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Page 6720 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
Summary: “The relations between the lattice structures of fuzzy preorders, fuzzy consequence operators, fuzzy closure systems and co-closure systems are studied.  ...  and fuzzy closure and co-closure systems.  ... 

On the relation between fuzzy closing morphological operators, fuzzy consequence operators induced by fuzzy preorders and fuzzy closure and co-closure systems

Jorge Elorza, Ramón Fuentes-González, Jean Bragard, Pedro Burillo
2013 Fuzzy sets and systems (Print)  
We also show that the coherence property is the key to link the four following families: fuzzy closing morphological operators, fuzzy consequence operators, fuzzy preorders and fuzzy closure and co-closure  ...  In a previous paper, Elorza and Burillo explored the coherence property in fuzzy consequence operators.  ...  We thank the anonymous referees for their valuable suggestions that have helped to improve the content and the presentation of this paper.  ... 
doi:10.1016/j.fss.2012.08.010 fatcat:5cn63uycznamvmoai5tnnjlrfm

On Galois Connections and Soft Computing [chapter]

F. García-Pardo, I. P. Cabrera, P. Cordero, Manuel Ojeda-Aciego
2013 Lecture Notes in Computer Science  
After recalling the different interpretations usually assigned to the term Galois connection, both in the crisp and in the fuzzy case, we survey on several of their applications in Computer Science and  ...  The definition of idempotent mapping, closure operator and kernel operator follows in the same way as crisp case. Definition 2 (Fuzzy Galois Connections/Adjunctions).  ...  -If (f, g) : A B then g • f is kernel operator and f • g is closure operator.  ... 
doi:10.1007/978-3-642-38682-4_26 fatcat:ata3rgwaibajdmghck7ewj4f6e

Categories of L-Fuzzy C̆ech Closure Spaces and L-Fuzzy Co-Topological Spaces

Irina Perfilieva, Ahmed A. Ramadan, Enas H. Elkordy
2020 Mathematics  
In particular, we establish relationships between L-fuzzy (fuzzifying) Čech closure spaces, L-fuzzy (fuzzifying) co-topological spaces and L-fuzzy (fuzzifying) approximation spaces based on reflexive L-fuzzy  ...  Recently, fuzzy systems have become one of the hottest topics due to their applications in the area of computer science.  ...  Recall the paper by Fang and Yue [20] , in which the relationship between L-fuzzy closure systems and L-fuzzy topological spaces was discussed from a categorical viewpoint.  ... 
doi:10.3390/math8081274 fatcat:axz74pz6bvax5nsnv5clxjtoce

Towards a meaningful fuzzy analysis of urbanistics data

Benjoe A. Juliano
1996 Information Sciences  
A fuzzy Hassefication technique was applied to data gathered from this project. Then an algorithm that compares Hasse diagrams was u~d.  ...  Applications ABSTRACT We present and elaborate on a method for analyzing and interpreting data from an Urbanistics project.  ...  (3) Returning to this preprocessing phase, the local preorder closure of T< T-1 is calculated using the following formulation from Bandler and Kohout [2] : the local preorder closure of a relation  ... 
doi:10.1016/0020-0255(96)00077-1 fatcat:cdne5tzp4fdxjmflluyuxgbiji

Galois Connections Between Unbalanced Structures in a Fuzzy Framework [chapter]

Inma P. Cabrera, Pablo Cordero, Emilio Muñoz-Velasco, Manuel Ojeda-Aciego
2020 Communications in Computer and Information Science  
structures that have been considered so far in this context: fuzzy preposets, fuzzy preordered structures, and fuzzy T-digraphs.  ...  The construction of Galois connections between unbalanced structures has received considerable attention in the recent years.  ...  and TIN2017-89023-P, and Junta de Andalucía project UMA2018-FEDERJA-001.  ... 
doi:10.1007/978-3-030-50153-2_54 fatcat:s6haypu5bjfqdd6qzxttc6lid4

Distance closures on complex networks

TIAGO SIMAS, LUIS M. ROCHA
2015 Network Science  
This allows us to: (1) study alternative distance closures, such as those based on diffusion, metric, and ultra-metric distances; (2) identify the operators closest to the metric closure of distance graphs  ...  Distinct transitive closures in Fuzzy graphs lead to closures of their isomorphic distance graphs with widely different structural properties.  ...  " BCS-0527249, and Fundação para a Ciência e a Tecnologia, Portugal.  ... 
doi:10.1017/nws.2015.11 fatcat:oz3wztp5nzcilfetu2pkztkug4

Distance Closures on Complex Networks [article]

Tiago Simas, Luis M Rocha
2014 arXiv   pre-print
This allows us to: (1) study alternative distance closures, such as those based on diffusion, metric, and ultra-metric distances; (2) identify the operators closest to the metric closure of distance graphs  ...  Distinct transitive closures in Fuzzy graphs lead to closures of their isomorphic distance graphs with widely different structural properties.  ...  " BCS-0527249, and Fundação para a Ciência e a Tecnologia, Portugal.  ... 
arXiv:1312.2459v3 fatcat:gulsxmlmfvgalbug677woaixhi

Adjunctions in Quantaloid-enriched Categories [article]

Lili Shen
2015 arXiv   pre-print
Finally, as applications, the theory of formal concept analysis and that of rough sets are extended to theories based on fuzzy relations between fuzzy sets.  ...  and contravariant functorial from the category of distributors and infomorphisms to the category of Q-closure spaces; second, it is shown that the assignments of a distributor to the fixed points of the  ...  The terminologies "Q-closure operator" and "Q-interior operator" come from their similarity to closure operators and interior operators in topology. Proposition 4.1.7.  ... 
arXiv:1408.0321v2 fatcat:esc5jzx5ebhfxmmekse3vizvhy

Fuzzy-Set Based Logics — an History-Oriented Presentation of their Main Developments [chapter]

Didier Dubois, Francesc Esteva, Lluís Godo, Henri Prade
2007 Handbook of the History of Logic  
Jan Lukasiewicz (1878Lukasiewicz ( -1956 and his followers have developed three-valued logics, and other many-valued systems, since 1920 [ Lukasiewicz, 1920] .  ...  This issue can be related to a misunderstanding regarding the law of excluded middle and the law of non-contradiction, and the connections between many-valued logics and modal logics.  ...  to study closure operators and related notions like closure systems and consequence relations in other, more general fuzzy logic settings.  ... 
doi:10.1016/s1874-5857(07)80009-4 fatcat:s4i5zfomgzbxnfbuif5ffsesea

Generalized fuzzy rough approximation operators based on fuzzy coverings

Tong-Jun Li, Yee Leung, Wen-Xiu Zhang
2008 International Journal of Approximate Reasoning  
Based on a fuzzy covering of a universe of discourse, two pairs of generalized lower and upper fuzzy rough approximation operators are constructed by means of an implicator I and a triangular norm T.  ...  Topological properties of the generalized fuzzy rough approximation operators and characterizations of the fuzzy T-partition by the generalized upper fuzzy rough approximation operators are further established  ...  U, and C 0 FR a fuzzy closure operator.  ... 
doi:10.1016/j.ijar.2008.01.006 fatcat:qnjcq5lewrh57ofncwdhumoccm

Axiomatizing logics of fuzzy preferences using graded modalities [article]

Amanda Vidal, Francesc Esteva, Lluis Godo
2019 arXiv   pre-print
Finally, we propose an axiomatic system for this logic in an extended language (where the preference modal operators are definable), and prove completeness with respect to the intended graded preference  ...  Actually, the presence of truth-constants in the language allows us to show that the modal operators Box and Diamond of the minimal modal logic are inter-definable.  ...  CZ.02.2.69/0.0/0.0/17 050/0008361 of the Operational programme Research, Development and Education of the Ministry of Education, Youth and Sport of the Czech Republic, co-financed by the European Union  ... 
arXiv:1909.07674v2 fatcat:mg7wm3qh6fgslaypd436fdcc5u

The posterity of Zadeh's 50-year-old paper

James C. Bezdek, Didier Dubois, Henri Prade
2015 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)  
OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.  ...  preorders and fuzzy similarity equations.  ...  O., Esteva, F., Garcia, P. and Godo, L., "On implicative closure operators in approximate reasoning," IJAR, 33, 2003, 159-184.  ... 
doi:10.1109/fuzz-ieee.2015.7337858 dblp:conf/fuzzIEEE/BezdekDP15 fatcat:jeydd2agx5eppps2bpy5z32mcm

Implicational (semilinear) logics I: a new hierarchy

Petr Cintula, Carles Noguera
2010 Archive for Mathematical Logic  
and suggests new directions for research in the field.  ...  of fuzzy logic.  ...  L ≤ 3 , with Nikolaos Galatos for pointing us out the terminology semilinear, and with the anonymous referee for his or her helpful corrections and critical comments.  ... 
doi:10.1007/s00153-010-0178-7 fatcat:rcgcnpgirbc2bjn52uz345axm4

Modal Characterisations of Probabilistic and Fuzzy Bisimulations [chapter]

Yuxin Deng, Hengyang Wu
2014 Lecture Notes in Computer Science  
This paper aims to investigate bisimulation on fuzzy systems.  ...  Furthermore, inspired by the work of Hermanns et al. on probabilistic systems, we provide a sound and complete modal characterisation of fuzzy bisimilarity.  ...  Many formal description tools for fuzzy systems, such as fuzzy Petri nets and fuzzy discrete event systems, are not fLTSs.  ... 
doi:10.1007/978-3-319-11737-9_9 fatcat:cenbl22w6jdpjpxoshwvpudegu
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