Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem

Rayappan Princy; Krishnaswamy Mohana

EN

Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem

Abstract

This paper introduces the concept of Spherical Bipolar Fuzzy sets (SBFS) as a combination of Spherical Fuzzy sets and Bipolar Valued Fuzzy Sets along with their properties. Arithmetic operations involving addition, multiplication and subtraction are presented together with their proofs. A multi criteria decision making method is established in which the evaluation values of alternatives respective to criteria are represented in SBFS. Finally, a numerical example shows the application of the proposed method.

Keywords

Intuitionistic fuzzy set (IFS), IFS2, neutrosophic fuzzy set (NFS), bipolar valued fuzzy set, spherical fuzzy set

References

F. Smarandache. A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic.Rehoboth: American Research Press (1999) 1-141.
G. İntepe, E. Bozdağ, T. Koç, The Selection of Technology Forecasting Method Using A Multi-Criteria Interval-Valued Intuitionistic Fuzzy Group Decision Making Approach, Computers and Industrial Engineering 65(2) (2013) 277-285.
F. Smarandache, Neutrosophic Set- A Generalization of The Intuitionistic Fuzzy Set, International Journal of Pure and Applied Mathematics 24(3) (2004) 1-15.
I. Grattan-Guinness, Fuzzy Membership Mapped onto Interval and Many-Valued Quantities, Mathematical Logic Quarterly 22(1) (1976) 149-160.
J. M. Garibaldi, T. Özen, Uncertain Fuzzy Reasoning: A Case Study in Modelling Expert Decision Making. IEEE Transactions on Fuzzy Systems 15(1) (2007) 16-30.
K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy sets and Systems 20(1) (1986) 87-96.
L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965) 338-353.
L. A. Zadeh, The Concept of a Linguistic Variable and its application to Approximate Reasoning, Information Sciences 8(3) (1975) 199-249.
Y. Yang, F. Chiclana, Intuitionistic Fuzzy Sets: Spherical Representation and Distances, International Journal of Intelligent Systems 24(4) (2009) 399-420.
R. R. Yager, On The Theory of Bags, International Journal of General Systems 13(1) (1986) 23–37.

V. Torra, Hesitant Fuzzy Sets, International Journal of Intelligent Systems 25(6) (2010) 529-539.
K. Atanassov, Geometrical Interpretation of The Elements of The Intuitionistic Fuzzy Objects, Preprint IM-MFAIS, 1-89, Sofia. Reprinted: International Journal Bioautomation 20 (S1) (2016) 27-42.
K. Atanassov, Intuitionistic Fuzzy Sets, Springer, Heidelberg (1999).
P. J. Ren, Z. Xu, X. J. Gou, Pythagorean Fuzzy TODIM Approach to Multi-Criteria Decision Making, Applied Soft Computing 31 (2016) 246–259.
X. Gou, Z. Xu, P. Ren, The Properties of Continuous Pythagorean Fuzzy Information, International Journal of Intelligent Systems 31(5) (2016) 401-424.
S. Broumi, M. Murugappan, M. Talea, A. Bakali, F. Smarandache, P. K. Singh, A. Dey, Single Valued (2𝑛+1) Sided Polygonal Neutrosophic Numbers and Single Valued (2𝑛) Sided Polygonal Neutrosophic Numbers, Neutrosophic Sets and Systems 25 (2019) 54-65.
S. Broumi, M. Talea, A. Bakali, P. K. Singh, F. Smarandache, Energy and Spectrum Analysis of Interval Valued Neutrosophic Graph using MATLAB, Neutrosophic Sets and Systems 24 (2019) 46-60.
S. Broumi, M. Talea, A. Bakali, F. Smarandache, P. K. Singh, M. Murugappan, V. V. Rao, A Neutrosophic Technique Based Efficient Routing Protocol for MANET Based on Its Energy and Distance, Neutrosophic Sets and Systems 24 (2019) 61-69.
S. Broumi, A. Dey, M. Talea, A. Bakali, F. Smarandache, D. Nagarajan, M. Lathamaheswari, R. Kumar, Shortest Path Problem using Bellman Algorithm under Neutrosophic Environment, Complex and Intelligent Systems 5 (2019) 409-416. https://doi.org/10.1007/s40747-019-0101-8
S. Broumi, M. Talea, A. Bakali, F. Smarandache, D. Nagarajan, M. Lathamaheswari, M. Parimala, Shortest Path Problem in Fuzzy, Intuitionistic Fuzzy and Neutrosophic Environment: An Overview, Complex and Intelligent Systems 5 (2019) 371-378. https://doi.org/10.1007/s40747-019-0098-z
I. Antonov, On A New Geometrical Interpretation of The Intuitionistic Fuzzy Sets, Notes on Intuitionistic Fuzzy Sets 1(1) (1995) 29–31.
Z. Gong, X. Xu, Y. Yang, Y. Zhou, H. Zhang, The Spherical Distance for Intuitionistic Fuzzy Sets and Its Application in Decision Analysis, Technological and Economic Development of Economy 22(3) (2016) 393-415.
R. Sambuc, Function 𝛷-Flous, Application a l’aide au Diagnostic en Pathologie Thyroidienne. University of Marseille (1975).
K. M. Lee, 2000, Bipolar Valued Fuzzy Sets and Their Operations, Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand, (2000) 307-312.
K. M. Lee, Comparison of Interval Valued Fuzzy Sets, Intuitionistic Fuzzy Sets and Bipolar-Valued Fuzzy Sets, Journal of Korean Institute of Intelligent Systems 14(2) (2004) 125-129.
F. K. Gündoğu, C. Kahraman, Spherical Fuzzy Sets and Spherical Fuzzy TOPSIS Method, Journal of Intelligent & Fuzzy Systems 36(1) (2019) 337-352.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Rayappan Princy ^* This is me
0000-0002-4899-4038
India

Krishnaswamy Mohana This is me
India

Publication Date

September 30, 2020

Submission Date

July 22, 2019

Acceptance Date

September 6, 2020

Published in Issue

Year 2020 Number: 32

IZ

https://izlik.org/JA86YD25PF

APA

Princy, R., & Mohana, K. (2020). Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem. Journal of New Theory, 32, 58-70. https://izlik.org/JA86YD25PF

AMA

1.Princy R, Mohana K. Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem. JNT. 2020;(32):58-70. https://izlik.org/JA86YD25PF

Chicago

Princy, Rayappan, and Krishnaswamy Mohana. 2020. “Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem”. Journal of New Theory, nos. 32: 58-70. https://izlik.org/JA86YD25PF.

EndNote

Princy R, Mohana K (September 1, 2020) Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem. Journal of New Theory 32 58–70.

IEEE

[1]R. Princy and K. Mohana, “Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem”, JNT, no. 32, pp. 58–70, Sept. 2020, [Online]. Available: https://izlik.org/JA86YD25PF

ISNAD

Princy, Rayappan - Mohana, Krishnaswamy. “Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem”. Journal of New Theory. 32 (September 1, 2020): 58-70. https://izlik.org/JA86YD25PF.

JAMA

1.Princy R, Mohana K. Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem. JNT. 2020;:58–70.

MLA

Princy, Rayappan, and Krishnaswamy Mohana. “Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem”. Journal of New Theory, no. 32, Sept. 2020, pp. 58-70, https://izlik.org/JA86YD25PF.

Vancouver

1.Rayappan Princy, Krishnaswamy Mohana. Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem. JNT [Internet]. 2020 Sep. 1;(32):58-70. Available from: https://izlik.org/JA86YD25PF