Z-SONLAR NAZARIYASI VA ULARNI KLASSIK NOANIQ SONLARGA AYLANTIRISH ALGORITMI

Yusupova Dilfuza Muxammadqodirovna

Authors

Yusupova Dilfuza Muxammadqodirovna Ipak yo‘li innovatsiyalar universiteti , Muhammad al-Xorazmiy nomidagi Toshkent axborot texnologiyalari universiteti

Keywords:

Z-son, ehtimollik taqsimoti, ishonchlilik o‘lchovi, noravshan o‘zgaruvchi, trapetsiya ko‘rinishidagi noravshan son, uchburchak ko‘rinishidagi noravshan son, Z-baholash

Abstract

Ushbu maqolada Z-son tushunchasi, uning matematik ta’rifi va grafik ifodasi bayon etiladi. Z-son — bu (A, B) ko‘rinishidagi tartiblangan juftlik bo‘lib, A komponenti noaniq o‘zgaruvchining haqiqiy qiymatlariga qo‘yilgan cheklovlarni, B komponenti esa ushbu qiymatlarning ishonchlilik o‘lchovini ifodalaydi. Tadqiqotda Z-sonlarning diskret va uzluksiz ko‘rinishlari, ularning ehtimollik taqsimotlari bilan aloqasi, shuningdek, +Z-son tushunchasi tahlil qilinadi. Asosiy e’tibor Z-sonlarni klassik noaniq sonlarga aylantirish algoritmiga qaratiladi. Taklif etilgan usulda B komponenti integrallash orqali aniq son shakliga o‘tkazilib, A komponenti bilan vaznli tarzda birlashtiriladi. Natijada, trapetsiya yoki uchburchak ko‘rinishdagi noaniq sonlar klassik noaniq sonlarga konvertatsiya qilinadi. Ushbu yondashuv noaniq baholashlarni optimallashtirish va qaror qabul qilish tizimlarida samarali qo‘llanishi mumkin.

References

1. MUHAMMAD A., INAYAT U. Solution of Z-number-based multi-objective linear programming models with different membership functions // Information Sciences. – 2024. – Vol. 659. – P. 120100.

2. GONGAO Q., JUANRUI L., BINGYI K., BIN Y. The aggregation of Z-numbers based on overlap functions and grouping functions and its application on group decision making // Information Sciences. – 2023. – Vol. 623. – P. 857–899.

3. ZADEH L.A. A note on Z-numbers // Information Sciences. – 2011. – Vol. 181. – P. 2923–2932.

4. DUBOIS D., PRADE D. The mean value of a fuzzy number // Fuzzy Sets and Systems. – 1987. – Vol. 24. – P. 279–300.

5. ANJARIA K. Knowledge derivation from Likert scale using Z-numbers // Information Sciences. – 2022. – Vol. 590. – P. 234–252.

6. ZAMRI N., AHMAD F., ROSE A.N.M., MAKHTAR M. A fuzzy TOPSIS with Z-numbers approach for evaluation on accident at the construction site // Proceedings of the 2nd International Conference on Soft Computing and Data Mining. – Bandung, Indonesia, 18–20 August 2016. – Vol. 549. – P. 41–50.

7. JISKANI I.M., YASLI F., HOSSEINI S., REHMAN A.U., UDDIN S. Improved Z-number based fuzzy fault tree approach to analyze health and safety risks in surface mines // Resources Policy. – 2022. – Vol. 76. – P. 102591.

8. ZHU R.N., LI Y.A., CHENG R.L., KANG B.Y. An improved model in fusing multi-source information based on Z-numbers and POWA operator // Computational and Applied Mathematics. – 2021. – Vol. 41. – P. 16.

9. GHAHTARANI A. A new portfolio selection problem in bubble condition under uncertainty: Application of Z-number theory and fuzzy neural network // Expert Systems with Applications. – 2021. – Vol. 177. – P. 114944.

10. ZHANG Q.S., JIANG S.Y. On weighted possibilistic mean, variance and correlation of interval-valued fuzzy numbers // CMR. – 2010. – Vol. 26. – P. 105–118.

11. KANG B., WEI D., LI Y., DENG Y. A method of converting Z-number to classical fuzzy number // Journal of Information and Computational Science. – 2012. – Vol. 9. – P. 703–709.

12. ALIEV R.A., ALIZADEH A.V., HUSEYNOV O.H. The arithmetic of discrete Z-numbers // Information Sciences. – 2015. – Vol. 290. – P. 134–155.

13. ALIEV R.A., HUSEYNOV O.H., ZEINALOVA L.M. The arithmetic of continuous Z-numbers // Information Sciences. – 2016. – Vol. 373. – P. 441–460.

14. JIANG W., XIE C.H., LUO Y., TANG Y.C. Ranking Z-numbers with an improved ranking method for generalized fuzzy numbers // Journal of Intelligent and Fuzzy Systems. – 2017. – Vol. 32. – P. 1931–1943.

15. ALIEV R.A., PEDRYCZ W., HUSEYNOV O.H. Functions defined on a set of Z-numbers // Information Sciences. – 2018. – Vol. 423. – P. 353–375.

16. ALIZADEH A.V., ALIYEV R.R., HUSEYNOV O.H. Algebraic properties of Z-numbers under additive arithmetic operations // Proceedings of the 13th International Conference on Application of Fuzzy Systems and Soft Computing. – Warsaw, Poland, 27–28 August 2018. – Vol. 896. – P. 893–900.

17. ALIEV R.A., ALIZADEH A.V. Algebraic properties of Z-numbers under multiplicative arithmetic operations // Proceedings of the 13th International Conference on Application of Fuzzy Systems and Soft Computing. – Warsaw, Poland, 27–28 August 2018. – Vol. 896. – P. 33–41.

18. PENG H.G., ZHANG H.Y., WANG J.Q., LI L. An uncertain Z-number multicriteria group decision-making method with cloud models // Information Sciences. – 2019. – Vol. 501. – P. 136–154.