JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (1): 75-82.doi: 10.6040/j.issn.1671-9352.4.2020.149

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Granule description using possible attribute analysis

Jie TANG1,2(),Ling WEI1,2,*(),Rui-si REN1,2,Si-yu ZHAO1,2,3   

  1. 1. School of Mathematics, Northwest University, Xi'an 710127, Shaanxi, China
    2. Institute of Concepts, Cognition and Intelligence, Northwest University, Xi'an 710127, Shaanxi, China
    3. College of Mathematics and Information Science, Xianyang Normal University, Xianyang 712000, Shaanxi, China
  • Received:2020-06-19 Online:2021-01-01 Published:2021-01-05
  • Contact: Ling WEI E-mail:15385559385@163.com;wl@nwu.edu.cn

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Abstract:

Granular computing is a method and effective tool of solving complicated problems by using information granularity. During the process of granularity, it is often accompanied with granule description, and granule description becomes a fundamental problem in granular computing. Inspired by necessary attribute analysis, this paper proposes granule description using possible attribute analysis. First, taking the extents of property oriented concepts as definable granules in the formal context, and defining the description of definable granule. Then, using the stability of concepts to define minimal generator of concept so that definable granule's description becomes concise. Finally, the advantage of granule description using possible attribute analysis is discussed by an example of task assignment.

Key words: granular computing, granule description, formal concept analysis, stability, possible attribute

CLC Number: 

  • O29

Table 1

Formal context K"

G a b c d e f
1 × × ×
2 × ×
3 × × ×
4 × × × ×
5 × × × ×
6 × ×

Fig.1

Property oriented concept lattice Lp(G, M, I)"

Table 2

Nontrivial positive definable granules and their minimal generators"

正可定义粒 面向属性概念 δB(C) 极小生成子
1246 (1246, abdef) ≥1/2 abdef
346 (346, abcef) ≤1/2 ace
125 (125, abcdf) ≤1/2 bcdf
136 (136, acdef) ≤1/2 ace
236 (236, abcde) ≤1/2 ace
36 (36, ace) ≥1/2 ace
46 (46, abef) ≥1/2 abef
26 (26, abde) ≤1/2 ae/bd
16 (16, adef) ≤1/2 ae
12 (12, abdf) ≤1/2 bd
25 (25, bcdf) ≥1/2 bcdf
1 (1, adf) ≥1/2 adf
2 (2, bd) ≥1/2 bd
6 (6, ae) ≥1/2 ae

Table 3

Positive definable granule families and their minimal generators"

正可定义粒族 极小生成子
1246 abdef
346, 136, 236, 36 ace
125, 25 bcdf
46 abef
26 ae或bd
16, 6 ae
12, 2 bd
1 adf

Table 4

Irreducible elements and their minimal generators"

并不可约元 极小生成子
(36, ace) ace
(46, abef) abef
(25, bcdf) bcdf
(1, adf) adf
(2, bd) bd
(6, ae) ae

Table 5

Formal context Kc"

G a b c d e f
1 × × ×
2 × × × ×
3 × × ×
4 × ×
5 × ×
6 × × × ×

Fig.2

Property oriented concept lattice Lp(G, M, Ic)"

Table 6

Nontrivial negative definable granules and their minimal generators"

负可定义粒 面向属性概念 δB(C) 极小生成子
1346 (1346, bcdef) ≤1/2 bcdf
346 (346, bcdf) ≥1/2 bcdf
245 (245, acdef) ≤1/2 acef
145 (145, abcde) ≤1/2 ae/cd
125 (125, abcef) ≤1/2 acef
35 (35, abdef) ≤1/2 ae
25 (25, acef) ≥1/2 acef
45 (45, acde) ≤1/2 ae/cd
14 (14, bcde) ≤1/2 cd
15 (15, abce) ≤1/2 ae
1 (1, bce) ≥1/2 bce
3 (3, bdf) ≥1/2 bdf
4 (4, cd) ≥1/2 cd
5 (5, ae) ≥1/2 ae

Table 7

Negative definable families and their minimal generators"

负可定义粒族 极小生成子
1346, 346 bcdf
245, 125, 25 acef
145, 45 ae或cd
35, 15, 5 ae
14, 4 cd
1 bce
3 bdf
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