JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (1): 68-74.doi: 10.6040/j.issn.1671-9352.4.2020.156

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F-C variable threshold concept lattices based on dependence spaces

Jing ZHANG(),Jian-min MA*()   

  1. School of Science, Chang'an University, Xi'an 710064, Shaanxi, China
  • Received:2020-06-15 Online:2021-01-01 Published:2021-01-05
  • Contact: Jian-min MA E-mail:jiing_z@126.com;cjm-zm@126.com

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Abstract:

For a fuzzy formal context, a congruence relation is defined based on a variable precision operator on the power set of attributes. A congruence relation is obtained. Based on it, a dependence space is shown. By constructing a closure operator according to the congruence relation, the relationships between the closure operator and the variable precision concepts are discussed. Furthermore, applying the properties of the closure operator, we get that any fixed point of the closure operator is exactly the intension of some variable precision concept. Based on these, an algorithm to construct all variable precision concepts is obtained. Experiments are used to verify the feasibility of the proposed method.

Key words: fuzzy formal context, dependence space, congruence relation, closure operator

CLC Number: 

  • TP18

Table 1

Fuzzy formal context"

U a b c d e
x1 0.6 1.0 0.6 0.7 1.0
x2 0.7 0.8 1.0 0.8 0.5
x3 1.0 0.7 1.0 0.6 0.3
x4 1.0 0.6 0.9 1.0 0.2

Table 2

The intensions of F-C variable threshold concepts for δ=1"

B 1 2 3 4
abcde 0.6 0.5 0.3 0.2
ac 0.6 0.7 1.0 0.9
be 1.0 0.5 0.3 0.2
ad 0.6 0.7 0.6 1.0
c 0.6 1.0 1.0 0.9
a 0.6 0.7 1.0 1.0
Ø 1.0 1.0 1.0 1.0

Fig.1

F-C variable threshold concept lattices for δ=1.0, 0.8, 0.7"

Table 3

Comparison of algorithm running time with increased object set and unchanged attribute set"

|U| 5 10 15 20 25
Algorithm in this paper 0.253 1.091 8.875 46.752 117.323
Original algorithm 0.527 7.169 34.893 106.605 319.498

Table 4

Comparison of algorithm running time with increased attribute set and unchanged object set"

|A| 5 10 15 20 25
Algorithm in this paper 0.467 0.951 0.998 1.115 1.214
Original algorithm 0.625 6.362 37.214 124.872 356.699

Fig.2

Running time"

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