The International Journal of Fuzzy Logic and Intelligent Systems

eISSN 2093-744X
pISSN 1598-2645

Proposed algorithm to develop the IVIF concept

Input:An IVIF envirnment , whereas , and ℜ̃ express IVIF relation.
Output:Set of IVIFFCs
Extent:{§,[A(§)L',A(§)I'],[ΩA(§)L',ΩA(§)I']},
Intent:{,[B(yj)L',B()I'],[ΩB(yj)L',ΩB()I']}, where ⋎ ≤ n and ⋌ ≤ m.
1Determine the subsets S of given IV IF attribues 2m.
2for ⋌ = 1 to 2m.
3 Determine the value of the acceptance membership = ([1.00, 1.00], [0.00, 0.00]) for each subsets
4 Use the scrolling operator to locate the encompassing object set ():{,[BSL'(),BSI'()],[ΩBSL'(),ΩBSI'()]}.
5 The down operator (↓) provides the following object set: {§,[A(§)L',A(§)I'],[ΩA(§)L',ΩA(§)I']}
6 The calculation of the membership value for the acquired set of objects can be determined in the following manner:ASL'=minBSL'[μL'˜(§,)],ASI'=minBSL'[μI'˜(§,)],ΩASL'=maxΩBSL'[μΩL'˜(§,)],ΩASI'=maxΩBSI'[μΩI'˜(§,)].
7 Determine the attribute set that covers the specified object set using the upper operator, denoted as ↑ (UP). {§,[A(§)L',A(§)I'],[ΩA(§)L',ΩA(§)I']}.
8 Now, calculate the membership value for the obtained attribute set using the following procedure:BSL'=maxASL'[μL'˜(§,)],BSI'=minASI'[μI'˜(§,)],ΩBSL'=maxΩASL'[μΩL'˜(§,)],ΩBSI'=maxΩASI'[μΩI'˜(§,)].
9 The formal concepts (AS, BS) are derived from the selected subset.
10end for
11In a similar way, more concepts can be developed with the other subsets.
12Build the IVIF concept lattice.
International Journal of Fuzzy Logic and Intelligent Systems 2024;24:360~377 https://doi.org/10.5391/IJFIS.2024.24.4.360
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