Spherical Bipolar Fuzzy Sets and Its Application in Multi Criteria Decision Making Problem
Yıl 2020,
Sayı: 32, 58 - 70, 30.09.2020
Rayappan Princy
Krishnaswamy Mohana
Öz
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.
Kaynakça
- 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.
Yıl 2020,
Sayı: 32, 58 - 70, 30.09.2020
Rayappan Princy
Krishnaswamy Mohana
Kaynakça
- 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.