Document Type : Research Paper


Department of Mathematics, Sikkim Manipal Institute of Technology Sikkim Manipal University, Sikkim, India.


In this paper, the  notion of $ps-ro$ $\beta$-open (closed) fuzzy sets on a fuzzy topological space($fts$) has been introduced as a new tool to study $fts$, the properties of these sets are investigated and shown to be unrelated to the common concept of fuzzy $\beta$-open (closed) sets. Based on these fuzzy sets, $ps-ro$ fuzzy $\beta$-continuity and $ps-ro$ fuzzy $\beta$-open (closed) functions are proposed and they are also found to be different from the idea of fuzzy $\beta$-continuous and fuzzy $\beta$-open (closed) functions, respectively. Further, their  characterizations and relationships with existing allied concepts are investigated.


[1] A. Deb Ray and P. Chettri, On pseudo $\delta$-open fuzzy sets and pseudo fuzzy $\delta$-continuous functions, Int. J. Contemp. Math. Sciences, 5 (29) (2010), pp. 1403-1411.
[2] A. Deb Ray and P. Chettri, Fuzzy pseudo nearly compact spaces and $ps-ro$ continuous functions, J. Fuzzy Math., 19 (3) (2011), pp. 737-746.
[3] A. Deb Ray and P. Chettri, Further on fuzzy pseudo near compactness and $ps-ro$ fuzzy continuous functions, Theory Appl. Math. Comput. Sci., 6 (2) (2016), pp. 96–102.
[4] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), pp. 182-190.
[5] G. Balasubramanian, On fuzzy $\beta$-open sets and fuzzy $\beta$-separation axioms, Kybernetika, 35 (1999), pp. 215-223. 
[6] H.R. Moradi, A. Kamali and B. Singh, Some New Properties of Fuzzy Strongly $g^*$-closed sets and $\delta g^*$-Closed Sets in Fuzzy Topological Spaces, Sahand Commun. Math. Anal., 2 (2)(2015), pp. 13-21.
[7] J. H. Park and B. Y. Lee, Fuzzy semi-preopen sets and fuzzy semi-precontinuous mappings, Fuzzy Sets Syst., 67 (1994), pp. 359-364.
[8] K. K. Azad, On fuzzy semi-continuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl., 82 (1981), pp. 41-32.
[9] L. A. Zadeh, Fuzzy Sets, Information and Control, J. Symb. Log., 8 (1965), pp. 338-353.
[10] M.E Abd. El-Monseb, S.N. El-Deeb and R.A. Mahmould, $\beta$-open sets and $\beta$-continuous mappings, Bull. Fac. Sci. Assiut Univ, 12 (1983), pp. 77-90.
[11] N. Velicko, H-closed topological spaces, Amer. Soc. Transl., 78 (2) (1968), pp. 103-118. 
[12] P. Chettri, S. Gurung and S. Halder, On $ps-ro$ Semiopen Fuzzy Set and $ps-ro$ Fuzzy Semicontinuous, Semiopen functions, Tbil. Math. J., 7 (1) (2014), pp. 87-97.
[13] P. Chettri, S. Gurung, On $ps-ro$ Preopen(closed) Fuzzy Set and $ps-ro$ FuzzyPrecontinuity, J. Fuzzy Math., 27 (2) (2019), pp. 447-458. 
[14] P. Pao-Ming and L. Ying-Ming, Fuzzy topology I. Neighbourhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), pp. 571-599.
[15] S. S. Thakur, Surendra Singh, On fuzzy semi-preopen sets and fuzzy semi-precontinuity, Fuzzy Sets Syst., 98 (1998), pp. 383-391.
[16] V. Chandrasekar1 and S. Parimala, Fuzzy e-regular spaces and strongly e-irresolute mappings, Sahand Commun. Math. Anal., 10 (1)(2018), pp. 135-156.