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Minimizing and maximizing a linear objective function under a fuzzy max - * relational equation and an inequality constraint

Zofia Matusiewicz (2022)

Kybernetika

This paper provides an extension of results connected with the problem of the optimization of a linear objective function subject to max - * fuzzy relational equations and an inequality constraint, where * is an operation. This research is important because the knowledge and the algorithms presented in the paper can be used in various optimization processes. Previous articles describe an important problem of minimizing a linear objective function under a fuzzy max - * relational equation and an inequality constraint,...

Mixed Levels of Indestructibility

Arthur W. Apter (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

Starting from a supercompact cardinal κ, we force and construct a model in which κ is both the least strongly compact and least supercompact cardinal and κ exhibits mixed levels of indestructibility. Specifically, κ 's strong compactness, but not its supercompactness, is indestructible under any κ -directed closed forcing which also adds a Cohen subset of κ. On the other hand, in this model, κ 's supercompactness is indestructible under any κ -directed closed forcing which does not add a Cohen subset...

Mixed pseudo-associativities of Bandler-Kohout compositions of relations

Jolanta Sobera (2007)

Kybernetika

This paper considers compositions of relations based on the notion of the afterset and the foreset, i. e., the subproduct, the superproduct and the square product introduced by Bandler and Kohout with modification proposed by De Baets and Kerre. There are proven all possible mixed pseudo-associativity properties of Bandler – Kohout compositions of relations.

Möbius fitting aggregation operators

Anna Kolesárová (2002)

Kybernetika

Standard Möbius transform evaluation formula for the Choquet integral is associated with the 𝐦𝐢𝐧 -aggregation. However, several other aggregation operators replacing 𝐦𝐢𝐧 operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all 3-copulas are shown to be fitting and moreover, all fitting weighted means are characterized. This new method...

Modelos auxiliares para problemas de programación lineal con coeficientes imprecisos en las restricciones.

Luis M. de Campos Ibáñez, José Luis Verdegay (1989)

Trabajos de Investigación Operativa

En este artículo se considera un programa de Programación Lineal en el que los coeficientes del sistema de inecuaciones lineales, que definen el conjunto de restricciones, están dados de forma imprecisa o vaga. Se supone entonces que tales coeficientes pueden ser definidos mediante números difusos. Se propone un enfoque de resolución basado en las distintas versiones existentes para la comparación de números difusos. Finalmente, se obtienen diferentes modelos auxiliares de Programación Lineal, que...

Monotonic valuations of π σ -triads and evaluations of ideals

Josef Mlček (1993)

Commentationes Mathematicae Universitatis Carolinae

We develop problems of monotonic valuations of triads. A theorem on monotonic valuations of triads of the type π σ is presented. We study, using the notion of the monotonic valuation, representations of ideals by monotone and subadditive mappings. We prove, for example, that there exists, for each ideal J of the type π on a set A , a monotone and subadditive set-mapping h on P ( A ) with values in non-negative rational numbers such that J = h - 1 ' ' { r ∈ Q ; r ≥ 0 & r ≐ 0 } . Some analogical results are proved for ideals of the types σ , σ π and...

More about spaces with a small diagonal

Alan Dow, Oleg Pavlov (2006)

Fundamenta Mathematicae

Hušek defines a space X to have a small diagonal if each uncountable subset of X² disjoint from the diagonal has an uncountable subset whose closure is disjoint from the diagonal. Hušek proved that a compact space of weight ω₁ which has a small diagonal will be metrizable, but it remains an open problem to determine if the weight restriction is necessary. It has been shown to be consistent that each compact space with a small diagonal is metrizable; in particular, Juhász and Szentmiklóssy proved...

More Easton theorems for level by level equivalence

Arthur W. Apter (2012)

Colloquium Mathematicae

We establish two new Easton theorems for the least supercompact cardinal that are consistent with the level by level equivalence between strong compactness and supercompactness. These theorems generalize Theorem 1 in our earlier paper [Math. Logic Quart. 51 (2005)]. In both our ground model and the model witnessing the conclusions of our present theorems, there are no restrictions on the structure of the class of supercompact cardinals.

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