in in ddeexx in in ggsseett } } ( ( 1 1 ) ) 33FFAACCIIAALLSSEEMMAANNTT IC IC SSDDEESSCCRR IP IP TTIIOONNSSuuppppoossee , , aanndd M , , , , is is ccoommpp le le te te ly ly d d is is tr tr ib ib u u ti t v iv e e la la tti t c ic e e , , “ “ x x ” ” rreepprreesseenn ts ts th th eeAA cc coorrdd in in ggto to AAFFSSffrraammeewwoorrkk , , t h th is is ppaappeerrpprrooppoosseessaa : ndexing set } , and crete antic set ξ, in th

doi:10.1201/b18660-164

Chapter

in in ddeexx in in ggsseett } } ( ( 1 1 ) ) 33FFAACCIIAALLSSEEMMAANNTT IC IC SSDDEESSCCRR IP IP TTIIOONNSSuuppppoossee , , aanndd M , , , , is is ccoommpp le le te te ly ly d d is is tr tr ib ib u u ti t v iv e e la la tti t c ic e e , , “ “ x x ” ” rreepprreesseenn ts ts th th eeAA cc coorrdd in in ggto to AAFFSSffrraammeewwoorrkk , , t h th is is ppaappeerrpprrooppoosseessaa

Chapter

ABSTRACT

Suppose ,A B EMii I jj J∑ ∑ ∈∈ ∈ , and M , ,( )∧ ∨ is completely distributive lattice, “x” represents the relationship of “and” or “or”, we can get the following

∑i∈I Ai ∨ ∑ j∈J Bj= ∑k∈I⌊⌋J Ck (2)

In formula (2), (3) “∪” indicates the relationship between I and J which is neither mixed nor aggregated. When u∈I, Cu=Au will be concluded; when u∈J, Cu=Bu.