TY - JOUR T1 - 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 TT - YENİ TANIMLANMIŞ BULANIK BULUT ENTROPİSİNE GÖRE E(α,β), Z(α,β,ω) ve Z(α,β,ω,θ) BULANIK BULUT MODAL OPERATÖRLERİNİN EŞİTLİĞİ AU - Bal, Arif AU - Tarsuslu, Sinem AU - Gündoğdu, Dilara AU - Çuvalcıoğlu, Gökhan PY - 2025 DA - October Y2 - 2025 DO - 10.33773/jum.1725478 JF - Journal of Universal Mathematics JO - JUM PB - Gökhan ÇUVALCIOĞLU WT - DergiPark SN - 2618-5660 SP - 70 EP - 84 VL - 8 IS - 2 LA - en AB - 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. KW - Intuitionistic Fyzzy Sets KW - Normalized sigma-distance meausre KW - sigma entropy KW - intuitionistic fuzzy modal operators N2 - 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. CR - Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20 (1), 87–96. CR - Atanassov, K. T. (2012). On intuitionistic fuzzy sets theory. Springer. CR - Çuvalcıoğlu, G. (2007). Some properties of Eα,β operator. Advanced Studies on Contemporary Mathematics, 14 (2), 305–309. CR - Çuvalcıoğlu, G. (2010). Expand the modal operator diagram with Zω α,β. Journal of the Jangjeon Mathematical Society, 13, 403–412. CR - 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. CR - Ebanks, B. R. (1983). On measure of fuzziness and their representations. Journal of Mathematical Analysis and Applications, 94 (1), 24–37. CR - Fan, J.-L., & Ma, Y. L. (2001). On some properties of distance measure. Fuzzy Sets and Systems, 117, 355–361. CR - Fan, J.-L., & Ma, Y. L. (2002). Some new entropy formulas. Fuzzy Sets and Systems, 128, 277–284. CR - Kaufmann, A. (1975). Introduction to the theory of fuzzy subsets. Academic Press. CR - Kosko, B. (1992). Neural networks and fuzzy systems. Prentice-Hall. CR - Liu, X. C. (1992). Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets and Systems, 52 (3), 305–318. CR - 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. CR - Szmidt, E., & Kacprzyk, J. (2005). New measures of entropy for intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 11 (2), 12–20. CR - Szmidt, E., & Kacprzyk, J. (2001). Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118 (3), 467–477. CR - 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. CR - Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353. 84 UR - https://doi.org/10.33773/jum.1725478 L1 - https://dergipark.org.tr/en/download/article-file/4983991 ER -