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Year 2020, Volume: 41 Issue: 1, 22 - 37, 22.03.2020

İrfan Deli , Emel Kırmızı Öztürk

https://doi.org/10.17776/csj.574518
Cited By: 5

Abstract

References

  • [1] Zadeh L.A., Fuzzy Sets. Information and Control, 8 (1965) 338-353.
  • [2] Atanassov K., Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20 (1996) 87-96.
  • [3] Smarandache F., A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic. Rehoboth: American Research Press, (1998) 1-158.
  • [4] Wang H., Smarandache Zhang F.Q. and Sunderraman R., Single valued neutrosophic sets. Multispace and Multistructure 4 (2010) 410-413.
  • [5] Deli I., Broumi S., Smarandache F., Neutrosophic refined sets and their applications in medical diagnosis. Journal of New Theory, 6 (2014) 88-98.
  • [6] Hajek P. and Olej V., Defuzzification Methods in Intuitionistic Fuzzy Inference Systems of Takagi-Sugeno Type, 11th International Conference on Fuzzy Systems and Knowledge Discovery, China, Ağustos 2014.
  • [7] Li D. F., Decision and Game Theory in Management with Intuitionistic Fuzzy Sets, Studies in Fuzziness and Soft Computing Volume 308 Springer, 2014.
  • [8] Xu Z.. Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 15(6) (2007), 1179-1187.
  • [9] Zhang, Z., Trapezoidal interval type-2 fuzzy aggregation operators and their application to multiple attribute group decision making. Neural Comput. and Applic. 29 (2018) 1039-1054.
  • [10] Enginoğlu S. and Demiriz S, A Comparison With The Convergent, Cesàro Convergent and Riesz Convergent Sequences of Fuzzy Numbers, Conference: Fuzzyss'15 4th International Fuzzy Systems Symposium, İstanbul, 2015.
  • [11] Rao P.P.B. and Shankar N.R., Ranking Fuzzy Numbers with a Distance Method using Circum center of Centroids and an Index of Modality, Advances in Fuzzy Systems 2011 (2011) http://dx.doi.org/10.1155/2011/178308 .
  • [12] Wang Y.M., Yang J.B., Xu D.L., Chin K. S., On the centroids of fuzzy numbers. Fuzzy Sets and Systems 157 (2006) 919 – 926.
  • [13] Wang Y.M., Centroid defuzzification and the maximizing set and minimizing set ranking based on alpha level sets, Computers and Industrial Engineering 57(1) (2009), 228-236.
  • [14] Nayagam V.L.G., Jeevaraj S., Sivaraman G., Complete Ranking of Intuitionistic Fuzzy Numbers. Fuzzy Inf. Eng., 8 (2016) 237-254.
  • [15] Prakash K.A., Suresh M., Vengataasalam S., A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept, Mathematical Sciences, 10(4) (2016), 177–184.
  • [16] Rezvani S., Ranking method of trapezoidal intuitionistic fuzzy numbers. Annals of Fuzzy Mathematics and Informatics 5 (2013) 515-523.
  • [17] Roseline S., Amirtharaj H., Methods to Find the Solution for the Intuitionistic Fuzzy Assignment Problem with Ranking of Intuitionistic Fuzzy Numbers. International Journal of Innovative Research in Science, Engineering and Technology 4 (2015) 10008-10014.
  • [18] Velu L.G.N., Selvaraj J., Ponnialagan D., A New Ranking Principle for Ordering Trapezoidal Intuitionistic Fuzzy Numbers. Complexity, (2017) https://doi.org/10.1155/2017/3049041.
  • [19] Varghese A., Kuriakose S., Centroid of an intuitionistic fuzzy number. Notes on Intuitionistic Fuzzy Sets., 18 (2012) 19–24.
  • [20] Biswas P., Pramanik S. and Giri B.C., Value and ambiguity index based ranking method of single-valued trapezoidal neutrosophic numbers and its application to multi-attribute decision making, Neutrosophic Sets and Systems, 12 (2016) 127-138.
  • [21] Broumi S., Talea M., Bakali A., Smarandache F. and Vladareanu L., Computation of Shortest Path Problem in a Network with SV-Trapezoidal Neutrosophic Numbers, Proceedings of the 2016 International Conference on Advanced Mechatronic Systems, Melbourne, Australia, November 30 - December 3.
  • [22] Deli I., Şubaşı Y., A ranking method of single valued neutrosophic numbers and its applications to multi attribute decision making problems. International Journal of Machine Learning and Cybernetics, 8(4) (2017), 1309–1322.
  • [23] Deli I., Şubaşı Y., Some weighted geometric operators with SVTrN-numbers and their application to multi-criteria decision-making problems. Journal of Intelligent and Fuzzy Systems, 32(1) (2017), 291-301.
  • [24] Liu P., Chu Y., Li Y., Chen Y., Some Generalized Neutrosophic Number Hamacher Aggregation Operators and Their Application to Group Decision Making. International Journal of Fuzzy Systems 16 (2014) 242-255
  • [25] Öztürk E.K., Some New Approaches on Single Valued Trapezoidal neutrosophic Numbers and Their Applications to Multiple Criteria Decision Making Problems. (In Turkish) (Master’s Thesis, Kilis 7 Aralık University, Graduate School of Natural and Applied Science 2018.
  • [26] Şubaş Y., Neutrosophic numbers and their application to Multi-attribute decision making problems. (In Turkish) (Master’s Thesis, Kilis 7 Aralık University, Graduate School of Natural and Applied Science 2015.
  • [27] Ye J., Some weighted aggregation operators of trapezoidal neutrosophic numbers and their multiple attribute decision making method. Informatica 28 (2017) 387-402.
  • [28] Basset M.A., Mohamed M. and Sangaiah A.K., Neutrosophic AHP-Delphi Group decision making model based on trapezoidal neutrosophic numbers, J. Ambient. Intell. Human. Comput., 9(5) (2018), 1427–1443.
  • [29] Biswas P., Pramanik S. and Giri B.C., Aggregation of triangular fuzzy neutrosophic set information and its application to multi-attribute decision making. Neutrosophic Sets and Systems, 12 (2016) 20-38.
  • [30] Broumi S., Talea M., Bakali A., Smarandache F. and Vladareanu L., Shortest Path Problem Under Triangular Fuzzy Neutrosophic Information, 10th International Conference on Software, (2016) Knowledge, Information Management and Applications (SKIMA).
  • [31] Liu P. and Zhang X.H., Some Maclaurin Symmetric Mean Operators for Single-Valued Trapezoidal Neutrosophic Numbers and Their Applications to Group Decision Making. Int. J. Fuzzy Syst., 20(1) (2018), 45–61.
  • [32] Liang R.X., Wang J.Q. and Li L., Multi-criteria group decision-making method based on interdependent inputs of single-valued trapezoidal neutrosophic information. Neural Comput. and Applic., 30(1) (2017), 241–260.
  • [33] Liang R. X., Wang J.Q. and Zhang H.Y., A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information, Neural Comput. and Applic., 30(11) (2017), 3383–3398.

A defuzzification method on single-valued trapezoidal neutrosophic numbers and multiple attribute decision making

Year 2020, Volume: 41 Issue: 1, 22 - 37, 22.03.2020

İrfan Deli , Emel Kırmızı Öztürk

https://doi.org/10.17776/csj.574518
Cited By: 5

Abstract

In this paper, we give multiple attribute decision-making (MADM) method where both the attribute value and attribute weight of alternatives are single-valued trapezoidal neutrosophic numbers (SVTN-numbers). In spite of existing ranking methods, no one can rank SVTN-numbers with human intuition consistently in all cases. Therefore, we introduce a novel defuzzification method for ranking SVTN-numbers. To do this, some basic definitions and operations on the concepts of fuzzy set, fuzzy number, intuitionistic fuzzy set, intuitionistic fuzzy number, single-valued neutrosophic set, SVTN-number are presented. Then, concepts of I. score function and II. score function to reduce the SVTN-numbers to fuzzy numbers are defined. Finally, multiple criteria decision-making (MCDM) method for multiple criteria decision-making problems by using the concept of I. score function and II. score function of SVTN-numbers and defuzzification of fuzzy numbers are developed. Also, we have used a numerical example to verify the feasibility and the superiority of the proposed method compared to the existing methods.

Keywords

Neutrosophic set single valued trapezoidal neutrosophic number score function defuzzification multiple attribute decision-making.

References

  • [1] Zadeh L.A., Fuzzy Sets. Information and Control, 8 (1965) 338-353.
  • [2] Atanassov K., Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20 (1996) 87-96.
  • [3] Smarandache F., A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic. Rehoboth: American Research Press, (1998) 1-158.
  • [4] Wang H., Smarandache Zhang F.Q. and Sunderraman R., Single valued neutrosophic sets. Multispace and Multistructure 4 (2010) 410-413.
  • [5] Deli I., Broumi S., Smarandache F., Neutrosophic refined sets and their applications in medical diagnosis. Journal of New Theory, 6 (2014) 88-98.
  • [6] Hajek P. and Olej V., Defuzzification Methods in Intuitionistic Fuzzy Inference Systems of Takagi-Sugeno Type, 11th International Conference on Fuzzy Systems and Knowledge Discovery, China, Ağustos 2014.
  • [7] Li D. F., Decision and Game Theory in Management with Intuitionistic Fuzzy Sets, Studies in Fuzziness and Soft Computing Volume 308 Springer, 2014.
  • [8] Xu Z.. Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 15(6) (2007), 1179-1187.
  • [9] Zhang, Z., Trapezoidal interval type-2 fuzzy aggregation operators and their application to multiple attribute group decision making. Neural Comput. and Applic. 29 (2018) 1039-1054.
  • [10] Enginoğlu S. and Demiriz S, A Comparison With The Convergent, Cesàro Convergent and Riesz Convergent Sequences of Fuzzy Numbers, Conference: Fuzzyss'15 4th International Fuzzy Systems Symposium, İstanbul, 2015.
  • [11] Rao P.P.B. and Shankar N.R., Ranking Fuzzy Numbers with a Distance Method using Circum center of Centroids and an Index of Modality, Advances in Fuzzy Systems 2011 (2011) http://dx.doi.org/10.1155/2011/178308 .
  • [12] Wang Y.M., Yang J.B., Xu D.L., Chin K. S., On the centroids of fuzzy numbers. Fuzzy Sets and Systems 157 (2006) 919 – 926.
  • [13] Wang Y.M., Centroid defuzzification and the maximizing set and minimizing set ranking based on alpha level sets, Computers and Industrial Engineering 57(1) (2009), 228-236.
  • [14] Nayagam V.L.G., Jeevaraj S., Sivaraman G., Complete Ranking of Intuitionistic Fuzzy Numbers. Fuzzy Inf. Eng., 8 (2016) 237-254.
  • [15] Prakash K.A., Suresh M., Vengataasalam S., A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept, Mathematical Sciences, 10(4) (2016), 177–184.
  • [16] Rezvani S., Ranking method of trapezoidal intuitionistic fuzzy numbers. Annals of Fuzzy Mathematics and Informatics 5 (2013) 515-523.
  • [17] Roseline S., Amirtharaj H., Methods to Find the Solution for the Intuitionistic Fuzzy Assignment Problem with Ranking of Intuitionistic Fuzzy Numbers. International Journal of Innovative Research in Science, Engineering and Technology 4 (2015) 10008-10014.
  • [18] Velu L.G.N., Selvaraj J., Ponnialagan D., A New Ranking Principle for Ordering Trapezoidal Intuitionistic Fuzzy Numbers. Complexity, (2017) https://doi.org/10.1155/2017/3049041.
  • [19] Varghese A., Kuriakose S., Centroid of an intuitionistic fuzzy number. Notes on Intuitionistic Fuzzy Sets., 18 (2012) 19–24.
  • [20] Biswas P., Pramanik S. and Giri B.C., Value and ambiguity index based ranking method of single-valued trapezoidal neutrosophic numbers and its application to multi-attribute decision making, Neutrosophic Sets and Systems, 12 (2016) 127-138.
  • [21] Broumi S., Talea M., Bakali A., Smarandache F. and Vladareanu L., Computation of Shortest Path Problem in a Network with SV-Trapezoidal Neutrosophic Numbers, Proceedings of the 2016 International Conference on Advanced Mechatronic Systems, Melbourne, Australia, November 30 - December 3.
  • [22] Deli I., Şubaşı Y., A ranking method of single valued neutrosophic numbers and its applications to multi attribute decision making problems. International Journal of Machine Learning and Cybernetics, 8(4) (2017), 1309–1322.
  • [23] Deli I., Şubaşı Y., Some weighted geometric operators with SVTrN-numbers and their application to multi-criteria decision-making problems. Journal of Intelligent and Fuzzy Systems, 32(1) (2017), 291-301.
  • [24] Liu P., Chu Y., Li Y., Chen Y., Some Generalized Neutrosophic Number Hamacher Aggregation Operators and Their Application to Group Decision Making. International Journal of Fuzzy Systems 16 (2014) 242-255
  • [25] Öztürk E.K., Some New Approaches on Single Valued Trapezoidal neutrosophic Numbers and Their Applications to Multiple Criteria Decision Making Problems. (In Turkish) (Master’s Thesis, Kilis 7 Aralık University, Graduate School of Natural and Applied Science 2018.
  • [26] Şubaş Y., Neutrosophic numbers and their application to Multi-attribute decision making problems. (In Turkish) (Master’s Thesis, Kilis 7 Aralık University, Graduate School of Natural and Applied Science 2015.
  • [27] Ye J., Some weighted aggregation operators of trapezoidal neutrosophic numbers and their multiple attribute decision making method. Informatica 28 (2017) 387-402.
  • [28] Basset M.A., Mohamed M. and Sangaiah A.K., Neutrosophic AHP-Delphi Group decision making model based on trapezoidal neutrosophic numbers, J. Ambient. Intell. Human. Comput., 9(5) (2018), 1427–1443.
  • [29] Biswas P., Pramanik S. and Giri B.C., Aggregation of triangular fuzzy neutrosophic set information and its application to multi-attribute decision making. Neutrosophic Sets and Systems, 12 (2016) 20-38.
  • [30] Broumi S., Talea M., Bakali A., Smarandache F. and Vladareanu L., Shortest Path Problem Under Triangular Fuzzy Neutrosophic Information, 10th International Conference on Software, (2016) Knowledge, Information Management and Applications (SKIMA).
  • [31] Liu P. and Zhang X.H., Some Maclaurin Symmetric Mean Operators for Single-Valued Trapezoidal Neutrosophic Numbers and Their Applications to Group Decision Making. Int. J. Fuzzy Syst., 20(1) (2018), 45–61.
  • [32] Liang R.X., Wang J.Q. and Li L., Multi-criteria group decision-making method based on interdependent inputs of single-valued trapezoidal neutrosophic information. Neural Comput. and Applic., 30(1) (2017), 241–260.
  • [33] Liang R. X., Wang J.Q. and Zhang H.Y., A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information, Neural Comput. and Applic., 30(11) (2017), 3383–3398.
There are 33 citations in total.

Details

Primary Language Turkish
Journal Section Natural Sciences
Authors

İrfan Deli 0000-0003-1875-1067

Emel Kırmızı Öztürk 0000-0003-1875-1067

Publication Date March 22, 2020
Submission Date June 10, 2019
Acceptance Date January 31, 2020
Published in Issue Year 2020Volume: 41 Issue: 1

Cite

APA Deli, İ., & Kırmızı Öztürk, E. (2020). A defuzzification method on single-valued trapezoidal neutrosophic numbers and multiple attribute decision making. Cumhuriyet Science Journal, 41(1), 22-37. https://doi.org/10.17776/csj.574518

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