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Articles de revues sur le sujet « Fuzzy formal concept analysis »

Auteur : Grafiati

Publié le 10 mars 2023

Mis à jour le 31 juillet 2025

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1

Mohammed, Alwersh, and Kovács László. "Fuzzy formal concept analysis: approaches, applications and issues." Computer Science and Information Technologies 3, no. 2 (2022): 126–36. https://doi.org/10.11591/csit.v3i2.pp126-136.

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Formal concept analysis (FCA) is today regarded as a significant technique for knowledge extraction, representation, and analysis for applications in a variety of fields. Significant progress has been made in recent years to extend FCA theory to deal with uncertain and imperfect data. The computational complexity associated with the enormous number of formal concepts generated has been identified as an issue in various applications. In general, the generation of a concept lattice of sufficient complexity and size is one of the most fundamental challenges in FCA. The goal of this work is to pro

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Supriyati, Endang. "FUZZY FORMAL CONCEPT ANALYSIS UNTUK KEMIRIPAN DOKUMEN." Simetris : Jurnal Teknik Mesin, Elektro dan Ilmu Komputer 1, no. 1 (2013): 21. http://dx.doi.org/10.24176/simet.v1i1.111.

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ABSTRAK Fuzzy logic dapat dimasukkan ke dalam ontologi untuk representasi ketidakpastian informasi yang ditemukan di banyak aplikasi domain karena kurangnya jelas batas-batas antara konsep domain. Fuzzy ontologi dihasilkan dari konsep hirarki yang telah ditetapkan. Namun, untuk membangun sebuah konsep hirarki untuk domain tertentu dapat menjadi tugas yang sulit dan membosankan. Untuk mengatasi masalah ini, diusulkan Fuzzy Formal Concept Analysis(FFCA). Titik awal dari metode diusulkan dalam paper ini adalah definisi dari konteks , relasi kemiripan pada domain ontologi kemudian memetakan ke dal

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FORMICA, ANNA. "CONCEPT SIMILARITY IN FUZZY FORMAL CONCEPT ANALYSIS FOR SEMANTIC WEB." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 18, no. 02 (2010): 153–67. http://dx.doi.org/10.1142/s0218488510006465.

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This paper presents a method for evaluating concept similarity within Fuzzy Formal Concept Analysis. In the perspective of developing the Semantic Web, such a method can be helpful when the digital resources found on the Internet cannot be treated equally and the integration of fuzzy data becomes fundamental for the search and discovery of information in the Web.

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Haddache, Mohamed, Allel Hadjali, and Hamid Azzoune. "Skyline refinement exploiting fuzzy formal concept analysis." International Journal of Intelligent Computing and Cybernetics 14, no. 3 (2021): 333–62. http://dx.doi.org/10.1108/ijicc-11-2020-0181.

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PurposeThe study of the skyline queries has received considerable attention from several database researchers since the end of 2000's. Skyline queries are an appropriate tool that can help users to make intelligent decisions in the presence of multidimensional data when different, and often contradictory criteria are to be taken into account. Based on the concept of Pareto dominance, the skyline process extracts the most interesting (not dominated in the sense of Pareto) objects from a set of data. Skyline computation methods often lead to a set with a large size which is less informative for

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Konecny, Jan, and Ondrej Krídlo. "On biconcepts in formal fuzzy concept analysis." Information Sciences 375 (January 2017): 16–29. http://dx.doi.org/10.1016/j.ins.2016.09.042.

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Konecny, Jan, and Michal Krupka. "Block relations in formal fuzzy concept analysis." International Journal of Approximate Reasoning 73 (June 2016): 27–55. http://dx.doi.org/10.1016/j.ijar.2016.02.004.

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Shao, Ming-Wen, Min Liu, and Wen-Xiu Zhang. "Set approximations in fuzzy formal concept analysis." Fuzzy Sets and Systems 158, no. 23 (2007): 2627–40. http://dx.doi.org/10.1016/j.fss.2007.05.002.

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Alwersh, Mohammed, and Kovács László. "Fuzzy formal concept analysis: approaches, applications and issues." Computer Science and Information Technologies 3, no. 2 (2022): 126–36. http://dx.doi.org/10.11591/csit.v3i2.p126-136.

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Formal concept analysis (FCA) is today regarded as a significant technique for knowledge extraction, representation, and analysis for applications in a variety of fields. Significant progress has been made in recent years to extend FCA theory to deal with uncertain and imperfect data. The computational complexity associated with the enormous number of formal concepts generated has been identified as an issue in various applications. In general, the generation of a concept lattice of sufficient complexity and size is one of the most fundamental challenges in FCA. The goal of this work is to pro

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Mohammed Alwersh and László Kovács. "Fuzzy formal concept analysis: approaches, applications and issues." Computer Science and Information Technologies 3, no. 2 (2022): 126–36. http://dx.doi.org/10.11591/csit.v3i2.pp126-136.

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Formal concept analysis (FCA) is today regarded as a significant technique for knowledge extraction, representation, and analysis for applications in a variety of fields. Significant progress has been made in recent years to extend FCA theory to deal with uncertain and imperfect data. The computational complexity associated with the enormous number of formal concepts generated has been identified as an issue in various applications. In general, the generation of a concept lattice of sufficient complexity and size is one of the most fundamental challenges in FCA. The goal of this work is to pro

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Liu, Yan, Sheng Quan Liu, and Peng Li. "Tourism Domain Ontology Construction Method Based on Fuzzy Formal Concept Analysis." Applied Mechanics and Materials 347-350 (August 2013): 2809–13. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.2809.

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In this paper, fuzzy formal concept analysis is introduced to the tourism domain ontology construction process, first fuzzy formal concept analysis of uncertain information in the domain of tourism,then through the conceptual clustering generated fuzzy concept hierarchy, lastly mapping to get fuzzy ontology prototype. A example shows that the method is feasible and effective.

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Wang, Ting Zhong, and Hong Sheng Xu. "Constructing Domain Ontology Based on Fuzzy Set and Concept Lattice." Applied Mechanics and Materials 63-64 (June 2011): 715–18. http://dx.doi.org/10.4028/www.scientific.net/amm.63-64.715.

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The major content in FCA is to extract formal concepts and connections between them from data in form of formal context so as to form a lattice structure of formal concepts. Fuzzy set theory and fuzzy logic are acknowledged as an appropriate formalism for capturing imprecise and vague knowledge. The paper offers a methodology for building ontology for knowledge sharing and reusing based on fuzzy concept lattices union. This paper makes up these defects by applying formal concept analysis theory and fuzzy sets to construct concept hierarchies of ontology, and the experiments shows the CPU Time

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Poelmans, Jonas, Dmitry I. Ignatov, Sergei O. Kuznetsov, and Guido Dedene. "Fuzzy and rough formal concept analysis: a survey." International Journal of General Systems 43, no. 2 (2014): 105–34. http://dx.doi.org/10.1080/03081079.2013.862377.

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Ojeda-Hernández, Manuel, Domingo López-Rodríguez, and Pablo Cordero. "Fuzzy Algebras of Concepts." Axioms 12, no. 4 (2023): 324. http://dx.doi.org/10.3390/axioms12040324.

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Preconcepts are basic units of knowledge that form the basis of formal concepts in formal concept analysis (FCA). This paper investigates the relations among different kinds of preconcepts, such as protoconcepts, meet and join-semiconcepts and formal concepts. The first contribution of this paper, is to present a fuzzy powerset lattice gradation, that coincides with the preconcept lattice at its 1-cut. The second and more significant contribution, is to introduce a preconcept algebra gradation that yields different algebras for protoconcepts, semiconcepts, and concepts at different cuts. This

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Xin, Xian-Wei, Ji-Hua Song, Zhan-Ao Xue, and Wei-Ming Peng. "Intuitionistic fuzzy three-way formal concept analysis based attribute correlation degree." Journal of Intelligent & Fuzzy Systems 40, no. 1 (2021): 1567–83. http://dx.doi.org/10.3233/jifs-200002.

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As an important expanded of the classical formal concept, the three-way formal concept analysis integrates more information with the three-way decision theory. However, to the best of our knowledge, few scholars have studied the intuitionistic fuzzy three-way formal concept analysis. This paper proposes an intuitionistic fuzzy three-way formal concept analysis model based on the attribute correlation degree. To achieve this, we comprehensively analyze the composition of attribute correlation degree in the intuitionistic fuzzy environment, and introduce the corresponding calculation methods for

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Singh, Prem Kumar, Aswani Kumar Cherukuri, and Jinhai Li. "Concepts reduction in formal concept analysis with fuzzy setting using Shannon entropy." International Journal of Machine Learning and Cybernetics 8, no. 1 (2014): 179–89. http://dx.doi.org/10.1007/s13042-014-0313-6.

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Akbar, Mohammad Deni, and Yoshihiro Mizoguchi. "Fuzzy Implication and Functional Dependency on Formal Context." Jurnal Matematika Integratif 15, no. 2 (2020): 69. http://dx.doi.org/10.24198/jmi.v15.n2.21693.69.

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Fuzzy formal concept analysis(FFCA) is a development of formal concept analysis(FCA) with the degree of relation between objects and attributes. Using FCA approach, we will investigate the condition logical implication for fuzzy functional dependency. We also use Armstrong's rule to define soundness and completeness of our implication and fuzzy functional dependency model. We show difference and equivalence condition between fuzzy implication and fuzzy functional dependency. This condition can be used to develop the algorithm for finding attribute dependency.

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Akbar, Mohammad Deni, and Yoshihiro Mizoguchi. "Fuzzy Implication and Functional Dependency on Formal Context." Jurnal Matematika Integratif 15, no. 2 (2019): 69. http://dx.doi.org/10.24198/jmi.v15i2.21693.

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Fuzzy formal concept analysis(FFCA) is a development of formal concept analysis(FCA) with the degree of relation between objects and attributes. Using FCA approach, we will investigate the condition logical implication for fuzzy functional dependency. We also use Armstrong's rule to define soundness and completeness of our implication and fuzzy functional dependency model. We show difference and equivalence condition between fuzzy implication and fuzzy functional dependency. This condition can be used to develop the algorithm for finding attribute dependency.

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Ofiсerov, V. P., and S. V. Smirnov. "FUZZY FORMAL CONCEPT ANALYSIS IN THE CONSTRUCTION OF ONTOLOGIES." Ontology of Designing 26, no. 7 (2017): 487–95. http://dx.doi.org/10.18287/2223-9537-2017-7-4-487-495.

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Boffa, Stefania, Petra Murinová, Vilém Novák, and Petr Ferbas. "Graded cubes of opposition in fuzzy formal concept analysis." International Journal of Approximate Reasoning 145 (June 2022): 187–209. http://dx.doi.org/10.1016/j.ijar.2022.03.006.

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Boffa, Stefania, Petra Murinová, and Vilém Novák. "Graded polygons of opposition in fuzzy formal concept analysis." International Journal of Approximate Reasoning 132 (May 2021): 128–53. http://dx.doi.org/10.1016/j.ijar.2021.02.007.

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Fenza, Giuseppe, and Sabrina Senatore. "Friendly web services selection exploiting fuzzy formal concept analysis." Soft Computing 14, no. 8 (2009): 811–19. http://dx.doi.org/10.1007/s00500-009-0469-2.

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Lai, Hongliang, and Dexue Zhang. "Concept lattices of fuzzy contexts: Formal concept analysis vs. rough set theory." International Journal of Approximate Reasoning 50, no. 5 (2009): 695–707. http://dx.doi.org/10.1016/j.ijar.2008.12.002.

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Butka, Peter, Jozef Pócs, and Jana Pócsová. "Representation of Fuzzy Concept Lattices in the Framework of Classical FCA." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/236725.

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We describe a representation of the fuzzy concept lattices, defined via antitone Galois connections, within the framework of classical Formal Concept Analysis. As it is shown, all needed information is explicitly contained in a given formal fuzzy context and the proposed representation can be obtained without a creation of the corresponding fuzzy concept lattice.

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Zhang, Chengling, Jinjin Li, and Yidong Lin. "Matrix-based reduction approach for one-sided fuzzy three-way concept lattices." Journal of Intelligent & Fuzzy Systems 40, no. 6 (2021): 11393–410. http://dx.doi.org/10.3233/jifs-202573.

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Three-way concept analysis is a mathematical model of the combination of formal concept analysis and three-way decision, and knowledge discovery plays a significant impact on formal fuzzy contexts since such datasets are frequently encountered in real life. In this paper, a novel type of one-sided fuzzy three-way concept lattices is presented in a given formal fuzzy context with its complement, in which a ternary classification is available. In such case, we comprehensively explore the connections between the proposed models and classical fuzzy concept lattices among elements, sets, and orders

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Shenoy, Manjula, Dr K. C. Shet, and Dr U. Dinesh Acharya. "Ontology Mapping using Fuzzy Decision Tree and Formal Concept Analysis." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 8, no. 1 (2013): 743–50. http://dx.doi.org/10.24297/ijct.v8i1.6825.

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An ontology describes and defines the terms used to describe and represent an area of knowledge. Different people or organizations come up with their own ontology; having their own view of the domain. So, for systems to interoperate, it becomes necessary to map these heterogeneous ontologies.This paper discusses the state of the art methods and outlines a new approach with improved precision and recall. Also the system finds other than 1:1 relationships.

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Kumar, Ch Aswani. "FUZZY CLUSTERING-BASED FORMAL CONCEPT ANALYSIS FOR ASSOCIATION RULES MINING." Applied Artificial Intelligence 26, no. 3 (2012): 274–301. http://dx.doi.org/10.1080/08839514.2012.648457.

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De Maio, Carmen, Giuseppe Fenza, Vincenzo Loia, and Sabrina Senatore. "Hierarchical web resources retrieval by exploiting Fuzzy Formal Concept Analysis." Information Processing & Management 48, no. 3 (2012): 399–418. http://dx.doi.org/10.1016/j.ipm.2011.04.003.

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Wang, Yingxu. "Fuzzy Semantic Models of Fuzzy Concepts in Fuzzy Systems." International Journal of Fuzzy Systems and Advanced Applications 9 (March 13, 2022): 57–62. http://dx.doi.org/10.46300/91017.2022.9.9.

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The fuzzy properties of language semantics are a central problem towards machine-enabled natural language processing in cognitive linguistics, fuzzy systems, and computational linguistics. A formal method for rigorously describing and manipulating fuzzy semantics is sought for bridging the gap between humans and cognitive fuzzy systems. The mathematical model of fuzzy concepts is rigorously described as a hyperstructure of fuzzy sets of attributes, objects, relations, and qualifications, which serves as the basic unit of fuzzy semantics for denoting languages entities in semantic analyses. The

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Sang, Binbin, Binghan Long, Jinzhong Pang, and Weihua Xu. "The Method of Data Analysis in Intuitionistic Fuzzy Generalized Consistent Decision Formal Context." Entropy 21, no. 3 (2019): 262. http://dx.doi.org/10.3390/e21030262.

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Concept lattice has been successfully applied to various fields as an effective tool for data analysis and knowledge discovery, with attribute reduction being the key problem. This paper combines the intuitionistic fuzzy theory with the concept lattice theory and proposes one kind of concept lattice in intuitionistic fuzzy generalized consistent decision formal context. Furthermore, an approach to attribute a reduction in the discernibility matrix is proposed and investigated, making the discovery of implicit knowledge easier and the representation simpler in the data system and perfecting the

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Jindal, Rajni, Shivani Jain, and K. R. Seeja. "Computing semantic relatedness using latent semantic analysis and fuzzy formal concept analysis." International Journal of Reasoning-based Intelligent Systems 13, no. 2 (2021): 92. http://dx.doi.org/10.1504/ijris.2021.10036809.

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Jain, Shivani, K. R. Seeja, and Rajni Jindal. "Computing semantic relatedness using latent semantic analysis and fuzzy formal concept analysis." International Journal of Reasoning-based Intelligent Systems 13, no. 2 (2021): 92. http://dx.doi.org/10.1504/ijris.2021.114635.

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Wang, Li Dong, Dian Xuan Gong, and Xin Wang. "A Fuzzy Concept Similarity Measure Based on Lattice Structures." Applied Mechanics and Materials 50-51 (February 2011): 78–82. http://dx.doi.org/10.4028/www.scientific.net/amm.50-51.78.

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With the rapid development of the semantic web, determining the degree of similarity between concepts from same or different ontologies plays an increasing crucial role. In this paper, a new similarity model based on lattice structural information is proposed to evaluate the similarity degree between fuzzy concepts in the framework of fuzzy formal concept analysis. The proposed method preserves more structural information, which can be viewed as another extension and development of de Souza and Davis’s model in fuzzy context.

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Kang, Xiangping, Deyu Li, Suge Wang, and Kaishe Qu. "Formal concept analysis based on fuzzy granularity base for different granulations." Fuzzy Sets and Systems 203 (September 2012): 33–48. http://dx.doi.org/10.1016/j.fss.2012.03.003.

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De Maio, C., G. Fenza, M. Gallo, V. Loia, and S. Senatore. "Formal and relational concept analysis for fuzzy-based automatic semantic annotation." Applied Intelligence 40, no. 1 (2013): 154–77. http://dx.doi.org/10.1007/s10489-013-0451-7.

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Mezni, Haithem, and Taher Abdeljaoued. "A cloud services recommendation system based on Fuzzy Formal Concept Analysis." Data & Knowledge Engineering 116 (July 2018): 100–123. http://dx.doi.org/10.1016/j.datak.2018.05.008.

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Fenza, Giuseppe, Mariacristina Gallo, Vincenzo Loia, Alessandra Petrone, and Claudio Stanzione. "Concept-drift detection index based on fuzzy formal concept analysis for fake news classifiers." Technological Forecasting and Social Change 194 (September 2023): 122640. http://dx.doi.org/10.1016/j.techfore.2023.122640.

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Atif, Jamal, Isabelle Bloch, and Céline Hudelot. "Some Relationships Between Fuzzy Sets, Mathematical Morphology, Rough Sets, F-Transforms, and Formal Concept Analysis." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 24, Suppl. 2 (2016): 1–32. http://dx.doi.org/10.1142/s0218488516400080.

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In this paper we extend some previously established links between the derivation operators used in formal concept analysis and some mathematical morphology operators to fuzzy concept analysis. We also propose to use mathematical morphology to navigate in a fuzzy concept lattice and perform operations on it. Links with other lattice-based for malisms such as rough sets and F-transforms are also established. This paper proposes a discussion and new results on such links and their potential interest.

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Wang, Wen Chao, and Jiang Lu. "Ontology Construction Using Multiple Concept Lattices." Advanced Materials Research 926-930 (May 2014): 1975–78. http://dx.doi.org/10.4028/www.scientific.net/amr.926-930.1975.

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The paper proposes an ontology construction approach that combines Fuzzy Formal Concept Analysis, Wikipedia and WordNet in a process that constructs multiple concept lattices for sub-domains. Those sub-domains are divided from the target domain. The multiple concept lattices approach can mine concepts and determine relations between concepts automatically, and construct domain ontology accordingly. This approach is suitable for the large domain or complex domain which contains obvious sub-domains.

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Valverde-Albacete, Francisco José, and Carmen Peláez-Moreno. "Four-Fold Formal Concept Analysis Based on Complete Idempotent Semifields." Mathematics 9, no. 2 (2021): 173. http://dx.doi.org/10.3390/math9020173.

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Formal Concept Analysis (FCA) is a well-known supervised boolean data-mining technique rooted in Lattice and Order Theory, that has several extensions to, e.g., fuzzy and idempotent semirings. At the heart of FCA lies a Galois connection between two powersets. In this paper we extend the FCA formalism to include all four Galois connections between four different semivectors spaces over idempotent semifields, at the same time. The result is K¯-four-fold Formal Concept Analysis (K¯-4FCA) where K¯ is the idempotent semifield biasing the analysis. Since complete idempotent semifields come in duall

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Formica, Anna. "Semantic Web search based on rough sets and Fuzzy Formal Concept Analysis." Knowledge-Based Systems 26 (February 2012): 40–47. http://dx.doi.org/10.1016/j.knosys.2011.06.018.

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Cintra, M. E., H. A. Camargo, and M. C. Monard. "Genetic generation of fuzzy systems with rule extraction using formal concept analysis." Information Sciences 349-350 (July 2016): 199–215. http://dx.doi.org/10.1016/j.ins.2016.02.026.

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Benítez-Caballero, M. José, Jesús Medina, Eloísa Ramírez-Poussa, and Dominik Ślȩzak. "Rough-set-driven approach for attribute reduction in fuzzy formal concept analysis." Fuzzy Sets and Systems 391 (July 2020): 117–38. http://dx.doi.org/10.1016/j.fss.2019.11.009.

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Ravi, Kumar, Vadlamani Ravi, and P. Sree Rama Krishna Prasad. "Fuzzy formal concept analysis based opinion mining for CRM in financial services." Applied Soft Computing 60 (November 2017): 786–807. http://dx.doi.org/10.1016/j.asoc.2017.05.028.

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Martin, Trevor, Yun Shen, and Andrei Majidian. "Discovery of time-varying relations using fuzzy formal concept analysis and associations." International Journal of Intelligent Systems 25, no. 12 (2010): 1217–48. http://dx.doi.org/10.1002/int.20450.

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Liu, Haitao, Ioan Dzitac, and Sicong Guo. "Factors Space and its Relationship with Formal Conceptual Analysis: A General View." International Journal of Computers Communications & Control 13, no. 1 (2018): 83. http://dx.doi.org/10.15837/ijccc.2018.1.3033.

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Conceptual generation is a key point and basic problem in artificial intelligence, which has been probed in the Formal Concept Analysis (FCA) established by G. Wille. Factors Space (FS) is also a branch of cognition math initiated by P.Z. Wang at the end of last century, which has been applied in information processing with fuzzy concepts effectively. This paper briefly introduces the historic background of FS and its relationship with FCA. FS can be seen as a good partner of FCA on conceptual description and structure extraction; combining FCA with FS, we can get more clear and simple stateme

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Singh, Prem Kumar, Cherukuri Aswani Kumar, and Abdullah Gani. "A comprehensive survey on formal concept analysis, its research trends and applications." International Journal of Applied Mathematics and Computer Science 26, no. 2 (2016): 495–516. http://dx.doi.org/10.1515/amcs-2016-0035.

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AbstractIn recent years, FCA has received significant attention from research communities of various fields. Further, the theory of FCA is being extended into different frontiers and augmented with other knowledge representation frameworks. In this backdrop, this paper aims to provide an understanding of the necessary mathematical background for each extension of FCA like FCA with granular computing, a fuzzy setting, interval-valued, possibility theory, triadic, factor concepts and handling incomplete data. Subsequently, the paper illustrates emerging trends for each extension with application

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Belohlavek, Radim, Jiří Dvořák, and Jan Outrata. "Fast factorization by similarity in formal concept analysis of data with fuzzy attributes." Journal of Computer and System Sciences 73, no. 6 (2007): 1012–22. http://dx.doi.org/10.1016/j.jcss.2007.03.016.

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Chen, Yi-Hui, Eric Jui-Lin Lu, and Ya-Wen Cheng. "Categorization of Multiple Documents Using Fuzzy Overlapping Clustering Based on Formal Concept Analysis." International Journal of Software Engineering and Knowledge Engineering 30, no. 05 (2020): 631–47. http://dx.doi.org/10.1142/s0218194020500229.

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Most clustering algorithms build disjoint clusters. However, clusters might be overlapped because documents may belong to two or more categories in the real world. For example, a paper discussing the Apple Watch may be categorized into either 3C, Fashion, or even Clothing and Shoes. Therefore, overlapping clustering algorithms have been studied such that a resource can be assigned to one or more clusters. Formal Concept Analysis (FCA), which has many practical applications in information science, has been used in disjoin clustering, but has not been studied in overlapping clustering. To make o

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Djouadi, Yassine, and Henri Prade. "Possibility-theoretic extension of derivation operators in formal concept analysis over fuzzy lattices." Fuzzy Optimization and Decision Making 10, no. 4 (2011): 287–309. http://dx.doi.org/10.1007/s10700-011-9106-5.

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BĚLOHLÁVEK, RADIM, BERNARD DE BAETS, JAN OUTRATA, and VILEM VYCHODIL. "CHARACTERIZING TREES IN CONCEPT LATTICES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16, supp01 (2008): 1–15. http://dx.doi.org/10.1142/s0218488508005212.

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Concept lattices are systems of conceptual clusters, called formal concepts, which are partially ordered by the subconcept/superconcept relationship. Concept lattices are basic structures used in formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree. On the other hand, tree-like classification schemes are appealing and are produced by several clustering methods. In this paper, we present necessary and sufficient conditions on input data for the output concept lattice to form a tree after one removes its least element. We present these co

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