Attribute Extended Algorithm of Lattice-Valued Concept Lattice Based on Congener Formal Context

Algorithm 2

Generation algorithm of formal concepts.

Input: the 𝑛-ary lattice-valued concept lattice 𝐿(𝐺,𝑀,𝐿_𝑛,𝐼)̃

Output: the 𝑛-ary lattice-valued attribute extended concept lattice 𝐿(𝐺,𝑀₊,𝐿_𝑛,𝐼₊̃)

Begin

 while ((𝐺,𝑀,𝐿_𝑛,𝐼)̃≠Φ) do

  Calculate the formal concepts (𝐴,𝐵) of 𝐾=(𝐺,𝑀,𝐿_𝑛,𝐼)̃

  for each  (𝐴,𝐵)∈𝐿(𝐺,𝑀,𝐿_𝑛,𝐼)̃, denote  𝐴=𝐴(𝑔₁),𝐴(𝑔₂),…,𝐴(𝑔_𝑟)∈𝚨,

    𝐵=𝐵(𝑚₁),𝐵(𝑚₂),…,𝐵(𝑚_𝑠)∈𝚨   do

   if   ∃𝑛∈𝑀₊, s.t., 𝐼₊̃(𝑔,𝑛)=𝐼(̃𝑔,𝑚_𝑗1)∧𝐼(̃𝑔,𝑚_𝑗2),𝑚_𝑗1,𝑚_𝑗2∈𝑀   then

     𝐵₊=𝐵(𝑚₁),…,𝐵(𝑚_𝑠),𝐵(𝑚_𝑗1)∧𝐵(𝑚_𝑗2)

     (𝐴,𝐵₊)∈𝐿(𝐺,𝑀₊,𝐿_𝑛,𝐼₊̃)

   else

     (𝐴,𝐵₊)∉𝐿(𝐺,𝑀₊,𝐿_𝑛,𝐼₊̃)

   endif;

    if   ∃𝑛∈𝑀₊, s.t., 𝐼₊̃(𝑔,𝑛)=∧^𝑘_𝑝=1𝐼(̃𝑔,𝑚_𝑗𝑝),𝑚_𝑗1,𝑚_𝑗2,…,𝑚_𝑗𝑘∈𝑀   then

      𝐵₊=𝐵(𝑚₁),…,𝐵(𝑚_𝑠),∧^𝑘_𝑝=1𝐼(̃𝑔,𝑚_𝑗𝑝)

      (𝐴,𝐵₊)∈𝐿(𝐺,𝑀₊,𝐿_𝑛,𝐼₊̃)

    else

      (𝐴,𝐵₊)∉𝐿(𝐺,𝑀₊,𝐿_𝑛,𝐼₊̃)

    endif;

     if   ∃𝑛∈𝑀₊, s.t., 𝐼₊̃(𝑔,𝑛)=𝐼,𝐼∈𝐿_𝑛

     then

       (𝐴,𝐵₊)∈𝐿(𝐺,𝑀₊,𝐿_𝑛,𝐼₊̃)

     else

       (𝐴,𝐵₊)∉𝐿(𝐺,𝑀₊,𝐿_𝑛,𝐼₊̃)

     endif;

    endif

   endif;

  endfor;

end