Consistency of Probability Decision Rules and Its Inference in Probability Decision Table

Table 2

A probability decision table.

𝑈⧵𝐴∪{𝑏}	𝑎1	⋯	𝑎𝑚	𝑏
	(𝑣^1𝑎1,𝑝^𝑥1𝑎1(𝑣^1𝑎1))	⋯	(𝑣^1𝑎𝑚,𝑝^𝑥1𝑎𝑚(𝑣^1𝑎𝑚))	(𝑣^1𝑏,𝑝^𝑥1𝑏(𝑣^1𝑏))
𝑥1	⋮	⋮	⋮	⋮
	(𝑣^𝑟1𝑎1,𝑝^𝑥1𝑎1(𝑣^𝑟1𝑎1))	⋯	(𝑣^𝑟𝑚𝑎𝑚,𝑝^𝑥1𝑎𝑚(𝑣^𝑟𝑚𝑎𝑚))	(𝑣^𝑠𝑏,𝑝^𝑥1𝑏(𝑣^𝑠𝑏))
⋮	⋮	⋮	⋮	⋮
	(𝑣^1𝑎1,𝑝^𝑥𝑛𝑎1(𝑣^1𝑎1))	⋯	(𝑣^1𝑎𝑚,𝑝^𝑥𝑛𝑎𝑚(𝑣^1𝑎𝑚))	(𝑣^1𝑏,𝑝^𝑥𝑛𝑏(𝑣^1𝑏))
𝑥𝑛	⋮	⋮	⋮	⋮
	(𝑣^𝑟1𝑎1,𝑝^𝑥𝑛𝑎1(𝑣^𝑟1𝑎1))	⋯	(𝑣^𝑟𝑚𝑎𝑚,𝑝^𝑥𝑛𝑎𝑚(𝑣^𝑟𝑚𝑎𝑚))	(𝑣^𝑠𝑏,𝑝^𝑥𝑛𝑏(𝑣^𝑠𝑏))