Attribute Reduction in Intuitionistic Fuzzy Concept Lattices

Table 4

The results of Example 40.

Concept	Extension	Intension	Discernibility function of 𝑋𝑖
1	𝑥1	{⟨0.9,0.0⟩,⟨0.8,0.1⟩,⟨0.2,0.8⟩,⟨0.2,0.5⟩,⟨0.9,0.0⟩}	𝑎1∨𝑎5
2	𝑥2	{⟨0.8,0.0⟩,⟨0.8,0.1⟩,⟨0.8,0.1⟩,⟨0.3,0.5⟩,⟨0.0,0.8⟩}	(𝑎1∧𝑎4)∨𝑎3
3	𝑥3	{⟨0.0,0.8⟩,⟨0.0,0.6⟩,⟨0.1,0.9⟩,⟨0.8,0.2⟩,⟨0.0,0.8⟩}	𝑎3∧𝑎4
4	𝑥5	{⟨0.0,0.0⟩,⟨0.1,0.0⟩,⟨0.0,0.0⟩,⟨0.9,0.1⟩,⟨0.0,0.8⟩}	(𝑎1∧𝑎2)∨𝑎3∨𝑎4
5	𝑥6	{⟨0.6,0.4⟩,⟨0.9,0.0⟩,⟨0.0,0.9⟩,⟨0.8,0.2⟩,⟨0.0,0.8⟩}	(𝑎1∧𝑎4)∨𝑎2
6	𝑥1,𝑥2	{⟨0.8,0.0⟩,⟨0.8,0.1⟩,⟨0.2,0.8⟩,⟨0.2,0.5⟩,⟨0.0,0.8⟩}	𝑎1∨(𝑎3∧𝑎4)
7	𝑥1,𝑥7	{⟨0.9,0.1⟩,⟨0.8,0.1⟩,⟨0.2,0.8⟩,⟨0.2,0.6⟩,⟨0.0,0.8⟩}	𝑎1
8	𝑥2,𝑥3	{⟨0.0,0.8⟩,⟨0.0,0.6⟩,⟨0.1,0.9⟩,⟨0.3,0.5⟩,⟨0.0,0.8⟩}	𝑎3∧𝑎4
9	𝑥2,𝑥4	{⟨0.7,0.2⟩,⟨0.8,0.1⟩,⟨0.7,0.1⟩,⟨0.2,0.6⟩,⟨0.0,0.8⟩}	𝑎3
10	𝑥2,𝑥5	{⟨0.0,0.0⟩,⟨0.1,0.0⟩,⟨0.0,0.1⟩,⟨0.3,0.5⟩,⟨0.0,0.8⟩}	(𝑎1∧𝑎3)∨(𝑎1∧𝑎4) ∨(𝑎3∧𝑎4)
11	𝑥2,𝑥6	{⟨0.6,0.4⟩,⟨0.8,0.1⟩,⟨0.0,0.9⟩,⟨0.3,0.5⟩,⟨0.0,0.8⟩}	(𝑎1∧𝑎4)∨(𝑎2∧𝑎4)
12	𝑥5,𝑥6	{⟨0.0,0.4⟩,⟨0.1,0.0⟩,⟨0.0,0.9⟩,⟨0.8,0.2⟩,⟨0.0,0.8⟩}	(𝑎1∧𝑎4)∨𝑎2
13	𝑥1,𝑥2,𝑥3	{⟨0.0,0.8⟩,⟨0.0,0.6⟩,⟨0.1,0.9⟩,⟨0.2,0.5⟩,⟨0.0,0.8⟩}	𝑎3∧𝑎4
14	𝑥1,𝑥2,𝑥5	{⟨0.0,0.0⟩,⟨0.1,0.1⟩,⟨0.0,0.8⟩,⟨0.2,0.5⟩,⟨0.0,0.8⟩}	𝑎1∨(𝑎3,𝑎4)
15	𝑥1,𝑥2,𝑥6	{⟨0.6,0.4⟩,⟨0.8,0.1⟩,⟨0.0,0.9⟩,⟨0.2,0.5⟩,⟨0.0,0.8⟩}	(𝑎1∧𝑎4)∨(𝑎2∧𝑎4)
16	𝑥1,𝑥2,𝑥7	{⟨0.8,0.1⟩,⟨0.8,0.1⟩,⟨0.2,0.8⟩,⟨0.2,0.6⟩,⟨0.0,0.8⟩}	𝑎1
17	𝑥2,𝑥4,𝑥5	{⟨0.0,0.2⟩,⟨0.1,0.1⟩,⟨0.0,0.1⟩,⟨0.2,0.6⟩,⟨0.0,0.8⟩}	𝑎3
18	𝑥2,𝑥5,𝑥6	{⟨0.0,0.4⟩,⟨0.1,0.0⟩,⟨0.0,0.9⟩,⟨0.3,0.5⟩,⟨0.0,0.8⟩}	(𝑎1∧𝑎4)∨(𝑎2∧𝑎4)
19	𝑥3,𝑥5,𝑥6	{⟨0.0,0.8⟩,⟨0.0,0.6⟩,⟨0.0,0.9⟩,⟨0.8,0.2⟩,⟨0.0,0.8⟩}	𝑎4
20	𝑥1,𝑥2,𝑥4,𝑥7	{⟨0.7,0.2⟩,⟨0.8,0.1⟩,⟨0.2,0.8⟩,⟨0.2,0.6⟩,⟨0.0,0.8⟩}	𝑎1∨𝑎3
21	𝑥1,𝑥2,𝑥5,𝑥6	{⟨0.0,0.4⟩,⟨0.1,0.1⟩,⟨0.0,0.9⟩,⟨0.2,0.5⟩,⟨0.0,0.8⟩}	(𝑎1∧𝑎4)∨(𝑎2∧𝑎4)
22	𝑥1,𝑥2,𝑥5,𝑥7	{⟨0.0,0.1⟩,⟨0.1,0.1⟩,⟨0.0,0.8⟩,⟨0.2,0.6⟩,⟨0.0,0.8⟩}	𝑎1
23	𝑥2,𝑥3,𝑥5,𝑥6	{⟨0.0,0.8⟩,⟨0.0,0.6⟩,⟨0.0,0.9⟩,⟨0.3,0.5⟩,⟨0.0,0.8⟩}	𝑎4
24	𝑥1,𝑥2,𝑥3,𝑥4,𝑥7	{⟨0.0,0.8⟩,⟨0.0,0.6⟩,⟨0.1,0.9⟩,⟨0.2,0.6⟩,⟨0.0,0.8⟩}	𝑎3
25	𝑥1,𝑥2,𝑥3,𝑥5,𝑥6	{⟨0.0,0.8⟩,⟨0.0,0.6⟩,⟨0.0,0.9⟩,⟨0.2,0.5⟩,⟨0.0,0.8⟩}	𝑎4
26	𝑥1,𝑥2,𝑥4,𝑥5,𝑥7	{⟨0.0,0.2⟩,⟨0.1,0.1⟩,⟨0.0,0.8⟩,⟨0.2,0.6⟩,⟨0.0,0.8⟩}	𝑎1∨𝑎3
27	𝑥1,𝑥2,𝑥4,𝑥6,𝑥7	{⟨0.6,0.4⟩,⟨0.8,0.1⟩,⟨0.0,0.9⟩,⟨0.2,0.6⟩,⟨0.0,0.8⟩}	𝑎1∨𝑎2
28	𝑥1,𝑥2,𝑥4,𝑥5,𝑥6,𝑥7	{⟨0.0,0.4⟩,⟨0.1,0.1⟩,⟨0.0,0.9⟩,⟨0.2,0.6⟩,⟨0.0,0.8⟩}	𝑎1∨𝑎2
29	𝑈	{⟨0.0,0.8⟩,⟨0.0,0.6⟩,⟨0.0,0.9⟩,⟨0.2,0.6⟩,⟨0.0,0.8⟩}	—
30	∅	{⟨1.0,0.0⟩,⟨1.0,0.0⟩,⟨1.0,0.0⟩,⟨1.0,0.0⟩,⟨1.0,0.0⟩}	∨^7𝑖=1𝑎𝑖
RED(𝐾)	{𝑎1,𝑎3,𝑎4}