Research Article

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

Volume: 8 Number: 2 October 19, 2025
EN TR

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

Abstract

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.

Keywords

References

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  2. Atanassov, K. T. (2012). On intuitionistic fuzzy sets theory. Springer.
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  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.

Details

Primary Language

English

Subjects

Algebra and Number Theory, Pure Mathematics (Other)

Journal Section

Research Article

Publication Date

October 19, 2025

Submission Date

June 24, 2025

Acceptance Date

August 15, 2025

Published in Issue

Year 2025 Volume: 8 Number: 2

APA
Bal, A., Tarsuslu, S., Gündoğdu, D., & Çuvalcıoğlu, G. (2025). 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. Journal of Universal Mathematics, 8(2), 70-84. https://doi.org/10.33773/jum.1725478
AMA
1.Bal A, Tarsuslu S, Gündoğdu D, Çuvalcıoğlu G. 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. JUM. 2025;8(2):70-84. doi:10.33773/jum.1725478
Chicago
Bal, Arif, Sinem Tarsuslu, Dilara Gündoğdu, and Gökhan Çuvalcıoğlu. 2025. “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”. Journal of Universal Mathematics 8 (2): 70-84. https://doi.org/10.33773/jum.1725478.
EndNote
Bal A, Tarsuslu S, Gündoğdu D, Çuvalcıoğlu G (October 1, 2025) 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. Journal of Universal Mathematics 8 2 70–84.
IEEE
[1]A. Bal, S. Tarsuslu, D. Gündoğdu, and G. Çuvalcıoğlu, “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”, JUM, vol. 8, no. 2, pp. 70–84, Oct. 2025, doi: 10.33773/jum.1725478.
ISNAD
Bal, Arif - Tarsuslu, Sinem - Gündoğdu, Dilara - Çuvalcıoğlu, Gökhan. “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”. Journal of Universal Mathematics 8/2 (October 1, 2025): 70-84. https://doi.org/10.33773/jum.1725478.
JAMA
1.Bal A, Tarsuslu S, Gündoğdu D, Çuvalcıoğlu G. 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. JUM. 2025;8:70–84.
MLA
Bal, Arif, et al. “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”. Journal of Universal Mathematics, vol. 8, no. 2, Oct. 2025, pp. 70-84, doi:10.33773/jum.1725478.
Vancouver
1.Arif Bal, Sinem Tarsuslu, Dilara Gündoğdu, Gökhan Çuvalcıoğlu. 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. JUM. 2025 Oct. 1;8(2):70-84. doi:10.33773/jum.1725478