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Volume 8
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Article

On Bipolar Fuzzy Gradation of Openness

by
Subhadip Roy
1,
Jeong-Gon Lee
2,*,
Syamal Kumar Samanta
3,
Anita Pal
1 and
Ganeshsree Selvachandran
4
1
Department of Mathematics, National Institute of Technology Durgapur, Durgapur 713209, West Bengal, India
2
Division of Applied Mathematics, Wonkwang University, Iksan 54538, Korea
3
Department of Mathematics, Visva Bharati, Santiniketan 731235, West Bengal, India
4
Department of Actuarial Science and Applied Statistics, Faculty of Business and Information Science, UCSI University, Jalan Menara Gading, Cheras, Kuala Lumpur 56000, Malaysia
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 510; https://doi.org/10.3390/math8040510
Submission received: 2 March 2020 / Revised: 23 March 2020 / Accepted: 25 March 2020 / Published: 2 April 2020
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications 2020)
Versions Notes

Abstract

The concept of bipolar fuzziness is of relatively recent origin where in addition to the presence of a property, which is done in fuzzy theory, the presence of its counter-property is also taken into consideration. This seems to be much natural and realistic. In this paper, an attempt has been made to incorporate this bipolar fuzziness in topological perspective. This is done by introducing a notion of bipolar gradation of openness and to redefine the bipolar fuzzy topology. Furthermore, a notion of bipolar gradation preserving map is given. A concept of bipolar fuzzy closure operator is also introduced and its characteristic properties are studied. A decomposition theorem involving our bipolar gradation of openness and Chang type bipolar fuzzy topology is established. Finally, some categorical results of bipolar fuzzy topology (both Chang type and in our sense) are proved.
Keywords: bipolar gradation of openness; bipolar gradation of closedness; bipolar fuzzy topology; bipolar gradation preserving map bipolar gradation of openness; bipolar gradation of closedness; bipolar fuzzy topology; bipolar gradation preserving map

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MDPI and ACS Style

Roy, S.; Lee, J.-G.; Samanta, S.K.; Pal, A.; Selvachandran, G. On Bipolar Fuzzy Gradation of Openness. Mathematics 2020, 8, 510. https://doi.org/10.3390/math8040510

AMA Style

Roy S, Lee J-G, Samanta SK, Pal A, Selvachandran G. On Bipolar Fuzzy Gradation of Openness. Mathematics. 2020; 8(4):510. https://doi.org/10.3390/math8040510

Chicago/Turabian Style

Roy, Subhadip, Jeong-Gon Lee, Syamal Kumar Samanta, Anita Pal, and Ganeshsree Selvachandran. 2020. "On Bipolar Fuzzy Gradation of Openness" Mathematics 8, no. 4: 510. https://doi.org/10.3390/math8040510

APA Style

Roy, S., Lee, J.-G., Samanta, S. K., Pal, A., & Selvachandran, G. (2020). On Bipolar Fuzzy Gradation of Openness. Mathematics, 8(4), 510. https://doi.org/10.3390/math8040510

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