An extension of the ordering based on nullnorms

Emel Aşıcı

Displaying similar documents to “An extension of the ordering based on nullnorms”

On covariety lattices

Tomasz Brengos (2008)

Discussiones Mathematicae - General Algebra and Applications

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This paper shows basic properties of covariety lattices. Such lattices are shown to be infinitely distributive. The covariety lattice $L_{C V} (K)$ of subcovarieties of a covariety K of F-coalgebras, where F:Set → Set preserves arbitrary intersections is isomorphic to the lattice of subcoalgebras of a $P_{κ}$ -coalgebra for some cardinal κ. A full description of the covariety lattice of Id-coalgebras is given. For any topology τ there exist a bounded functor F:Set → Set and a covariety K of F-coalgebras,...

Lattice-inadmissible incidence structures

Frantisek Machala, Vladimír Slezák (2004)

Discussiones Mathematicae - General Algebra and Applications

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Join-independent and meet-independent sets in complete lattices were defined in [6]. According to [6], to each complete lattice (L,≤) and a cardinal number p one can assign (in a unique way) an incidence structure $J_{L}^{p}$ of independent sets of (L,≤). In this paper some lattice-inadmissible incidence structures are founded, i.e. such incidence structures that are not isomorphic to any incidence structure $J_{L}^{p}$ .

Construction methods for uni-nullnorms and null-uninorms on bounded lattice

Ümit Ertuğrul, M. Nesibe Kesicioğlu, Funda Karaçal (2019)

Kybernetika

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In this paper, two construction methods have been proposed for uni-nullnorms on any bounded lattices. The difference between these two construction methods and the difference from the existing construction methods have been demonstrated and supported by an example. Moreover, the relationship between our construction methods and the existing construction methods for uninorms and nullnorms on bounded lattices are investigated. The charactertics of null-uninorms on bounded lattice $L$ are...

An extension method for t-norms on subintervals to t-norms on bounded lattices

Funda Karaçal, Ümit Ertuğrul, M. Nesibe Kesicioğlu (2019)

Kybernetika

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In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on $L$ from the t-norm on a subinterval of $L$ need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other...

Join-closed and meet-closed subsets in complete lattices

František Machala, Vladimír Slezák (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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To every subset $A$ of a complete lattice $L$ we assign subsets $J (A)$ , $M (A)$ and define join-closed and meet-closed sets in $L$ . Some properties of such sets are proved. Join- and meet-closed sets in power-set lattices are characterized. The connections about join-independent (meet-independent) and join-closed (meet-closed) subsets are also presented in this paper.

On a generalization of Craig lattices

Hao Chen (2013)

Journal de Théorie des Nombres de Bordeaux

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In this paper we introduce generalized Craig lattices, which allows us to construct lattices in Euclidean spaces of many dimensions in the range $3332 - 4096$ which are denser than the densest known Mordell-Weil lattices. Moreover we prove that if there were some nice linear binary codes we could construct lattices even denser in the range $128 - 3272$ . We also construct some dense lattices of dimensions in the range $4098 - 8232$ . Finally we also obtain some new lattices of moderate dimensions such as $68, 84, 85, 86$ , which are denser...

On the direct product of uninorms on bounded lattices

Emel Aşıcı, Radko Mesiar (2021)

Kybernetika

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In this paper, we study on the direct product of uninorms on bounded lattices. Also, we define an order induced by uninorms which are a direct product of two uninorms on bounded lattices and properties of introduced order are deeply investigated. Moreover, we obtain some results concerning orders induced by uninorms acting on the unit interval $[0, 1]$ .

A class of multiplicative lattices

Tiberiu Dumitrescu, Mihai Epure (2021)

Czechoslovak Mathematical Journal

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We study the multiplicative lattices $L$ which satisfy the condition $a = (a : (a : b)) (a : b)$ for all $a, b \in L$ . Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group $ℤ$ or $ℝ$ . A sharp lattice $L$ localized at its maximal elements are totally ordered sharp lattices. The converse is true if $L$ has finite character.