Intuitionistic Fuzzy Set (IFS)

Intuitionistic Fuzzy Set (IFS)

• The intuitionistic fuzzy set (IFS) introduced in 1983 by Krassimir T. Atanassov asgeneralization of fuzzy sets.

Şekil 3. A sezgisel bulanık kümesi (Garg ,Rani ve Sharma, 2013)

Basic Relations and Operations On IFSs

Basic Relations and Operations On IFSs

Example

• Let E = {a, b, c, d, e}, let the IFSs A and B have the forms:

A = {(a, 0.5, 0.3), (b, 0.1, 0.7), (c, 1.0,0.0), (d, 0.0, 0.0), (e, 0.0,1.0)},

B = {(a, 0.7, 0.1), (b, 0.3, 0.2), (c, 0.5, 0.5), (d, 0.2, 0.2), (e, 1.0,0.0)}.

Then

Algebra Laws in IFSs

Algebra Laws in IFSs

Triangular Intuitionistic Fuzzy Number (TIFN)

ATIFN is a fuzzy set on R with the form

Triangular Intuitionistic Fuzzy Number (TIFN)

Triangular Intuitionistic Fuzzy Number (TIFN)

Triangular Intuitionistic Fuzzy Number (TIFN)

Aritmetic Operations on Triangular Intuitionistic

Fuzzy Numbers (TIFN)

α –cut of Triangular Intuitionistic Fuzzy Number (TIFN)

Sezgisel bulanık sayının üye olmama fonksiyonunun α kesim kümesi:

• Sezgisel bulanık sayının üye olmama fonksiyonunun α kesim kümesi:

α –cut of Triangular Intuitionistic Fuzzy Number (TIFN)

α –cut of Triangular Intuitionistic Fuzzy Number (TIFN)

Trapezoidal Intuitionistic Fuzzy Number (TRIFN)

Operations on Trapezoidal Intuitionistic Fuzzy Number (TRIFN)