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Quasi-Copulas, Copulas and Fuzzy Implicators

Radko Mesiar, Anna Koles
<span title="">2020</span> <i title="Atlantis Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wjdkfhqywrdefeqoyzjz3os76i" style="color: black;">International Journal of Computational Intelligence Systems</a> </i> &nbsp;
In addition, we introduce a construction method for fuzzy implicators based on any two copulas and a Lebesgue integrable fuzzy implicator, and discuss some of its special cases.  ...  Based on these relations, we introduce, discuss and exemplify several new construction methods for fuzzy implicators, and also discuss several dualities on the class of all 1-Lipschitz fuzzy implicators  ...  CONFLICT OF INTEREST Both authors have participated equally on the work on this paper. ACKNOWLEDGMENTS Both authors are grateful for the support of the project APVV-18-0052. R.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2991/ijcis.d.200527.004">doi:10.2991/ijcis.d.200527.004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/reh5mh3ikvguhigu2yamzkhisu">fatcat:reh5mh3ikvguhigu2yamzkhisu</a> </span>
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Fuzzy implicators related to (quasi-)copulas

Anna Kolesárová, Radko Mesiar
<span title="">2019</span> <i title="Atlantis Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q47jwxc36zhozejiwja7mtgcsu" style="color: black;">Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)</a> </i> &nbsp;
In addition, we introduce a construction method for fuzzy implicators based on any two copulas and a Lebesgue integrable fuzzy implicator, and discuss some special cases as well.  ...  In this paper, we study relations between fuzzy implicators and some kinds of fuzzy conjunctors, in particular, quasi-copulas and copulas.  ...  Mesiar on this paper was supported by the NPUII project LQ1602 and the project APVV-17-0066.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2991/eusflat-19.2019.35">doi:10.2991/eusflat-19.2019.35</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/eusflat/KolesarovaM19.html">dblp:conf/eusflat/KolesarovaM19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a4tijgwulre37e73ncojwcoslu">fatcat:a4tijgwulre37e73ncojwcoslu</a> </span>
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Probabilistic Implications

Przemyslaw Grzegorzewski
<span title="">2011</span> <i title="Atlantis Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q47jwxc36zhozejiwja7mtgcsu" style="color: black;">Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011)</a> </i> &nbsp;
The suggested implications are based on conditional copulas and make a bridge between probability theory and fuzzy logic.  ...  A new family of implication operators, called probabilistic implications, is introduced.  ...  It is not surprising that starting from different classical definitions and using diversity of methods we may obtain a many fuzzy implications having different properties.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2991/eusflat.2011.67">doi:10.2991/eusflat.2011.67</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/eusflat/Grzegorzewski11.html">dblp:conf/eusflat/Grzegorzewski11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fiyjrdfcefevnmg7maskzijpzy">fatcat:fiyjrdfcefevnmg7maskzijpzy</a> </span>
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Probabilistic implications

Przemysław Grzegorzewski
<span title="">2013</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wcbukkuh2vbrpcbz2f4z2a2g6u" style="color: black;">Fuzzy sets and systems (Print)</a> </i> &nbsp;
The suggested implications are based on conditional copulas and make a bridge between probability theory and fuzzy logic.  ...  A new family of implication operators, called probabilistic implications, is introduced.  ...  It is not surprising that starting from different classical definitions and using diversity of methods we may obtain a many fuzzy implications having different properties.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.fss.2013.01.003">doi:10.1016/j.fss.2013.01.003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eagymrcpwnavnmdr4kjjrzewwi">fatcat:eagymrcpwnavnmdr4kjjrzewwi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180725061751/https://download.atlantis-press.com/article/2252/pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a9/c4/a9c41c9dcb79bdd9d3dd72101ac74404c5d49798.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.fss.2013.01.003"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Fuzzy preference modelling and some consequences for fuzzy implications and quasi-copulas

Dana Hlin na, Martin Kalina, Pavol Kra
<span title="">2013</span> <i title="Atlantis Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q47jwxc36zhozejiwja7mtgcsu" style="color: black;">Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology</a> </i> &nbsp;
As we show, an important property of fuzzy implications that enables us to construct a generator triple from a fuzzy implication, is the contrapositive symmetry.  ...  We study also conditions under which fuzzy implications can be used to construct generator triples.  ...  Acknowledgements Martin Kalina has been supported from the Science and Technology Assistance Agency under contract No. APVV-0073-10, and from the VEGA grant agency, grant number 1/0143/11.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2991/eusflat.2013.43">doi:10.2991/eusflat.2013.43</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/eusflat/HlinenaKK13.html">dblp:conf/eusflat/HlinenaKK13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/t4c7wpt4arbytde52bmx2dbknm">fatcat:t4c7wpt4arbytde52bmx2dbknm</a> </span>
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Guest Editorial Foreword to the Special Issue on Aggregation Operators

Gleb Beliakov, Tomasa Calvo, Radko Mesiar
<span title="">2007</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7dwepyc5xbc47narcaqganu4vu" style="color: black;">IEEE transactions on fuzzy systems</a> </i> &nbsp;
De Baets and De Meyer focus on the topic of copulas, and in particular construction of copulas in a patchwork-like assembly of arbitrary copulas.  ...  Implication functions are closely related to aggregation functions, and in some cases are constructed based on aggregation functions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tfuzz.2007.904112">doi:10.1109/tfuzz.2007.904112</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6unoaxpmq5fndiskgifb7agpnq">fatcat:6unoaxpmq5fndiskgifb7agpnq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120408193226/http://dro.deakin.edu.au/eserv/DU:30013545/beliakov-guesteditorial-2007.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/93/7d/937dc007d17a26c4d9e705046bfec02e0bd33696.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tfuzz.2007.904112"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

GENERALIZED COMPOSITION OF BINARY AGGREGATION OPERATORS

FABRIZIO DURANTE
<span title="">2005</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2mchw27ezjaivoukjltsyavclq" style="color: black;">International Journal of Uncertainty Fuzziness and Knowledge-Based Systems</a> </i> &nbsp;
Generalized composition of binary aggregation operators. Internat. J. Uncertain. Durante, R. Mesiar, and C. Sempi. On a family of copulas constructed from the diagonal section.  ...  On the characterization of a class of binary operations on bivariate distribu- tion functions. Publ. Math. Debrecen, 69(1-2):47-63, 2006. [9] F. Durante.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0218488505003679">doi:10.1142/s0218488505003679</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jqjokyzac5dqtoifb7zds4xu4u">fatcat:jqjokyzac5dqtoifb7zds4xu4u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829135834/http://www.flll.jku.at/div/research/technical_reports/Durante_List_of_Publications.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5b/e9/5be9cff41c531ab9ba05fd86c7f16d477753218f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0218488505003679"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> worldscientific.com </button> </a>

On special fuzzy implications

Balasubramaniam Jayaram, Radko Mesiar
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wcbukkuh2vbrpcbz2f4z2a2g6u" style="color: black;">Fuzzy sets and systems (Print)</a> </i> &nbsp;
Finally, some constructive procedures to obtain special fuzzy implications are proposed and methods of obtaining special implications from existing ones are given, showing that there are infinitely many  ...  fuzzy implications that are special but cannot be obtained as residuals of t-norms.  ...  He gratefully acknowledges the grant obtained from SAIA under the National Scholarship Programme (NSP) for the mobility of Teachers and Researchers that made this visit possible.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.fss.2008.11.004">doi:10.1016/j.fss.2008.11.004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rph2ygkd5fbs7ohctddzfyhxg4">fatcat:rph2ygkd5fbs7ohctddzfyhxg4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808094911/http://www.iith.ac.in/~jbala/publications/fss/fss_spl_imp.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/23/6b/236b9f1326666b8bfa82f49cc264f801b4e0205f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.fss.2008.11.004"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Approximate reasoning with aggregation functions satisfying GMP rules [article]

Dechao Li, Qingxue Zeng
<span title="2021-12-22">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We firstly study some properties of fuzzy implication generated by aggregation function.  ...  Moreover, we provide the quintuple implication principle (QIP) method with aggregation functions to solve FMP and FMT problems.  ...  Compliance with ethical standards Conflict of interest Author declares that he has no conflict of interest.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.15269v2">arXiv:2006.15269v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lynnfd36vzgepgpjnecw6htnay">fatcat:lynnfd36vzgepgpjnecw6htnay</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211225053444/https://arxiv.org/pdf/2006.15269v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7b/e8/7be89a6acbac0f85f0f766421d7e16668a71eeaf.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.15269v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Constructing implication functions from fuzzy negations

Aguilo Isabel, Suner Jaume, Torrens Joan
<span title="">2013</span> <i title="Atlantis Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q47jwxc36zhozejiwja7mtgcsu" style="color: black;">Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology</a> </i> &nbsp;
A class of implication functions is constructed from fuzzy negations.  ...  The interest of this new class lies in its simplicity and in the fact that when N is Idsymmetrical, the corresponding implication agrees with the residuum of a commutative semicopula.  ...  Following in this line we want to present in this communication a new method of obtaining implication functions from fuzzy negations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2991/eusflat.2013.45">doi:10.2991/eusflat.2013.45</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/eusflat/AguiloST13.html">dblp:conf/eusflat/AguiloST13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ynjvepnokrd5fg6e66xwhlorze">fatcat:ynjvepnokrd5fg6e66xwhlorze</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190220085537/http://pdfs.semanticscholar.org/217f/5aba9085f3781282bfcea59f3e4c24de2e30.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/21/7f/217f5aba9085f3781282bfcea59f3e4c24de2e30.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2991/eusflat.2013.45"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

ON THE CLASSES OF COPULAS AND QUASI-COPULAS WITH A GIVEN DIAGONAL SECTION

FABRIZIO DURANTE, JUAN FERNÁNDEZ-SÁNCHEZ
<span title="">2011</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2mchw27ezjaivoukjltsyavclq" style="color: black;">International Journal of Uncertainty Fuzziness and Knowledge-Based Systems</a> </i> &nbsp;
Moreover, a simple construction of copulas with a given convex diagonal section is introduced.  ...  We determine under which conditions on δ we have: (a) both C δ and Q δ consist of a singleton; (b) C δ = Q δ .  ...  Acknowledgements Part of this work was realized when Fabrizio Durante was on research stay at the Dipartimento di Matematica "Ennio De Giorgi", Università del Salento (Italy). He also thanks Prof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0218488511006848">doi:10.1142/s0218488511006848</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/p47c4syfuvfv3poepafe3xrxry">fatcat:p47c4syfuvfv3poepafe3xrxry</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190303052630/http://pdfs.semanticscholar.org/c346/1e182f3211c15aa5a31c32346066e67a1d89.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c3/46/c3461e182f3211c15aa5a31c32346066e67a1d89.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0218488511006848"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> worldscientific.com </button> </a>

On the transitivity of a parametric family of cardinality-based similarity measures

B. De Baets, S. Janssens, H. De Meyer
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sy2zvsxl4vdejh3zsp3utmplry" style="color: black;">International Journal of Approximate Reasoning</a> </i> &nbsp;
Fuzzification schemes based on a commutative quasi-copula are then used to transform these similarity measures for ordinary sets into similarity measures for fuzzy sets, rendering them applicable on graded  ...  We characterize the Łukasiewicz-transitive and product-transitive members of this family. Their importance derives from their one-to-one correspondence with pseudo-metrics.  ...  Nevertheless, a simpler method to construct fuzzy similarity measures is to start from a similarity measure for ordinary sets and to establish a set of fuzzification rules by which the measure is transformed  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ijar.2008.03.006">doi:10.1016/j.ijar.2008.03.006</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hvkmytme7bbwtntsmgtdkphwmu">fatcat:hvkmytme7bbwtntsmgtdkphwmu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170926034704/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/366/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDg4ODYxM3gwODAwMDQ2Nw%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/91/6c/916c8d6b829ca96080592d68108c120eac5e5426.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ijar.2008.03.006"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Spatial Interpolation Using Copula for non-Gaussian Modeling of Rainfall Data

Mehdi Omidi, Mohsen Mohammadzadeh
<span title="2018-12-01">2018</span> <i title="Armenian Green Publishing Co."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ptxng5fjjbfjnneifg2hp2n66i" style="color: black;">Journal of the Iranian Statistical Society</a> </i> &nbsp;
In the present paper, based on the weighted geometric mean of two Max-id copulas family, the spatial copula function is provided.  ...  One of the most useful tools for handling multivariate distributions of dependent variables in terms of their marginal distribution is a copula function.  ...  We also wish to acknowledge for the support from the Center of Excellence for Spatial Data Analysis in Tarbiat Modares University.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.29252/jirss.17.2.8">doi:10.29252/jirss.17.2.8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wcpxwxw3wrh4xmihet53enrn3u">fatcat:wcpxwxw3wrh4xmihet53enrn3u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190429061545/http://jirss.irstat.ir/files/site1/user_files_f6193f/mehdiom261-A-11-361-1-13431a6.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/93/1d/931df199275dc26654368191ea77dd7850f1ca88.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.29252/jirss.17.2.8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Logic and Approximation in Knowledge Based Systems [chapter]

Michael M. Richter
<span title="">2004</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The main focus is on problems where both representation methods have a natural place, such problem situations occur e.g. in e-commerce.  ...  We consider approximation oriented and logic oriented representation of knowledge.  ...  The disadvantage of the integral method is that two fuzzy functions with disjoint areas have always the same distance; the crisp method avoids this.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-25967-1_13">doi:10.1007/978-3-540-25967-1_13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/56ouipj6ifgzzfhiciqztdjaim">fatcat:56ouipj6ifgzzfhiciqztdjaim</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829001453/http://pages.cpsc.ucalgary.ca/~mrichter/Papers/Logic%20and%20Approximation.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/73/d0/73d02bd2f3e1354b832ac82b9cea773fee72d35e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-25967-1_13"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Semilinear copulas

Fabrizio Durante, Anna Kolesárová, Radko Mesiar, Carlo Sempi
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wcbukkuh2vbrpcbz2f4z2a2g6u" style="color: black;">Fuzzy sets and systems (Print)</a> </i> &nbsp;
Several construction methods are provided, especially concerning aggregation of semilinear copulas, and a special form of ordinal sum construction is introduced.  ...  A family of copulas, called semilinear, is constructed starting with some assumptions about the linearity of the copulas along some segments of the unit square.  ...  The fourth author gratefully acknowledges the support of the project "Metodi Stocastici in Finanza Matematica" of the Italian M.I.U.R.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.fss.2007.09.001">doi:10.1016/j.fss.2007.09.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dv3gqrro3bhqnl2tr3xg2pmr4a">fatcat:dv3gqrro3bhqnl2tr3xg2pmr4a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829174928/http://library.utia.cas.cz/separaty/2008/E/mesiar-semilinear%20copulas.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/89/f3/89f31324d265aca75fb463b8aa57d1ddfbca61d8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.fss.2007.09.001"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>
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