Abstract

In the present paper, we continue the study on fuzzy soft tri-topological spaces, and investigate the relationships among some main types of fuzzy soft open sets fuzzy soft tri-topological spaces. In particular, we study the relationships among the Fuzzy soft τ1 τ2 τ3-open (closed) set, Fuzzy Soft Tri-α-open (closed) set, Fuzzy Soft Tri-pre-open(closed) set and Fuzzy Soft Tri-semi-open (closed) set in Fuzzy Soft Tri-topological Spaces. And We analyze the relationships among these notions by providing theorems and counter examples.

References

• L.A.Zadeh, Fuzzy sets, Inform. and Control, 8 (1965) 338-353.
• C. C. Chou, J. M. Yih, J. F. Ding, TC Han, YH Lim, LJ Liu and WK Hsu. Application of a fuzzy EOQ model to the stock management in the manufacture system. Key Engineering Materials. (2012) 361-365.
• C. Eksin, G. uzelkaya M, E. Yesil and I. Eksin. Fuzzy logic approach to mimic decision making behaviour of humans in stock management game. Proceedings of the 2008 System Dynamics Conference; 2008.
• D. Molodtsov, Soft set theory-first results. Compu. Math. Appl.(37),(1999) 19-31.
• P.K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44 (2002) 1077-1083.
• D. Pie and D. Miao, From soft sets to information systems, Granu. comput. IEEE Inter. Conf. 2 (2005) 617–621.
• P. Maji, R. Biswas, A. Roy, Fuzzy soft sets, J. Fuzzy Math., 9(3), (2001) 589-602.
• A. R. Roy and P. K. Maji, A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math., 203, (2007) 412-418.
• H. Aktas. and N. Cagman, Soft sets and soft groups, Information Sciences, 177, (2007) 2726-2735.
• X. Yang, D. Yu, J. Yang and C. Wu, Generalization of soft set theory: from crisp to fuzzy case, In: Bing-Yuan Cao ,eds., Fuzzy Information and Engineering: Proceedings of ICFIE- 2007, Advances in Soft Computing 40, Springer, (2007) 345-355.
• X. Yang, T. Y. Lin, J. Yang, Y. Li and D. Yu, Combination of interval-valued fuzzy set and soft set, Comput. Math. Appl., 58, (2009) 521-527.
• J.C. Kelly, Bitopological Spaces, proc. London Math. Soc; 13, (1963) 71-83.
• I. L. Reilly, On bitopological separation properties. Nanta Math.29, (1972) 14-25.
• C. W. Patty, Bitopological spaces. Duke Math. J., 34, (1967) 387-392.
• B. Ittanagi, Soft Bitopological Spaces, Comp. & Math. with App.,107, (2014) 1-4.
• P. Mukherjee and C. Park, On fuzzy soft bitopological spaces, Mathematics and Computer Sciences Journal (MCSJ).,10(7), (2015) 1-8.
• A. F. Sayed, On Characterizations of Some Types of Fuzzy Soft Sets in Fuzzy Soft Bitopological Spaces, Journal of Advances in Mathematics and Computer Science, 24(3), (2017) 1-12.
• A. F. Sayed, some separation axioms in fuzzy soft bitopological spaces, J. Math. Comput. Sci. 8(1), (2018) 28-45
• M. Kovar, On 3-Topological version of Thet- Reularity, Internat. J. Matj, Sci., 23, (2000) 393- 398.
• S. Palaniammal , Study of Tri topological spaces, Ph.D Thesis. (2011).
• Asmhan Flieh Hassan, δ^*-open set in tritopological spaces, M.Sc. thesis, Kufa University. (2004)
• Asmhan Flieh Hassan, δ^*-connectedness in tritopological space, journal of Thi-Qar university, 6(3), (2011) 20-28.
• Asmhan Flieh Hassan, Neeran T. A. & Alyaa Y., δ^*-Base in tritopological space, journal of Kerbala university, 9(3), (2011) 344 – 352.
• Asmhan Flieh Hassan & Hanan A.H., A relations among the separation axioms in Topological, Bitopological and Tritopological Spaces, journal of Kerbala university, 5(2), (2007) 155 – 158.
• Asmhan Flieh Hassan, A relations among some kinds of continuous and open functions in Topological, Bitopological and Tritopological Spaces, journal of Basrah Researches(sciences), 35(4), (2009) 1-4.
• Asmhan Flieh Hassan, Countability and Separability in Tritopological Spaces (δ^*-Countability and δ^*-Separability). Mathematical Theory and Modeling,.7(1), (2017) 32-37.
• Asmhan F. Hassan, Soft Tritopological Spaces. International Journal of Computer Applications, 176(9), (2017) 26-30.
• Asmhan F. Hassan, An Introduction to Fuzzy Soft Tritopological Spaces., International Journal of Fuzzy Mathematical Archive, 17(1), (2019) 41-49.
• L. A. Al-Swidi and A. S. Saeed, Soft fuzzy and fuzzy soft set theory with applications, Noor Publishing, 2020.
• B. Tanay, M. Burc Kandemir, Topological structure of fuzzy soft sets, Computer & Mathematics with Applications, 61(10), (2011) 2952-2957.