سامانه مدیریت نشریات علمی دانشگاه صنعتی شاهرود

Satyanarayana, Bavanari, Baji, Shake, Devanandam, Dola. (1404). FUZZY NEUTROSOPHIC PRIME IDEALS OF BCK-ALGEBRAS. , 13(2), 109-117. doi: 10.22044/jas.2023.12903.1701
Bavanari Satyanarayana; Shake Baji; Dola Devanandam. "FUZZY NEUTROSOPHIC PRIME IDEALS OF BCK-ALGEBRAS". , 13, 2, 1404, 109-117. doi: 10.22044/jas.2023.12903.1701
Satyanarayana, Bavanari, Baji, Shake, Devanandam, Dola. (1404). 'FUZZY NEUTROSOPHIC PRIME IDEALS OF BCK-ALGEBRAS', , 13(2), pp. 109-117. doi: 10.22044/jas.2023.12903.1701
Satyanarayana, Bavanari, Baji, Shake, Devanandam, Dola. FUZZY NEUTROSOPHIC PRIME IDEALS OF BCK-ALGEBRAS. , 1404; 13(2): 109-117. doi: 10.22044/jas.2023.12903.1701

FUZZY NEUTROSOPHIC PRIME IDEALS OF BCK-ALGEBRAS

Journal of Algebraic Systems
مقاله 7، دوره 13، شماره 2، مهر 2025، صفحه 109-117    اصل مقاله (131.89 K)
نوع مقاله: Other
شناسه دیجیتال (DOI): 10.22044/jas.2023.12903.1701
نویسندگان
Bavanari Satyanarayana1؛ Shake Baji* 2؛ Dola Devanandam1
1Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar, Guntur-522 510, Andhra Pradesh, India.
2Department of Mathematics, Sir C R Reddy college of Engineering, Eluru-534 007, Andhra Pradesh, India.
چکیده
In this research paper, we introduce and analyze the notion of fuzzy neutrosophic prime ideals (FNPIs) in a commutative BCK-algebra $\mathcal{K}$. It represents a further extension of prime ideals in the context of fuzzy neutrosophic sets. We provide an example that shows that not every fuzzy neutrosophic ideal of a commutative BCK-algebra $\mathcal{K}$ is a FNPI of $\mathcal{K}$. We also prove that a fuzzy neutrosophic set of $\mathcal{K}$ is a FNPI of $\mathcal{K}$ if, for all $a,b,c \in [0,1] $, the upper (a,b)-level cut and lower c-level cut are prime ideals of $\mathcal{K}$.
کلیدواژه‌ها
Intuitionistic Fuzzy Prime Ideal(IFPI)؛ Fuzzy Neutrosophic Set(FNS)؛ Fuzzy Neutrosophic Ideal(FNI)؛ Fuzzy Neutrosophic Prime Ideal(FNPI)
مراجع
  1. S. Abdullah, Intuitionistic Fuzzy Prime Ideals of BCK-algebras, Ann. Fuzzy Math. In form., 7 (2014), 661–668.
  1. I. Arockiarani, I. R. Sumathi and J. M. Jency, Fuzzy Neutrosophic Soft Topological Spaces, IJMA, 4 (2013), 225–238.
  1. K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20 (1986), 87–96.
  2. E. Y. Deeba, A. B. Thaheem and J. Ahsan, On Prime Ideals of BCK-algebras, Math. Jpn., 36 (1991), 875–882.
  1. K. Iseki and S. Tanaka, An introduction to the Theory of the BCK-algebras, Math. Japan, 23 (1978), 1–26.
  1. K. Iseki and S. Tanaka, Ideal theory of BCK-algebras, Math. Jpn., 21 (1976), 351–366.
  2. W. K. Jeong, On Anti Fuzzy Prime Ideals in BCK-algebras, J. Chungcheong Math. Soc., 12 (1999), 15–21.
  1. Y. B. Jun and K. Kim, Intuitionistic Fuzzy Ideals of BCK-algebras, Int. J. Math. Math. Sci., 24 (2000), 839–849.
  1. Y. B. Jun and X. L. Xin, Fuzzy Prime Ideals and Invertible Fuzzy Ideals in BCK-algebras, Fuzzy Sets and Systems, 117 (2001), 471–476.
  1. B. Satyanarayana, Sk. Baji and U. Bindu Madhavi, Fuzzy Neutrosophic implicative and positive implicative ideals of BCK-algebras, kala sarovar, 25 (2022), 24–31.
  1. F. Smarandache, A Unifying Field in logics: Neutrosophic logic. Neutrosophy, Neutro sophic Set, Neutrosophic Probability, American Research Press, Rehoboth, Infinite Study, 2003.
 

12. F. Smarandache, Neutrosophic Set-a Generalization of the Intuitionistic Fuzzy Set, IEEE  Int. Conf. Granul. Comput, (2006), 38–42.

  1. O. G. Xi, Fuzzy BCK-Algebra, Math. Jpn., 36 (1991), 935–942.
  2. L. A. Zadeh, Fuzzy Sets, Information and control, 8 (1965), 338–353.
آمار
تعداد مشاهده مقاله: 226
تعداد دریافت فایل اصل مقاله: 243