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

#### Rayappan PRİNCY [1] , Krishnaswamy MOHANA [2]

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.
Intuitionistic fuzzy set (IFS), IFS2, neutrosophic fuzzy set (NFS), bipolar valued fuzzy set, spherical fuzzy set
• 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.
Primary Language en Mathematics Research Article Orcid: 0000-0002-4899-4038Author: Rayappan PRİNCY (Primary Author)Institution: Nirmala College for WomenCountry: India Author: Krishnaswamy MOHANA Institution: Nirmala College for WomenCountry: India Publication Date : September 30, 2020
 Bibtex @research article { jnt802271, journal = {Journal of New Theory}, issn = {}, eissn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2020}, volume = {}, pages = {58 - 70}, doi = {}, title = {Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem}, key = {cite}, author = {Pri̇ncy, Rayappan and Mohana, Krishnaswamy} } APA Pri̇ncy, R , Mohana, K . (2020). Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem . Journal of New Theory , (32) , 58-70 . Retrieved from https://dergipark.org.tr/en/pub/jnt/issue/56973/802271 MLA Pri̇ncy, R , Mohana, K . "Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem" . Journal of New Theory (2020 ): 58-70 Chicago Pri̇ncy, R , Mohana, K . "Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem". Journal of New Theory (2020 ): 58-70 RIS TY - JOUR T1 - Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem AU - Rayappan Pri̇ncy , Krishnaswamy Mohana Y1 - 2020 PY - 2020 N1 - DO - T2 - Journal of New Theory JF - Journal JO - JOR SP - 58 EP - 70 VL - IS - 32 SN - -2149-1402 M3 - UR - Y2 - 2020 ER - EndNote %0 Journal of New Theory Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem %A Rayappan Pri̇ncy , Krishnaswamy Mohana %T Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem %D 2020 %J Journal of New Theory %P -2149-1402 %V %N 32 %R %U ISNAD Pri̇ncy, Rayappan , Mohana, Krishnaswamy . "Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem". Journal of New Theory / 32 (September 2020): 58-70 . AMA Pri̇ncy R , Mohana K . Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem. JNT. 2020; (32): 58-70. Vancouver Pri̇ncy R , Mohana K . Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem. Journal of New Theory. 2020; (32): 58-70.

Authors of the Article
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