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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

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 construction...

An extension of the ordering based on nullnorms

Emel Aşıcı (2019)

Kybernetika

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.

An ILP model for a monotone graded classification problem

Peter Vojtáš, Tomáš Horváth, Stanislav Krajči, Rastislav Lencses (2004)

Kybernetika

Motivation for this paper are classification problems in which data can not be clearly divided into positive and negative examples, especially data in which there is a monotone hierarchy (degree, preference) of more or less positive (negative) examples. We present a new formulation of a fuzzy inductive logic programming task in the framework of fuzzy logic in narrow sense. Our construction is based on a syntactical equivalence of fuzzy logic programs FLP and a restricted class of generalised annotated...

An incremental approach to obtaining attribute reduction for dynamic decision systems

Liu Wenjun (2016)

Open Mathematics

In the 1960s Professor Hu Guoding proposed a method of measuring information based on the idea that connotation and denotation of a concept satisfies inverse ratio rule. According to this information measure, firstly we put forward the information quantity for information systems and decision systems; then, we discuss the updating mechanism of information quantity for decision systems; finally, we give an attribute reduction algorithm for decision tables with dynamically varying attribute values....

An indecomposable Banach space of continuous functions which has small density

Rogério Augusto dos Santos Fajardo (2009)

Fundamenta Mathematicae

Using the method of forcing we construct a model for ZFC where CH does not hold and where there exists a connected compact topological space K of weight ω ₁ < 2 ω such that every operator on the Banach space of continuous functions on K is multiplication by a continuous function plus a weakly compact operator. In particular, the Banach space of continuous functions on K is indecomposable.

An independency result in connectification theory

Alessandro Fedeli, Attilio Le Donne (1999)

Commentationes Mathematicae Universitatis Carolinae

A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let ψ be the following statement: “a perfect T 3 -space X with no more than 2 𝔠 clopen subsets is connectifiable if and only if no proper nonempty clopen subset of X is feebly compact". In this note we show that neither ψ nor ¬ ψ is provable in ZFC.

An inquiry-based method for Choquet integral-based aggregation of interface usability parameters

Miguel-Ángel Sicilia, Elena García Barriocanal, Tomasa Calvo (2003)

Kybernetika

The concept of usability of man-machine interfaces is usually judged in terms of a number of aspects or attributes that are known to be subject to some rough correlations, and that are in many cases given different importance, depending on the context of use of the application. In consequence, the automation of judgment processes regarding the overall usability of concrete interfaces requires the design of aggregation operators that are capable of modeling approximate or ill-defined interactions...

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