placeholder
and
and

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
Language
Year
  • 1
    Article
    Article
    2018
    ISSN: 0002-5240 
    Language: English
    In: Algebra universalis, 2018-04-20, Vol.79 (2), p.1-31
    Description: For L a complete lattice L and X = ( X , ( R i ) I ) a relational structure, we introduce the convolution algebra L X . This algebra consists of the lattice L X equipped with an additional n i -ary operation f i for each n i + 1 -ary relation R i of X . For α 1 , … , α n i ∈ L X and x ∈ X we set f i ( α 1 , … , α n i ) ( x ) = ⋁ { α 1 ( x 1 ) ∧ ⋯ ∧ α n i ( x n i ) : ( x 1 , … , x n i , x ) ∈ R i } . For the 2-element lattice 2, 2 X is the reduct of the familiar complex algebra X + obtained by removing Boolean complementation from the signature. It is shown that this construction is bifunctorial and behaves well with respect to one-one and onto maps and with respect to products. When L is the reduct of a complete Heyting algebra, the operations of L X are completely additive in each coordinate and L X is in the variety generated by 2 X . Extensions to the construction are made to allow for completely multiplicative operations defined through meets instead of joins, as well as modifications to allow for convolutions of relational structures with partial orderings. Several examples are given.
    Subject(s): Algebra ; Article ; Boolean algebra ; Construction ; Convolution ; In memory of Bjarni Jónsson ; Mathematics ; Mathematics and Statistics
    ISSN: 0002-5240
    E-ISSN: 1420-8911
    Source: Alma/SFX Local Collection
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 2
    Article
    Article
    2016
    ISSN: 0884-8173 
    Language: English
    In: International journal of intelligent systems, 2016-03, Vol.31 (3), p.257-275
    Description: The algebra of truth values of type‐2 fuzzy sets is the set of maps from the unit interval to itself with convolution ordering. In applications of type‐2 fuzzy sets, the full algebra is seldom used, but rather certain subalgebras that satisfy useful algebraic properties. The algebra of truth values of type‐2 fuzzy sets is not itself a lattice, but the subalgebras considered here are lattices and, in fact, are complete distributive lattices. The subalgebras of special interest are the lattice of convex normal maps, the lattice of convex strongly normal maps, and the lattice of upper semicontinuous convex normal maps. We review and summarize some interesting properties of these subalgebras. A special feature of our treatment is a representation of these algebras as sets of monotone functions with pointwise order, making the operations more intuitive.
    Subject(s): Algebra ; Convolution ; Fuzzy logic ; Fuzzy set theory ; Fuzzy sets ; Intervals ; Lattices ; Maps ; Monotone functions ; Representations
    ISSN: 0884-8173
    E-ISSN: 1098-111X
    Source: Hellenic Academic Libraries Link
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 3
    Article
    Article
    2009
    ISSN: 0884-8173 
    Language: English
    In: International journal of intelligent systems, 2009-01, Vol.24 (1), p.62-75
    Description: This paper contains some general comments on the algebra of truth values of fuzzy sets of type 2. It details the precise mathematical relationship with the algebras of truth values of ordinary fuzzy sets and of interval‐valued fuzzy sets. Subalgebras of the algebra of truth values and t‐norms on them are discussed. There is some discussion of finite type‐2 fuzzy sets. © 2008 Wiley Periodicals, Inc.
    ISSN: 0884-8173
    E-ISSN: 1098-111X
    Source: Hellenic Academic Libraries Link
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 4
    Book
    Book
    1981
    ISBN: 9783540108559  ISBN: 3540108556 
    ISSN: 0075-8434 
    Language: German
    Subject(s): Group theory ; Group Theory and Generalizations ; Mathematics ; Mathematics and Statistics
    ISBN: 9783540108559
    ISBN: 3540108556
    ISSN: 0075-8434
    E-ISSN: 1617-9692
    Source: Alma/SFX Local Collection
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 5
    Article
    Article
    2002
    ISSN: 0165-0114 
    Language: English
    In: Fuzzy sets and systems, 2002, Vol.129 (1), p.1-18
    Description: In this paper we consider the rth powers of a continuous t-norm for positive real numbers r, generalizing the notion of the diagonal (2nd power). We identify the increasing functions from the unit interval to itself that are realized as the rth power of some continuous t-norm. The strict and nilpotent cases are described in detail.
    Subject(s): Diagonal ; Exact sciences and technology ; General logic ; Isomorphism ; Logic and foundations ; Mathematical logic, foundations, set theory ; Mathematics ; Power of t-norm ; Sciences and techniques of general use ; Set theory ; t-norm
    ISSN: 0165-0114
    E-ISSN: 1872-6801
    Source: Backfile Package - All of Back Files EBS [ALLOFBCKF]
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 6
    Language: English
    Subject(s): Group theory ; Group Theory and Generalizations
    ISBN: 3540084479
    ISBN: 9783662172193
    ISBN: 9783540084471
    ISBN: 3662172194
    Source: Alma/SFX Local Collection
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 7
    Article
    Article
    2002
    ISSN: 0035-7596 
    Language: English
    In: The Rocky Mountain journal of mathematics, 2002-12-01, Vol.32 (4), p.1257-1265
    Subject(s): Algebra ; Exact sciences and technology ; Funding ; Group development ; Group theory ; Group theory and generalizations ; Mathematical rings ; Mathematical theorems ; Mathematics ; On the History of Abelian Group Theory ; Sciences and techniques of general use ; Topological groups, lie groups ; Topology
    ISSN: 0035-7596
    E-ISSN: 1945-3795
    Source: Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals
    Source: JSTOR Arts & Sciences XV
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 8
    Article
    Article
    2012
    ISSN: 0002-5240 
    Language: English
    In: Algebra universalis, 2012-04-07, Vol.67 (4), p.347-374
    Description: An algebra with two binary operations · and +  that are commutative, associative, and idempotent is called a bisemilattice. A bisemilattice that satisfies Birkhoff’s equation x · ( x + y ) =  x + ( x · y ) is a Birkhoff system. Each bisemilattice determines, and is determined by, two semilattices, one for the operation +  and one for the operation ·. A bisemilattice for which each of these semilattices is a chain is called a bichain. In this note, we characterize the finite bichains that are weakly projective in the variety of Birkhoff systems as those that do not contain a certain three-element bichain. As subdirectly irreducible weak projectives are splitting, this provides some insight into the fine structure of the lattice of subvarieties of Birkhoff systems.
    Subject(s): Algebra ; Article ; Mathematics ; Mathematics and Statistics
    ISSN: 0002-5240
    E-ISSN: 1420-8911
    Source: Alma/SFX Local Collection
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 9
    Book chapter
    Book chapter
    ISBN: 9783540729174  ISBN: 3540729178 
    ISSN: 0302-9743 
    Language: English
    In: Foundations of Fuzzy Logic and Soft Computing, p.56-65
    Description: The algebra of truth values for fuzzy sets of type-2, due to Zadeh, contains as subalgebras those of type-1 and of interval-valued fuzzy sets. It also contains many other interesting subalgebras, some of which could possibly serve as a basis of a useful fuzzy set theory. This paper is about one such subalgebra which we call the subalgebra of points, and which generalizes type-1. We investigate it as an algebra, and determine its automorphism group. In particular, we show that is it a characteristic subalgebra and that its automorphisms are exactly those induced by automorphisms of the containing truth value algebra of fuzzy sets of type-2.
    Subject(s): Fuzzy truth values ; interval-valued fuzzy set ; type-1 fuzzy set ; type-2 fuzzy set
    ISBN: 9783540729174
    ISBN: 3540729178
    ISSN: 0302-9743
    E-ISSN: 1611-3349
    Source: Springer Lecture Notes in Computer Science eBooks
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 10
    Language: English
    Description: Like most good educational interventions, problem-based learning (PBL) did not grow out of theory, but out of a practical problem. Medical students were bored, dropping out, and unable to apply what they had learned in lectures to their practical experiences a couple of years later. Neurologist Howard S. Barrows reversed the sequence, presenting students with patient problems to solve in small groups and requiring them to seek relevant knowledge in an effort to solve those problems. Out of his work, PBL was born. The application of PBL approaches has now spread far beyond medical education. Today, PBL is used at levels from elementary school to adult education, in disciplines ranging across the humanities and sciences, and in both academic and corporate settings. This book aims to take stock of developments in the field and to bridge the gap between practice and the theoretical tradition, originated by Barrows, that underlies PBL techniques. The book is divided into four sections, each containing contributions by leaders in the field. Chapters in the first section focus on the structure of PBL and the critical elements of the approach. Articulating the underlying problems to be addressed, the role of facilitators, and the process to be followed in achieving a successful PBL intervention are all discussed. The second section explores how PBL has been adapted to function in areas outside medicine, from climate science to teacher education, while the third section explores how the methodology has been combined with other approaches to teaching and learning, such as learning by design and project-based learning. The fourth section assesses the impact of PBL techniques on improving both research and teaching. An epilogue speculates about the future of PBL, synthesizing contributions from the previous chapters and suggesting key themes for further exploration.
    Subject(s): 1928 ; Barrows, Howard S ; EDUCATION ; Philosophy & Social Aspects ; Problem-based learning ; Science & Technology ; Teaching Methods & Materials
    ISBN: 9781557536822
    ISBN: 1557536821
    Source: Ebook Central - Academic Complete
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...