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

Ümit Ertuğrul; M. Nesibe Kesicioğlu; Funda Karaçal

Displaying similar documents to “Construction methods for uni-nullnorms and null-uninorms on bounded lattice”

An extension of the ordering based on nullnorms

Emel Aşıcı (2019)

Kybernetika

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In this paper, we generally study an order induced by nullnorms on bounded lattices. We investigate monotonicity property of nullnorms on bounded lattices with respect to the $F$ -partial order. Also, we introduce the set of incomparable elements with respect to the F-partial order for any nullnorm on a bounded lattice. Finally, we investigate the relationship between the order induced by a nullnorm and the distributivity property for nullnorms.

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 $[0, 1]$ .

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...

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 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 $J_{L}^{p}$ .

Free $𝔪$ -products of lattices. II

George Grätzer, David Kelly (1986)

Colloquium Mathematicae

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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...

Free $𝔪$ -products of lattices. I

George Grätzer, David Kelly (1984)

Colloquium Mathematicae

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Generalized $P_{0}$ -lattices of order ω+

T. Traczyk, W. Zarębski (1976)

Colloquium Mathematicae

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New constructions of uni-nullnorms on certain classes of bounded lattices by closure (interior) operators

Tao Wu (2024)

Kybernetika

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The primary aim of this article is to put forward new classes of uni-nullnorms on certain classes of bounded lattices via closure (interior) operators. Due to the new classes of uninorms combining both a t-norm $T$ and a t-conorm $S$ by various kinds of closure operators or interior operators, the relationships and properties among the same class of uninorms on $L$ , we obtain new classes of uni-nullnorms on $L$ via closure (interior) operators. The constructions of uni-nullnorms on some certain...