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An ɴ-ary λ-averaging based similarity classifier

Onesfole Kurama, Pasi Luukka, Mikael Collan
2016 International Journal of Applied Mathematics and Computer Science  
Here the λ-averaging operator is extended to the n-ary aggregation case by using t-norms and t-conorms.  ...  We introduce a new n-ary λ similarity classifier that is based on a new n-ary λ-averaging operator in the aggregation of similarities.  ...  In a (t-norm, t-conorm) pair one can apply any of the four different t-norms, T M , T L , T P , T D , in aggregation, and their corresponding t-conorms, S M , S L , S P , S D , each at a time depending  ... 
doi:10.1515/amcs-2016-0029 fatcat:6iq5anus3veytdnosduumgdw6q

On sensible fuzzy ideals of BCK-algebras with respect to at-conorm

M. Akram, Jianming Zhan
2006 International Journal of Mathematics and Mathematical Sciences  
We introduce the notion of sensible fuzzy ideals of BCK-algebras with respect to at-conorm and investigate some of their properties.  ...  Some properties of the direct product andS-product of fuzzy ideals of BCK-algebras with respect to at-conorm are also discussed.  ...  Acknowledgments The authors are deeply grateful to the Editor-in-Chief and referees for their valuable comments and suggestions for improving the paper.  ... 
doi:10.1155/ijmms/2006/35930 fatcat:6tfvhudnazfttm2fmfkh7a5tzq

Interval-Valued Restricted Equivalence Functions Applied on Clustering Techniques

Aranzazu Jurio, Miguel Pagola, Daniel Paternain, Carlos Lopez-Molina, Pedro Melo-Pinto
2009 European Society for Fuzzy Logic and Technology  
In this work we use interval-valued fuzzy sets in the Fuzzy C-Means algorithm for image segmentation.  ...  We introduce interval-valued restricted equivalence functions as a way of measuring the equivalence between the intervals associated to different pixels.  ...  REF , and given T and S any t-norm and any t-conorm, REF IV (x, y) = [T (REF (x, y), REF (x, y)), S(REF (x, y), REF (x, y))] is an interval-valued restricted equivalence function.  ... 
dblp:conf/eusflat/JurioPPLM09 fatcat:wnskyxy3avd3jkx4wjyt2i2dkm

Gray Scale Edge Detection using Interval-Valued Fuzzy Relations

Agustina Bouchet, Pelayo Quirós, Pedro Alonso, Virginia Ballarin, Irene Díaz, Susana Montes
2015 International Journal of Computational Intelligence Systems  
Gray scale edge detection can be modeled using Fuzzy Sets and, in particular, Interval-Valued Fuzzy Sets.  ...  This work is focused on studying the performance of several Interval-Valued Fuzzy Sets construction methods for detecting edges in a gray scale image.  ...  Acknowledgements This work has been partially supported by ERAS-MUS Mundus Project EUREKA SD 2013-2591 and by MINECO grant with reference TIN2014-59543-P.  ... 
doi:10.1080/18756891.2015.1129588 fatcat:67hxgenwrvhnzbotiowwzefm6m

Modeling Consumer Decision Making Process with Triangular Norms [chapter]

Agnieszka Jastrzebska, Wladyslaw Homenda
2012 Lecture Notes in Computer Science  
In the article we discuss how triangular norms can be applied to decision making modeling based on information encouraging the choice gathered in paired vectors.  ...  Developed methodology is based on combining different known triangular norms for given pairs of vectors representing various consumers, who are facing the same decision.  ...  Decisions are based on fuzzy information, which in fact is very common.  ... 
doi:10.1007/978-3-642-33260-9_33 fatcat:rkcp7q2p4rcepgbmhjweqy755e

An overview of cubic intuitionistic β−subalgebras

P. Muralikrishna, A. Borumand Saeid, R. Vinodkumar, G. Palani
2022 Proyecciones  
Moreover, the notion of -normed cubic intuitionistic β−subalgebras have been introduced and relevant results are studied.  ...  Also, discussed about the level set of cubic intuitionistic β−subalgebras and furnished some fascinating results on the cartesian product of cubic intuitionistic β−subalgebra.  ...  Here T L is a Tnorm , S L − is a Tconorm and S L is a T -conorm, T L is a T -norm. In all the T -norm and T -conorm Lukasiewicz property has been used.  ... 
doi:10.22199/issn.0717-6279-4929 fatcat:wkufrncnrrcuxnunfbkovyhwwu

Interval-Valued Fuzzy System for Segmentation of Prostate Ultrasound Images

Miguel Pagola, Edurne Barrenechea Tartas, Aranzazu Jurio, Mikel Galar, Pedro Couto, Farhang Sahba, Hamid R. Tizhoosh
2009 European Society for Fuzzy Logic and Technology  
Interval-valued fuzzy systems have been used due to their potential to capture uncertainty in a more robust way compared to ordinary fuzzy systems.  ...  The system has 20 rules and is trained with ideal images segmented by an expert.  ...  The most known case is obtained when using minimum as the t-norm and maximum as the t-conorm.  ... 
dblp:conf/eusflat/PagolaTJGCST09 fatcat:xx7wl7uz35dvrnmzkkvgd6u2l4

Fuzzy Set-Theoretic Operators and Quantifiers [chapter]

János Fodor, Ronald R. Yager
2000 Fundamentals of Fuzzy Sets  
Since these extensions are mainly pointwisely defined, we review basic results on the underlying unary or binary operations on the unit interval such as negations, t-norms, t-conorms, implications, coimplications  ...  We also show other operations which have no counterpart in the classical theory but play some important role in fuzzy sets (like symmetric sums, weak t-norms and conorms, compensatory AND). review the  ...  S,N is an S-implication based on the t-conorm ~-l(Sl/S(~(X),~(y))), with Sl/s(X,y) := 1 -T l /S(l -x, 1 -y), where we employ 1/0 := +00 and 1/(+00) := 0. • Therefore, under the above-mentioned conditions  ... 
doi:10.1007/978-1-4615-4429-6_3 fatcat:obcyvr6pzfbttdlpmtlfjenyaa

Parameterized T-Norm and Co-Norm based Intuitionistic Fuzzy Optimization Technique and its Application

Samir Dey, Tapan Kumar
2017 International Journal of Computer Applications  
In this paper, an approach is developed to solve multi-objective structural design using parameterized t-norms and t-co-norms based intuitionistic fuzzy optimization technique.  ...  Here binary tnorms, t-conorms are extended in the form of n-ary t-norms and t-co-norms and their basic properties are discussed with some special cases.  ...  The said model is solved by using t-norms and t-conorm based on intuitionistic fuzzy optimization technique.  ... 
doi:10.5120/ijca2017913620 fatcat:o35v74wq6fdnhas5r3sh7fx67e

Summarizing and propagating uncertain information with triangular norms

Piero P. Bonissone
1987 International Journal of Approximate Reasoning  
In the inference layer a large number of uncertainty calculi based on triangular norms (T-norms), intersection operators whose truth functionality entails low computational complexity, are described.  ...  In this structure, numerical slots take values on linguistic term sets with fuzzy-valued semantics. These term sets capture the input granularity usually provided by users or experts.  ...  By using a recursive definition based on the associativity of the T-conorms, it is possible to define T(0, 0) = 0 T(a, 1)= T(1, a)=a T(a, b)< T(c, d) if a<c and b<d T(a, b)= T(b, a) T(a, T(b, c))= T(T  ... 
doi:10.1016/0888-613x(87)90005-3 fatcat:q5ivh7umyjajvkmhbtk7tsot7e

Distance closures on complex networks

2015 Network Science  
Based on these results, we argue that choosing different distance closures can lead to different conclusions about indirect associations on network data, as well as the structure of complex networks, and  ...  In particular, we show that a specific diffusion distance is promising for community detection in complex networks, and is based on desirable axioms for logical inference or approximate reasoning on networks  ...  " BCS-0527249, and Fundação para a Ciência e a Tecnologia, Portugal.  ... 
doi:10.1017/nws.2015.11 fatcat:oz3wztp5nzcilfetu2pkztkug4

On properties of fuzzy associative I-ideals in IS-algebras with t-conorms

M. Akram
2006 International Mathematical Forum  
Connections between direct product and T -product of fuzzy associative I -ideals induced by t-norms are also studied. 2000 Mathematics Subject Classication. 06F35, 03G25, 94D05.  ...  We discuss the properties of homomorphic image and inverse image of T -fuzzy associative I -ideals in an IS-algebra.  ...  In application, the t-norm T and the t-conorm S can be regarded as functions that map the unit square into the unit interval. Y. B. Jun and K. H.  ... 
doi:10.12988/imf.2006.06099 fatcat:mo4c5hymrndblmkhlozrg77cwu

Distance Closures on Complex Networks [article]

Tiago Simas, Luis M Rocha
2014 arXiv   pre-print
Understanding and mapping this isomorphism is necessary to analyse models of complex networks based on weighted graphs.  ...  To expand the toolbox available to network science, we study the isomorphism between distance and Fuzzy (proximity or strength) graphs.  ...  " BCS-0527249, and Fundação para a Ciência e a Tecnologia, Portugal.  ... 
arXiv:1312.2459v3 fatcat:gulsxmlmfvgalbug677woaixhi

Classification by ordinal sums of conjunctive and disjunctive functions for explainable AI and interpretable machine learning solutions

Miroslav Hudec, Erika Mináriková, Radko Mesiar, Anna Saranti, Andreas Holzinger
2021 Knowledge-Based Systems  
The obtained theoretical results in ordinal sums are discussed and illustrated on examples.  ...  learning tasks and can contribute to the robustness of algorithms.  ...  Moreover, the support of the projects VEGA 1/0466/19 and VEGA 1/0006/19 by the Ministry of Education, Science, Research and Sport of the Slovak Republic are kindly appreciated.  ... 
doi:10.1016/j.knosys.2021.106916 fatcat:4t6jwim5svhffdbcpefb2tlx4a

Fuzzy mathematical morphologies: A comparative study

Isabelle Bloch, Henri Maitre
1995 Pattern Recognition  
Fuzzy sets Mathematical morphology Fuzzy mathematical morphology Dilation Erosion Opening Closing Fuzzification Triangular norms and conorms Stochastic geometry Approximate reasoning Decision making Uncertain  ...  For dealing with spatial information in this framework from the signal level to the highest decision level, several attempts have been made to define mathematical morphology on fuzzy sets.  ...  Interpretation of T-norms and T-conorms.  ... 
doi:10.1016/0031-3203(94)00312-a fatcat:4cl4rsabhzgpvf6pxycvibwuly
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