Some pairwise weakly Fuzzy mappings


  • Runu Dhar Maharaja Bir Bikram Univesity.



Fuzzy bitopological space, Pairwise weakly fuzzy, Fuzzy δ-semi pre-continuous, Fuzzy δ-semi pre-open mappings


The aim of this paper is to introduce some pairwise weakly fuzzy mappings, called pairwise weakly fuzzy δ-semi-pre-continuous mappings and pairwise weakly fuzzy δ-semi pre-open mappings in fuzzy bitopological spaces. The concept of pairwise weakly fuzzy δ-semi-precontinuous mappings is to be introduced in fuzzy bitopological spaces with the help of the concept of (i, j)-fuzzy pre-open and (i, j)-fuzzy δ-semi pre-open set. Then some of its basic properties and characterization theorems are to be investigated. Also the notion of pairwise weakly fuzzy δ-semi-pre-open mappings is to be introduced in fuzzy bitopological spaces with the help of the concept of (i, j)-fuzzy open set and (i, j)-fuzzy δ-semi pre-interior. Some of its basic properties and its relationship with other known mappings are also to be studied.

Author Biography

Runu Dhar, Maharaja Bir Bikram Univesity.

Dept. of Applied Mathematics.


K. Azad, “On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity”, Journal of mathematical analysis and applications, vol. 82, no. 1, pp. 14–32, Jul. 1981, doi: 10.1016/0022-247X(81)90222-5.

A. Bin Shahna, “On fuzzy strong semicontinuity and fuzzy precontinuity”, Fuzzy sets and systems, vol. 44, no. 2, pp. 303–308, Nov. 1991, doi: 10.1016/0165-0114(91)90013-G.

M. Caldas, S. Jafari and R. Saraf, “Fuzzy (δ, p) - T1 topological spaces”, Journal of Tripura mathematical society, vol. 9, pp. 1-4, 2007.

C. Chang, “Fuzzy topological spaces”, Journal of mathematical analysis and applications, vol. 24, no. 1, pp. 182–190, Oct. 1968, doi: 10.1016/0022-247X(68)90057-7.

K. Dubey, O. Panwar and R. Tiwari, “On weakly pairwise irresolute mappings”, Bulletin of Calcutta mathematical society, vol. 82, pp. 250-255, 1990.

A. Dutta and B. Tripathy, “On fuzzy b-θ open sets in fuzzy topological space”, Journal of intelligent & fuzzy systems, vol. 32, no. 1, pp. 137–139, Jan. 2017, doi: 10.3233/JIFS-151233

S. Ganguly and S. Saha, “A note on δ-continuity and δ-connected sets in fuzzy set theory”, Simon Stevin, vol. 62, pp. 127-141, 1988.

A. Kandil, “On Biproximities and fuzzy bitopological spaces”, Simon Stevin, vol. 63, pp. 45-66, 1989.

S. Sampath Kumar, “On fuzzy pairwise α-continuity and fuzzy pairwise pre-continuity”, Fuzzy sets and systems, vol. 62, no. 2, pp. 231–238, Mar. 1994, doi: 10.1016/0165-0114(94)90063-9.

S. Sampath Kumar, “Semi-open sets, semi-continuity and semi-open mappings in fuzzy bitopological spaces”, Fuzzy sets and systems, vol. 64, no. 3, pp. 421–426, Jun. 1994., doi: 10.1016/0165-0114(94)90166-X.

A. Mukherjee, and R. Dhar, “On weakly fuzzy δ-semi precontinuous mapping and weajly fuzzy δ-semi preirresolute mapping”, International journal of fuzzy mathematics, vol. 18, no. 1, pp. 209-216, 2010.

A. Mukherjee and R. Dhar, “On fuzzy δ-semi preopn sets and weakly fuzzy δ-semi preopen functions”, Acta ciencia indica, mathematics, vol. 35, no.1, pp. 11- 16, 2009.

A. Mukherjee and A. Dhar, “On pairwise weakly fuzzy δ-semi preirresolute mappings”, in Proceedings of international conference on rough sets, fuzzy sets and soft computing. November, 5 - 7, 2009, R. Bhaumik, Ed. Suryamaninagar, TR: Tripura University, 2011, pp. 392–399.

A. Mukherjee and S. Debnath, “On δ-semiopen sets in fuzzy setting”, Journal of Tripura mathematical society, vol. 8, pp. 51-54, 2006.

J. Park, “On fuzzy pairwise semi-precontinuity”, Fuzzy sets and systems, vol. 93, no. 3, pp. 375–379, Feb. 1998., doi: 10.1016/S0165-0114(96)00183-2.

P. Pu and Y. Liu, “Fuzzy topology I. neighbourhood structure of a fuzzy point and Moore - Smith convergence”, Journal of mathematical analysis & applications, vol. 76, no. 2, pp. 571-599, Aug. 1980, doi: 10.1016/0022-247X(80)90048-7.

D. Sarma and B. Tripathy, “Pairwise Generalized b-Ro Spaces in Bitopological Spaces”, Proyecciones (Antofagasta, En línea), vol. 36, no. 4, pp. 589-600, Dec. 2017, doi: 10.4067/S0716-09172017000400589.

S. Thakur and R. Khare, “Fuzzy semi δ-preopen sets and fuzz semi δ-precontinuous mappings”, Universitatea din Bacau studii si cerceturi strintitice seria mathematica, vol. 14, pp. 201-211, 2004.

S. Thakur and R. Malviya, “Semi-open sets and semi-continuity in fuzzy bitopological spaces”, Fuzzy sets and systems, vol. 79, no. 2, pp. 251–256, Apr. 1996, doi: 10.1016/0165-0114(95)00080-1.

S. Thakur and R. Malviya, Pairwise fuzzy irresolute mappings, Mathematica. bohemica, vol. 121, no. 3. pp. 273-280, 1996. [On line]. Available:

S. Thakur and S. Singh, “On fuzzy semi-preopen sets and fuzzy semi-precontinuity”, Fuzzy sets and systems, vol. 98, no. 3, pp. 383–391, Sep. 1998, doi: 10.1016/S0165-0114(96)00363-6.

B. Tripathy and G. Ray, “On δ- continuity in mixed fuzzy topologicalspaces”, Boletim da sociedade paranaense de matemtica, vol. 32, no. 2, pp. 175-187, 2014, doi: 10.5269/bspm.v32i2.20254.

B. Tripathy and G. Ray, “Weakly continuous functions on mixed fuzzy topological spaces”, Acta scienttiarum technology, vol. 36, no. 2, pp. 331- 335, 2014, doi: 10.4025/actascitechnol.v36i2.16241.

B. Tripathy and S. Debnath, “On fuzzy b-locally open sets in bitopological spaces”, Songklanakarin journal of science and technology, vol. 37, no. 1, pp. 93-96, 2015. [On line]. Available:

L. Zadeh, “Fuzzy sets”, Information and control, vol. 8, no. 3, pp. 338-353, Jun. 1965, doi: 10.1016/S0019-9958(65)90241-X.



How to Cite

R. Dhar, “Some pairwise weakly Fuzzy mappings”, Proyecciones (Antofagasta, On line), vol. 38, no. 4, pp. 707-717, Oct. 2019.