Bipolar fuzzy soft D-metric spaces

Year 2021, Volume: 70 Issue: 1, 64 - 73, 30.06.2021

Orhan Dalkılıç , Naime Demirtaş

https://doi.org/10.31801/cfsuasmas.774658

Cited By: 9

Abstract

The first aim to this paper is to introduce the notions of bipolar fuzzy soft metric space and bipolar fuzzy soft (D-)metric space. In order to define these concepts, the concept of bipolar fuzzy soft points has been brought to the literature and bipolar fuzzy soft points have been examined in detail. Moreover, the bipolar fuzzy soft sequences and bipolar fuzzy soft cauchy sequences were defined and some of their properties were examined. In addition to all this, many examples are given in order to better understand the concepts and features studied and contribute to a better understanding of the paper.

Keywords

Bipolar fuzzy soft sets, Bipolar fuzzy soft metric space, Bipolar fuzzy soft D-metric space

References

• Abdullah, S., Aslam, M., Ullah, K., Bipolar fuzzy soft sets and its applications in decision making problem, Journal of Intelligent and Fuzzy Systems, 27 (2) (2014), 729-742.
• Beaulaa, T., Gunaseeli, C., On fuzzy soft metric spaces, Malaya J. Mat., 2 (3) (2014), 197-202.
• Demirtaş, N., Hussain, S., Dalkılıç, O., New approaches of inverse soft rough sets and their applications in a decision making problem, Journal of applied mathematics and informatics, 38 (3-4) (2020), 335-349.
• Dhage, B.C., Generalized metric spaces mappings with fixed point, Bull. Calcutta Math. Soc., 84 (1992), 329-336.
• Gahler, S., 2-metrische Raume und iher topoloische Struktur, Math. Nachr., 26 (1963), 115-148.
• Molodtsov, D., Soft set theory-first results, Computers and Mathematics with Applications, 37 (1999), 19-31.
• Pawlak, Z., Rough sets, International Journal of Computer and Information Sciences, 11 (5) (1982), 341-356.
• Riaz, M., Hashmi, M. R., Linear Diophantine Fuzzy Set and its Applications towards Multi-Attribute Decision Making Problems, Journal of Intelligent & Fuzzy Systems, 37 (4) (2019), 5417-5439.
• Riaz, M., Smarandache, F., Firdous, A., Fakhar, A., On soft rough topology with multi-attribute group decision making, Mathematics, 7 (1) (2019), 1-18.
• Riaz, M., Tehrim, S. T., Bipolar Fuzzy Soft Mappings with Application to Bipolar Disorders, International Journal of Biomathematics, 12 (7) (2019) 1-31.
• Riaz, M., Tehrim, S. T., A robust extension of VIKOR method for bipolar fuzzy sets using connection numbers of SPA theory based metric spaces, Artificial Intelligence Review, 1 (31) (2020).
• Sayed, A.F., Alahmari, A., Fuzzy soft α-ψ-contractive type mappings and some fixed point theorems in fuzzy soft metric spaces, Ann. Fuzzy Math. Inform., 15 (1) (2018), 73-87.
• Tehrim, S. T., Riaz, M., A novel extension of TOPSIS to MCGDM with Bipolar Neutrosophic soft topology, Journal of Intelligent & Fuzzy Systems, 4 (2019), 5531-5549.
• Tehrim, S.T., Riaz, M., An Interval-Valued Bipolar Fuzzy Linguistic VIKOR Method using Connection Numbers of SPA Theory and Its Application to Decision Support System, Journal of Intelligent & Fuzzy Systems, 1 (18) (2020).
• Zadeh, L. A., Fuzzy sets, Inf. Control., 8 (1965), 338-353.
• Zhang, W.R., Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multiagent decision analysis, In Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference, 18-21 Dec., San Antonio, TX, USA, (1994).
• Zhang, W.R., Bipolar fuzzy sets, In Proceedings of the 1998 IEEE International Conference on Fuzzy Systems, 4-9 May., Anchorage, AK, USA, (1998).