## Construction of the $$L$$-fuzzy concept lattice.(English)Zbl 0927.06006

Summary: We propose two processes to obtain $$L$$-fuzzy concepts based on finite $$L$$-fuzzy contexts and the theory of P. Cousot and R. Cousot [Pac. J. Math. 82, 43-57 (1979; Zbl 0413.06004)]. The first algorithm calculates the $$L$$-fuzzy concepts derived from an $$L$$-fuzzy set and the second one constructs the whole $$L$$-fuzzy concept lattice. We also represent the $$L$$-fuzzy concept lattice graphically.

### MSC:

 06B99 Lattices 68T30 Knowledge representation 68T05 Learning and adaptive systems in artificial intelligence 03E72 Theory of fuzzy sets, etc. 06B23 Complete lattices, completions

### Citations:

Zbl 0827.06004; Zbl 0413.06004
Full Text:

### References:

 [1] Burmeister, P., Programm zur formalen begriffsanalyse TH, (1987), Darmstadt [2] Burusco, A.; Fuentes, R., The study of the L-fuzzy concept lattice, Mathware soft comput., 1, 3, 209-218, (1994) · Zbl 0827.06004 [3] Cousot, P.; Cousot, R., Constructive versions of Tarski’s fixed point theorems, Pacific J. math., 82, 43-57, (1979) · Zbl 0413.06004 [4] Davey, B.A.; Priestley, H.A., Introduction to lattices and order, (1990), Cambridge University Press Cambridge · Zbl 0701.06001 [5] Ganter, B., Programmbibliothek zur formalen begriffsanalyse, (1986), TH (Darmstadt) [6] Kaufmann, A., Introduction a la théorie des sous-ensembles flous à l’usage des ingénieurs, (1977), Masson Paris · Zbl 0346.94002 [7] Pedrycz, W., On generalized fuzzy relational equations and their applications, J. math. anal. appl., 107, 520-536, (1985) · Zbl 0581.04003 [8] Tarsky, A., A lattice theoretical fixpoint theorem and its applications, Pacific J. math., 5, 285-310, (1955) [9] Wille, R., Restructuring lattice theory: an approach based on hierarchies of concepts, (), 445-470 [10] Wille, R., Lattices in data analysis: how to draw them with a computer, (), 33-58 · Zbl 1261.68140 [11] Zadeh, L.A., Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606
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.