Multi-adjoint concept lattices with heterogeneous conjunctors and hedges. (English) Zbl 1322.06004

Summary: This paper is related, on the one hand, to the framework of multi-adjoint concept lattices with heterogeneous conjunctors and, on the other hand, to the use of intensifying hedges as truth-stressers. Specifically, we continue on the line of recent works by Belohlavek and Vychodil, which use intensifying hedges as a tool to reduce the size of a concept lattice. In this paper we use hedges as a reduction tool in the general framework of multi-adjoint concept lattices with heterogeneous conjunctors.


06B23 Complete lattices, completions
06A15 Galois correspondences, closure operators (in relation to ordered sets)
68T30 Knowledge representation
03G10 Logical aspects of lattices and related structures


Full Text: DOI


[1] Alcalde, C; Burusco, A; Fuentes-González, R; Zubia, I, The use of linguistic variables and fuzzy propositions in the L-fuzzy concept theory, Comput. Math. Appl., 62, 3111-3122, (2011) · Zbl 1232.68117
[2] Almendros-Jiménez, JM; Luna, A; Moreno, G, Fuzzy logic programming for implementing a flexible xpath-based query language, Electron. Notes Theor. Comput. Sci., 282, 3-18, (2012)
[3] Bartl, E; Belohlavek, R; Vychodil, V, Bivalent and other solutions of fuzzy relational equations via linguistic hedges, Fuzzy Sets Syst., 187, 103-112, (2012) · Zbl 1258.03080
[4] Belohlavek, R., Vychodil, V.: Fuzzy Equational Logic, volume 186 of Studies in Fuzziness and Soft Computing (2005) · Zbl 1083.03030
[5] Belohlavek, R; Vychodil, V, Fuzzy concept lattices constrained by hedges, J. Adv. Comput. Intell. Intell Inform., 11, 536-545, (2007)
[6] Belohlavek, R; Vychodil, V, Formal concept analysis and linguistic hedges, Int. J. Gen. Syst., 41, 503-532, (2012) · Zbl 1277.93045
[7] Butka, P., Pocsova, J., Pocs, J.: On some complexity aspects of generalized one-sided concept lattices algorithm. In: Proceedings of IEEE 10th International Symposium on Applied Machine Intelligence and Informatics (SAMI), pp. 231-236 (2012) · Zbl 1328.68217
[8] Cornelis, C; Medina, J; Verbiest, N, Multi-adjoint fuzzy rough sets: definition, properties and attribute selection, Int. J. Approx. Reason., 55, 412-426, (2014) · Zbl 1316.03028
[9] Díaz, J.C., Medina, J.: Multi-adjoint relation equations: definition, properties and solutions using concept lattices. Inf. Sci. 253, 100-109 (2013) · Zbl 1320.68173
[10] Dubois, D; Saint-Cyr, FD; Prade, H, A possibility-theoretic view of formal concept analysis, Fundamenta Informaticae, 75, 195-213, (2007) · Zbl 1108.68114
[11] Ganter, B., Wille, R.: Formal Concept Analysis Mathematical Foundation. Springer-Verlag, New York Incorporated (1999) · Zbl 0909.06001
[12] Ganter, B., Kuznetsov, S.O.: Pattern structures and their projections. In: International Conference on Conceptual Structures, volume 2120 of Lecture Notes in Computer Science, pp. 129-142. Springer Berlin, Heidelberg (2001) · Zbl 0994.68147
[13] Georgescu, G; Popescu, A, Concept lattices and similarity in non-commutative fuzzy logic, Fundamenta Informaticae, 53, 23-54, (2002) · Zbl 1023.03016
[14] Hájek, P.: Metamathematics of Fuzzy Logic (Trends in Logic). Springer (2001). November · Zbl 1226.06001
[15] Hájek, P, No article title, On very true. Fuzzy Sets Syst., 124, 329-333, (2001) · Zbl 0997.03028
[16] Julián, P; Moreno, G; Penabad, J, On fuzzy unfolding: A multi-adjoint approach, Fuzzy Sets Syst., 154, 16-33, (2005) · Zbl 1099.68017
[17] Kaiser, T.B., Schmidt, S.E.: A macroscopic approach to FCA and its various fuzzifications. In: Formal Concept Analysis, volume 7278 of Lecture Notes in Computer Science, pp. 140-147. Springer Berlin, Heidelberg (2012) · Zbl 1360.68810
[18] Kaiser, T.B., Schmidt, S.E.: Some remarks on the relation between annotated ordered sets and pattern structures. In: Pattern Recognition and Machine Intelligence, volume 6744 of Lecture Notes in Computer Science, pp. 43-48. Springer Berlin, Heidelberg (2011) · Zbl 1250.06001
[19] Konecny, J, Isotone fuzzy Galois connections with hedges, Inf. Sci., 181, 1804-1817, (2011) · Zbl 1226.06001
[20] Krajči, S, A generalized concept lattice, Log. J. IGPL, 13, 543-550, (2005) · Zbl 1088.06005
[21] Kuznetsov, S.O.: Pattern structures for analyzing complex data. In: Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, volume 5908 of Lecture Notes in Computer Science, pp. 33-44. Springer Berlin, Heidelberg (2009) · Zbl 1187.68587
[22] Lei, Y; Luo, M, Rough concept lattices and domains, Ann. Pure Appl. Log., 159, 333-340, (2009) · Zbl 1169.06004
[23] Medina, J, Multi-adjoint property-oriented and object-oriented concept lattices, Inf. Sci., 190, 95-106, (2012) · Zbl 1248.68479
[24] Medina, J; Ojeda-Aciego, M, Multi-adjoint t-concept lattices, Inf. Sci., 180, 712-725, (2010) · Zbl 1187.68587
[25] Medina, J; Ojeda-Aciego, M, On multi-adjoint concept lattices based on heterogeneous conjunctors, Fuzzy Sets Syst., 208, 95-110, (2012) · Zbl 1252.06003
[26] Medina, J; Ojeda-Aciego, M, Dual multi-adjoint concept lattices, Inf. Sci., 225, 47-54, (2013) · Zbl 1293.06001
[27] Medina, J; Ojeda-Aciego, M; Ruiz-Calviño, J, Relating generalized concept lattices with concept lattices for non-commutative conjunctors, Appl. Math. Lett., 21, 1296-1300, (2008) · Zbl 1187.06003
[28] Medina, J; Ojeda-Aciego, M; Ruiz-Calviño, J, Formal concept analysis via multi-adjoint concept lattices, Fuzzy Sets Syst., 160, 130-144, (2009) · Zbl 1187.68589
[29] Medina, J; Ojeda-Aciego, M; Vojtáš, P, Similarity-based unification: a multi-adjoint approach, Fuzzy Sets Syst., 146, 43-62, (2004) · Zbl 1073.68026
[30] Morcillo, PJ; Moreno, G; Penabad, J; Vázquez, C, Dedekind-macneille completion and Cartesian product of multi-adjoint lattices, Int. J. Comput. Math., 89, 1742-1752, (2012) · Zbl 1269.06003
[31] Pócs, J, On possible generalization of fuzzy concept lattices using dually isomorphic retracts, Inf. Sci., 210, 89-98, (2012) · Zbl 1250.06001
[32] Singh, P.K., Kumar, C.A.: Interval-valued fuzzy graph representation of concept lattice. In: Proceedings of 12th International Conference on Intelligent Systems Design and Applications (ISDA), pp. 604-609 (2012) · Zbl 1293.06001
[33] Yao, Y.Y.: Concept lattices in rough set theory. In: Proceedings of Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS’04), pp. 796-801 (2004) · Zbl 1187.06003
[34] Zadeh, L, A fuzzy set-theoretic interpretation of linguistic hedges, J. Cybern., 2, 4-34, (1972)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.