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http://ifigenia.org/wiki/issue:nifs/1/2/104-115
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| Title of paper:
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Concept lattices associated with interval-valued l-fuzzy contexts
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| Author(s):
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| Ana Burusco
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| Departamento de Matematica е Informatica, Universidad Publica de Navarra, Campus de Arrosadia. 31006 Pamplona. Espana
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| Ramon Fuentes-González
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| Departamento de Matematica е Informatica, Universidad Publica de Navarra, Campus de Arrosadia. 31006 Pamplona. Espana
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| Published in:
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"Notes on Intuitionistic Fuzzy Sets", Volume 1 (1995) Number 2, pages 104—115
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| Download:
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 PDF (4764 Kb, File info)
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| Abstract:
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In 1982, Wille published the paper titled Restructuring lattice theory: an approach based on hierarchies of concepts ([5]), where he developed a new theory called formal concept theory. In that paper, he analyzes 0/1 relations between the object and attribute sets.
Applying the L-Fuzzy set theory to the results of Wille, we have developed the L-Fuzzy concept theory that deals with L-Fuzzy relations inside of 0/1 relations. The final purpose of our theory is the knowledge acquisition and classification.
Taking as departure point the L-Fuzzy concept theory ([2]), we study in this paper contexts defined by interval-valued L-Fuzzy relations between the object and attribute sets. We give a new definition of L-Fuzzy concept valid for this case and analyze the structure of the L-Fuzzy concept set. We apply these results to a medical example.
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| Keywords:
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Knowledge acquisition and learning, Data analysis methods, Interval-valued L-fuzzy concepts.
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| References:
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- K. Atanassov, G. Gargov; Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31, (1989), 343-349.
- A. Burusco, R. Fuentes-Gonzalez; The Study of the L-Fuzzy Concept Lattice, Mathware and Soft Computing, Vol I, No. 3, (1994), 209-218.
- P. Cousot, R. Cousot, Constructive versions of Tarski's fixed point theorems, Pacific Journal of Mathematics,82 ,(1979) 43-57.
- A.Tarsky, A Lattice Theoretical Fixpoint Theorem and its Applications,Pathific J.Math.,5 ,(1955), 285-310.
- R. Wille, Restructuring lattice theory: an approach based on hierarchies of concepts,in: Rival I.(ed.),Ordered Sets, Reidel, Dordrecht-Boston, (1982) 445-470.
- L.A. Zadeh, The Concept of a Linguistic Variable and its Application to Approximate Reasoning-I. Information Sciences, 8,(1975), 199-249.
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