THE EQUALITY OF INTUITIONİSTİC FUZZY MODAL OPERATORS E(α,β), Z(α,β,ω) and Z(α,β,ω,θ) ACCORDINGLY NEW DEFINED INTUITIONISTIC FUZZY ENTROPY

Öz

A normal -entropy measure for intuitionistic fuzzy sets is proposed by using normalized Hamming distance. The operators〖 E〗_(α,β), Z_(α,β)^ω and Z_(α,β)^(ω,θ)are examined separately under obtained -entropy and it is shown that the fuzzification of that operators are equal under this -entropy.

Anahtar Kelimeler

• Intuitionistic Fyzzy Sets
• Normalized sigma-distance meausre
• sigma entropy
• intuitionistic fuzzy modal operators

YENİ TANIMLANMIŞ BULANIK BULUT ENTROPİSİNE GÖRE E(α,β), Z(α,β,ω) ve Z(α,β,ω,θ) BULANIK BULUT MODAL OPERATÖRLERİNİN EŞİTLİĞİ

Öz

Normalleştirilmiş Hamming uzaklığı kullanılarak sezgisel bulanık kümeler için normal bir -entropi ölçüsü önerilmiştir. Operatörler〖 E〗_(α,β), Z_(α,β)^ω ve Z_(α,β)^(ω,θ) elde edilen -entropi altında ayrı ayrı incelenmiş ve bu operatörlerin bulanıklaşmasının bu -entropi altında eşit olduğu gösterilmiştir.

Anahtar Kelimeler

• Sezgisel Bulanık Kümeler
• Normalleştirilmiş sigma uzaklık ölçüsü
• sigma entropi
• sezgisel bulanık operatörler

Kaynakça

1. Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20 (1), 87–96.
2. Atanassov, K. T. (2012). On intuitionistic fuzzy sets theory. Springer.
3. Çuvalcıoğlu, G. (2007). Some properties of Eα,β operator. Advanced Studies on Contemporary Mathematics, 14 (2), 305–309.
4. Çuvalcıoğlu, G. (2010). Expand the modal operator diagram with Zω α,β. Journal of the Jangjeon Mathematical Society, 13, 403–412.
5. Çuvalcıoğlu, G. (2013). On the diagram of one type modal operators on intuitionistic fuzzy sets, last expanding with Zω,θ α,β. Iranian Journal of Fuzzy Systems, 10 (1), 89–106.
6. Ebanks, B. R. (1983). On measure of fuzziness and their representations. Journal of Mathematical Analysis and Applications, 94 (1), 24–37.
7. Fan, J.-L., & Ma, Y. L. (2001). On some properties of distance measure. Fuzzy Sets and Systems, 117, 355–361.
8. Fan, J.-L., & Ma, Y. L. (2002). Some new entropy formulas. Fuzzy Sets and Systems, 128, 277–284.

9. Kaufmann, A. (1975). Introduction to the theory of fuzzy subsets. Academic Press.
10. Kosko, B. (1992). Neural networks and fuzzy systems. Prentice-Hall.
11. Liu, X. C. (1992). Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets and Systems, 52 (3), 305–318.
12. Szmidt, E., & Baldwin, J. (2003). New similarity measure for intuitionistic fuzzy set theory and mass assignment theory. Notes on Intuitionistic Fuzzy Sets, 9 (3), 60–76.
13. Szmidt, E., & Kacprzyk, J. (2005). New measures of entropy for intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 11 (2), 12–20.
14. Szmidt, E., & Kacprzyk, J. (2001). Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118 (3), 467–477.
15. Yager, R. R. (1979). On measure of fuzziness and negation, Part 1: Membership in the unit interval. International Journal of General Systems, 5, 221–229.
16. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353. 84