is a plausibility measure, and that each S -measure is submodular whenever S is 1-Lipschitz.

S V -Rings and S V -Porings

Niels Schwartz (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

S V -rings are commutative rings whose factor rings modulo prime ideals are valuation rings. S V -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 S V -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 S V -rings ( S V -porings) are introduced, and...

Sacks forcing collapses 𝔠 to 𝔟

Petr Simon (1993)

Commentationes Mathematicae Universitatis Carolinae

We shall prove that Sacks algebra is nowhere ( 𝔟 , 𝔠 , 𝔠 ) -distributive, which implies that Sacks forcing collapses 𝔠 to 𝔟 .

Sandwiching the Consistency Strength of Two Global Choiceless Cardinal Patterns

Arthur W. Apter (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We provide upper and lower bounds in consistency strength for the theories “ZF + ¬ A C ω + 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 + ¬ A C ω + 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...

Scalar cardinalities for divisors of a fuzzy cardinality.

Juan Casasnovas Casasnovas (2002)

Mathware and Soft Computing

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,...

Schanuel Nullstellensatz for Zilber fields

Paola D'Aquino, Angus Macintyre, Giuseppina Terzo (2010)

Fundamenta Mathematicae

We characterize the unsolvable exponential polynomials over the exponential fields introduced by Zilber, and deduce Picard's Little Theorem for such fields.

Searching degrees of self-contradiction in Atanassov's fuzzy sets.

Elena E. Castiñeira, Susana Cubillo, Carmen Torres (2006)

Mathware and Soft Computing

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,...

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