On extensions of triangular norms on bounded lattices
TLDR
Smallest and largest possible extensions of triangular norms on bounded lattices are discussed and necessary and sufficient conditions for the lattice guaranteeing that the extension is again a t-norm are revealed.About:
This article is published in Indagationes Mathematicae.The article was published on 2008-03-01 and is currently open access. It has received 72 citations till now. The article focuses on the topics: Bounded function & Lattice (order).read more
Citations
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Aggregation functions on bounded partially ordered sets and their classification
Magda Komorníková,Radko Mesiar +1 more
TL;DR: Several classes of aggregation functions on bounded partially ordered sets and special cases of lattices and chains are introduced and discussed, including several types of averaging aggregation functions.
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Characterizing when an ordinal sum of t-norms is a t-norm on bounded lattices
TL;DR: Several necessary and sufficient conditions are presented in this paper for ensuring whether an ordinal sum on a bounded lattice of arbitrary t-norms is, in fact, a t- norm for a particular family of t- norms.
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Extension of fuzzy logic operators defined on bounded lattices via retractions
E. S. Palmeira,B. C. Bedregal +1 more
TL;DR: The primary goal of this paper is to present a method of extending t-norms, t-conorms and fuzzy negations from a sublattice M to the bounded lattice L by considering a more general version of the idea of the sub lattice.
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A new way to extend t-norms, t-conorms and negations
TL;DR: This work presents a method of extending t-norms, t-conorms and fuzzy negations to a lattice-valued setting by preserving the largest possible number of properties of these fuzzy connectives which are invariants under homomorphisms.
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Lattice-valued overlap and quasi-overlap functions
TL;DR: This paper appropriates definitions of overlap functions considering the scope of lattices and introduced a more general definition, called of quasi-overlaps, which arise of abolishes the continuity condition.
References
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Book
Introduction to lattices and order
TL;DR: The Stone Representation Theorem for Boolean algebras and its application to lattices in algebra can be found in this article, where the structure of finite distributive lattices and finite Boolean algebraic structures are discussed.
Book
Metamathematics of Fuzzy Logic
TL;DR: This paper presents a meta-analysis of many-Valued Propositional Logic, focusing on the part of Lukasiewicz's Logic that deals with Complexity, Undecidability and Generalized Quantifiers and Modalities.
Book ChapterDOI
A Useful Four-Valued Logic
TL;DR: It is argued that a sophisticated question-answering machine that has the capability of making inferences from its data base should employ a certain four-valued logic, the motivating consideration being that minor inconsistencies in its data should not be allowed to lead to irrelevant conclusions.