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Generating methods for principal topologies on bounded lattices

Funda Karaçal, Ümit Ertuğrul, M. Nesibe Kesicioğlu (2021)

Kybernetika

In this paper, some generating methods for principal topology are introduced by means of some logical operators such as uninorms and triangular norms and their properties are investigated. Defining a pre-order obtained from the closure operator, the properties of the pre-order are studied.

Generation of fuzzy mathematical morphologies.

Pedro J. Burillo López, Noé Frago Paños, Ramón Fuentes González (2001)

Mathware and Soft Computing

Fuzzy Mathematical Morphology aims to extend the binary morphological operators to grey-level images. In order to define the basic morphological operations fuzzy erosion, dilation, opening and closing, we introduce a general method based upon fuzzy implication and inclusion grade operators, including as particular case, other ones existing in related literature. In the definition of fuzzy erosion and dilation we use several fuzzy implications (Annexe A, Table of fuzzy implications), the paper includes...

Generation of multi-dimensional aggregation functions.

Margalida Mas Grimalt, Gaspar Mayor Forteza, Jaume Suñer, Joan Torrens (1998)

Mathware and Soft Computing

In this paper we study two ways of generating multi-dimensional aggregation functions. First of all we obtain multi-dimensional OWA operators in two different ways, one of them through quantifiers and the other through sequences. In the first case, we see that all the operators we obtain are multi-dimensional aggregation functions. We then characterize the multi-dimensional aggregation functions that are generated by quantifiers. In the second case, we characterize the sequences that provide multi-dimensional...

Generic extensions of models of ZFC

Lev Bukovský (2017)

Commentationes Mathematicae Universitatis Carolinae

The paper contains a self-contained alternative proof of my Theorem in Characterization of generic extensions of models of set theory, Fund. Math. 83 (1973), 35–46, saying that for models M ⊆ N of ZFC with same ordinals, the condition A p r M , N ( κ ) implies that N is a κ -C.C. generic extension of M .

Generic sets in definably compact groups

Ya'acov Peterzil, Anand Pillay (2007)

Fundamenta Mathematicae

A subset X of a group G is called left genericif finitely many left translates of X cover G. Our main result is that if G is a definably compact group in an o-minimal structure and a definable X ⊆ G is not right generic then its complement is left generic. Among our additional results are (i) a new condition equivalent to definable compactness, (ii) the existence of a finitely additive invariant measure on definable sets in a definably compact group G in the case where G = *H...

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