On Bipolar Fuzzy Gradation of Openness

Subhadip Roy, Jeong-Gon Lee, Syamal Kumar Samanta, Anita Pal and Ganeshsree Selvachandran
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Subhadip Roy: Department of Mathematics, National Institute of Technology Durgapur, Durgapur 713209, West Bengal, India
Jeong-Gon Lee: Division of Applied Mathematics, Wonkwang University, Iksan 54538, Korea
Syamal Kumar Samanta: Department of Mathematics, Visva Bharati, Santiniketan 731235, West Bengal, India
Anita Pal: Department of Mathematics, National Institute of Technology Durgapur, Durgapur 713209, West Bengal, India
Ganeshsree Selvachandran: Department of Actuarial Science and Applied Statistics, Faculty of Business and Information Science, UCSI University, Jalan Menara Gading, Cheras, Kuala Lumpur 56000, Malaysia

Mathematics, 2020, vol. 8, issue 4, 1-12

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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