SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2014 / Cilt: 43 - Sayı: 2

?-separation axioms based on Lukasiewicz logic

O. R. SAYED
Pages
259–277
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, we clarify the relationsof these axioms with each other as well as the relations with otherfuzzifying separation axioms.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper, we introduce topological notions defined by meansof ?-open sets when these are planted into the framework of Ying'sfuzzifying topological spaces (by Lukasiewicz logic in [0, 1]).
📊
Key Findings & Data:We introduce T?-, T?1-, T?2(?- Hausdorff)-, T?3(?-regular)- and T?(?normal)-separation axioms.
💡
Conclusion & Impact:Moreover, we clarify the relationsof these axioms with each other as well as the relations with otherfuzzifying separation axioms.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In the present paper, we introduce topological notions defined by meansof ?-open sets when these are planted into the framework of Ying'sfuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). We introduce T?-, T?1-, T?2(?- Hausdorff)-, T?3(?-regular)- and T?(?normal)-separation axioms. Furthermore, the R0- and R?- separation axioms are studied and their relations with the T?1- and T?2-separation axioms are introduced. Moreover, we clarify the relationsof these axioms with each other as well as the relations with otherfuzzifying separation axioms.

🔖

Cite This Article

SAYED, O. R. (2022). ?-separation axioms based on Lukasiewicz logic. Hacettepe Journal of Mathematics and Statistics, Cilt: 43 - Sayı: 2, 259–277. https://ajindex.com/articles/530365

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  1. I. W. Alderton, ?-compactness of fuzzy topological spaces: A categorical approach, Quas- tiones Mathematicae, 20 (1997), 269-282.
  2. M. Caldas, D. N. Georgiou and S. Jafari, Characterizations of Low separation axioms via ?-open sets and ?-closure operator, Bol. Soc. Paran. Mat., 21 (1-2)(2003), 1-14.
  3. M. Caldas, S. Jafari R. M. Latif and T. Noiri, Characterizations of functions with strongly ?-closed graphs, Scientific Studies and Research Series Mathematics and Informatics 19 (1)(2009), 49-58.
  4. C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182-190.
  5. J. A. Goguen, The fuzzy Tychonoff theorem, J. Math.Anal. Appl., 43 (1973), 182-190. U. H¨ohle, Uppersemicontinuous fuzzy sets and applications, J. Math. Anal. Appl., 78 (1980), 659-673. U. H¨ohle, Many Valued Topology and its Applications, Kluwer Academic Publishers, Dor- drecht, 2001. U. H¨ohle, S. E. Rodabaugh, Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, in: Handbook of Fuzzy Sets Series, vol. 3, Kluwer Academic Publishers, Dordrecht, 1999. U. H¨ohle, S. E. Rodabaugh, A. ^Sostak, (Eds.), Special Issue on Fuzzy Topology, Fuzzy Sets and Systems, 73 (1995), 1-183. U. H¨ohle, A. ^Sostak, Axiomatic foundations of fixed-basis fuzzy topology, in: U. H¨ohle, S. E. Rodabaugh, (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, in: Handbook of Fuzzy Sets Series, vol. 3, Kluwer Academic Publishers, Dordrecht, 1999, 123-272.
  6. J. L. Kelley, General Topology, Van Nostrand, New York, 1955.
  7. F. H. Khedr, F. M. Zeyada and O. R. Sayed, ?-continuity and c?-continuity in fuzzifying topology, Fuzzy Sets and Systems, 116 (2000), 325-337.
  8. F.H. Khedr, F.M. Zeyada, O.R. Sayed, On separation axioms in fuzzifying topology Fuzzy Sets and Systems 119 (2001), 439-458.
  9. T. Kubiak, On Fuzzy Topologies, Ph.D. Thesis, Adam Mickiewicz University, Poznan, Poland, 1985
  10. Y. M. Liu, M. K. Luo, Fuzzy Topology, World Scientific, Singapore, 1998.
  11. S. N. Maheshwari and S. S. Thakur, On ?-irresolute mappings, Tamkang J. Math., 11 (1980) 209-214.
  12. M. Maki, R. Devi and K. Balachandran,Generalized ?-closed sets in topology, Bull. Fukuoka Univ. Ed. Part III, 42 (1993) 13-21. A. N. Mahshour M. H. Ghanim and M. A. Fathalla, ?-separation axioms and ?-compactness in fuzzy topological spaces, Rocky Mountain Journal of Mathematics, 16 (3)(1986) 591-600.
  13. T. Noiri, On ?-continuous functions, ~Casopis P?est. Mat., 109 (1984) 118-126.
  14. D. Qiu, Characterizations of fuzzy finite automata, Fuzzy Sets and Systems, 14