000 03033nam a22004455i 4500
001 978-3-642-16222-0
003 DE-He213
005 20140220083748.0
007 cr nn 008mamaa
008 101001s2011 gw | s |||| 0|eng d
020 _a9783642162220
_9978-3-642-16222-0
024 7 _a10.1007/978-3-642-16222-0
_2doi
050 4 _aQ342
072 7 _aUYQ
_2bicssc
072 7 _aCOM004000
_2bisacsh
082 0 4 _a006.3
_223
100 1 _aRecasens, Jordi.
_eauthor.
245 1 0 _aIndistinguishability Operators
_h[electronic resource] :
_bModelling Fuzzy Equalities and Fuzzy Equivalence Relations /
_cby Jordi Recasens.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2011.
300 _a262p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aStudies in Fuzziness and Soft Computing,
_x1434-9922 ;
_v260
505 0 _aIntroduction -- Granularity and Extensional Sets -- Isometries Between Indistinguishability Operators -- min-indistinguishability Operators and Hierarchical Trees -- Betweenness Relations -- Dimension and Basis -- Aggregation of Indistinguishability Operators -- Making Proximities Transitive -- Fuzzy Functions -- Indistinguishability Operators and Approximate Reasoning -- Vague Groups -- Finitely Valued Indistinguishability Operators.
520 _aIndistinguishability operators are essential tools in fuzzy logic since they fuzzify the concepts of equivalence relation and crisp equality. This book collects all the main aspects of these operators in a single volume for the first time. The stress is put on the study of their structure and the monograph starts presenting the different ways in which indistinguishability operators can be generated and represented. Special attention is paid to the Representation Theorem and the Sup-T product. Extensionality of fuzzy subsets is studied in detail and is related to their observability and to the granularity. The metric behaviour of indistinguishability operators and their connection with cluster analysis and hierarchical trees is established. Different ways to aggregate such operators are given as well as a number of methods to obtain transitive approximations of a fuzzy relation. Applications to approximate reasoning and to the study of fuzzy subgroups are also provided. The book ends with a chapter on finite-valued indistinguishability operators.
650 0 _aEngineering.
650 0 _aArtificial intelligence.
650 1 4 _aEngineering.
650 2 4 _aComputational Intelligence.
650 2 4 _aArtificial Intelligence (incl. Robotics).
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642162213
830 0 _aStudies in Fuzziness and Soft Computing,
_x1434-9922 ;
_v260
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-16222-0
912 _aZDB-2-ENG
999 _c107133
_d107133