Issue:Concept lattices associated with interval-valued L-fuzzy contexts

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http://ifigenia.org/wiki/issue:nifs/1/2/104-115

Title of paper: Concept lattices associated with interval-valued l-fuzzy contexts Author(s): Ana Burusco Departamento de Matematica е Informatica, Universidad Publica de Navarra, Campus de Arrosadia. 31006 Pamplona. Espana Ramon Fuentes-González Departamento de Matematica е Informatica, Universidad Publica de Navarra, Campus de Arrosadia. 31006 Pamplona. Espana Published in: "Notes on IFS", Volume 1 (1995) Number 2, pages 104—115 Download:  PDF (4764  Kb, File info) Abstract: 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. Keywords: Knowledge acquisition and learning, Data analysis methods, Interval-valued L-fuzzy concepts. References: 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. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.