본문 바로가기
KERD
논문KCI 등재

New aggregation operators of intuitionistic trapezoidal fuzzy multi-numbers based on Archimedean norms

Irfan Deli|Humeyra Karadol
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2024.02|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제27권 제1호|pp. 81-102|DOI 10.30948/afmi.2024.27.1.81

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Fuzzy numberFuzzy setsIntuitionistic trapezoidal fuzzy multi numbersArchimedean T-norm and T-conormMultiple criteria decision making

초록

In trapezoidal intuitionistic fuzzy multi numbers, an aggregation operator performs the task of aggregate the described information to generate a ranking of alternatives which are two critical tasks: a flexible and superior tool for the first task and an effective tool for the second task is aggregation operator. Therefore, in the study, we give new aggregation operators, based on Archimedean T-norm and T-conorm operations which is called Archimedean norms operator for aggregating trapezoidal intuitionistic fuzzy multi-information. Then, we develop a multi criteria decision making method based on the given operators. Finally, the feasibility and effectiveness of the method is demonstrated via a numerical example.

Abstract

In trapezoidal intuitionistic fuzzy multi numbers, an aggregation operator performs the task of aggregate the described information to generate a ranking of alternatives which are two critical tasks: a flexible and superior tool for the first task and an effective tool for the second task is aggregation operator. Therefore, in the study, we give new aggregation operators, based on Archimedean T-norm and T-conorm operations which is called Archimedean norms operator for aggregating trapezoidal intuitionistic fuzzy multi-information. Then, we develop a multi criteria decision making method based on the given operators. Finally, the feasibility and effectiveness of the method is demonstrated via a numerical example.

참고문헌 (55)

  1. L. A. Zadeh, "Fuzzy sets", Information and control, 8(3), pp.338~353 (1965)
  2. K. T. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20(1), pp.87~96 (1986)
  3. A. Ban, "Approximations of fuzzy numbers by trapezoidal fuzzy numbers preserving the ambiguity and value", Computers Mathematics with Applications, 61(5), pp.1379~1401 (2011)
  4. C. H. Cheng, "A new approach for ranking fuzzy numbers by distance method", Fuzzy sets and systems, 95(3), pp.307~317 (1998)
  5. Y. M. Wang, "On the centroids of fuzzy numbers", Fuzzy sets and systems, 157(7), pp.919~926 (2006)
  6. S. H. Wei, "A new similarity measure between generalized fuzzy numbers", SCIS ISIS SCIS ISIS 2006, Japan Society for Fuzzy Theory and Intelligent Informatics, pp.315~320 (2006)
  7. D. F. Li, "A difference-index based ranking method of trapezoidal intuitionistic fuzzy numbers and application to multiattribute decision making", Mathematical and Computational Applications, 20(1), pp.25~38 (2015)
  8. M. Xia, "Generalized intuitionistic fuzzy Bonferroni means", International Journal of Intelligent Systems, 27, pp.23~47 (2012)
  9. W. Wang, "Distance measure between intuitionistic fuzzy sets", Pattern recognition letters, 26(13), pp.2063~2069 (2005)
  10. X. Luo, "Exponential operational laws and new aggregation operators of intuitionistic fuzzy information based on Archimedean T-conorm and T-norm", International Journal of Machine Learning and Cybernetics, 9, pp.1261~1269 (2018)
  11. E. Szmidt, "Distances between intuitionistic fuzzy sets: straightforward approaches may not work", 2006 3rd International IEEE Conference Intelligent Systems, pp.716~721 (2006), IEEE
  12. J. H. Park, "Distance measure between intuitionistic fuzzy sets and its application to pattern recognition", Journal of The Korean Institute of Intelligent Systems, 19(4), pp.556~561 (2009)
  13. Z. Liang, "Similarity measures on intuitionistic fuzzy sets", Pattern recognition letters, 24(15), pp.2687~2693 (2003)
  14. G. A. R. G. Harish, "An improved cosine similarity measure for intuitionistic fuzzy sets and their applications to decision-making process", Hacettepe Journal of Mathematics and Statistics, 47(6), pp.1578~1594 (2018)
  15. Q. Lei, "Intuitionistic fuzzy integrals based on Archimedean t-conorms and t-norms", Inform. Sci, 327, pp.57~70 (2016)
  16. M. Xia, "Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm", Knowledge-Based Systems, 31, pp.78~88 (2012)
  17. L. Baccour, "Similarity measures for intuitionistic fuzzy sets: State of the art", Journal of Intelligent Fuzzy Systems, 24(1), pp.37~49 (2013)
  18. H. Garg, "Generalized geometric aggregation operators based on t-norm operations for complex intuitionistic fuzzy sets and their application to decision-making", Cognitive Computation, 12(3), pp.679~698 (2020)
  19. P. Grzegorzewski, "Distances between intuitionistic fuzzy sets and", or interval-valued fuzzy sets based on the Hausdorff metric, 2004, pp.148(2), 319~328
  20. J. Mo, "Archimedean geometric Heronian mean aggregation operators based on dual hesitant fuzzy set and their application to multiple attribute decision making", Soft Computing, 24, pp.14721~14733 (2020)
  21. R. T. Ngan, "H-max distance measure of intuitionistic fuzzy sets in decision making", Applied Soft Computing, 69, pp.393~425 (2018)
  22. Z. Pei, "A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets", Expert Systems with Applications, 39(3), pp.2560~2566 (2012)
  23. E. Szmidt, "Distances between intuitionistic fuzzy sets", Fuzzy sets and systems, 114(3), pp.505~518 (2000)
  24. C. Tan, "Atanassov’s intuitionistic fuzzy Quasi-Choquet geometric operators and their applications to multicriteria decision making", Fuzzy Optimization and Decision Making, 14, pp.139~172 (2015)
  25. S. P. Wan, "Power average of trapezoidal intuitionistic fuzzy numbers using strict t-norms and t-conorms", IEEE Transactions on Fuzzy Systems, 24(5), pp.1035~1047 (2015)
  26. M. Xia, "Interval-valued intuitionistic fuzzy matrix games based on Archimedean t-conorm and t-norm", International Journal of General Systems, 47(3), pp.278~293 (2018)
  27. Z. S. Xu, "An overview of distance and similarity measures of intuitionistic fuzzy sets", International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16(04), pp.529~555 (2008)
  28. D. Yu, "Group decision making based on generalized intuitionistic fuzzy prioritized geometric operator", International Journal of Intelligent Systems, 27(7), pp.635~661 (2012)
  29. Y. Song, "A new similarity measure between intuitionistic fuzzy sets and its application to pattern recognition", Abstract and Applied Analysis, 2014, pp.1~11 (2014)
  30. B. Yusoff, "A new similarity measure on intuitionistic fuzzy sets", International Journal of Mathematical and Computational Sciences, 5(6), pp.819~823 (2011)
  31. V. Ulu¸cay, "Trapezoidal fuzzy multi-number and its application to multicriteria decision-making problems", Neural Computing and Applications, 30(5), pp.1469~1478 (2018)
  32. I. Deli, "Distance measures on trapezoidal fuzzy multi-numbers and application to multi-criteria decision-making problems", Soft Computing, 25(8), pp.5979~5992 (2021)
  33. I. Deli, "Neutrosophic Algebraic Structures and Their Applications", pp.221~237 (2022), NSIA Publishing House, Neutrosphic Science International Association (NSIA), University of New Mexico, Gallup
  34. M. S¸ahin, "Dice vector similarity measure based on multi-criteria decision making with trapezoidal fuzzy multi-Numbers", International Conference on Mathematics and Mathematics Education (ICMME-2017), pp.11~13 (2017), Harran University
  35. M. S¸ahin, "Improved hybrid vector similarity measures and their applications on trapezoidal fuzzy multi numbers", Neutrosophic Triplet Structures, 1, pp.158~184 (2019)
  36. D. Kesen, "Decision Making Operators of Trapezoidal Fuzzy Multi Numbers and Their Application to Decision Making Problems", Master, pp.2022
  37. D. Kesen, "Data-Driven Modelling with Fuzzy Sets and their Applications to Knowledge Management", pp.2023, CRC Press
  38. V. Ulu¸cay, "Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems", Complex Intelligent Systems, 5(1), pp.65~78 (2019)
  39. H. Karad¨ol, "Some new concepts on intuitionistic trapezoidal fuzzy Multi-numbers and application to multi-criteria decision-making Problems", Master, pp.2023
  40. S. Sebastian, "Multi-Fuzzy Sets", International Mathematical Forum, 5(50), pp.2471~2476 (2010)
  41. G. Klir, "Fuzzy sets and fuzzy logic: theory and applications" (1995), Prentice Hall
  42. E. P. Klement, "Logical, algebraic, analytic, and probabilistic aspects of triangular norms" (2005), Elsevier
  43. G. Beliakov, "Aggregation functions: a guide for practitioners" (2007), Springer
  44. W. Z. Wang, "Intuitionistic fuzzy geometric aggregation operators based on Einstein operations", Int. J. Intell. Syst, 26, pp.1049~1075 (2011)
  45. D. Zhang, "Geometric score function of Pythagorean fuzzy numbers determined by the reliable information region and its application to group decision-making", Engineering Applications of Artificial Intelligence, 121, pp.1~15 (2023)
  46. X. Zhang, "Multicriteria Pythagorean fuzzy decision analysis: A hierarchical QUALIFLEX approach with the closeness index-based ranking methods", Inform. Sci, 330, pp.104~124 (2016)
  47. X. D. Peng, "Approaches to Pythagorean fuzzy stochastic multi-criteria decision making based on prospect theory and regret theory with new distance measure and score function", International Journal of intelligent system, 32(1), pp.1187~1214 (2017)
  48. D. Q. Li, "Distance measure of Pythagorean fuzzy sets", International Journal of intelligent systems, 33(2), pp.348~361 (2018)
  49. R. R. Yager, "Pythagorean membership grades, complex numbers and decision making", International Journal of Intelligent Systems, 28, pp.436~452 (2013)
  50. R. R. Yager, "Pythagorean membership grades in multicriteria decision making", IEEE Transactions on Fuzzy Systems, 22(4), pp.958~965 (2014)
  51. X. D. Peng, "Algorithm for Pythagorean fuzzy multi-criteria decision making based on WDBA with new score function", Fundamenta Informaticae, 165(2), pp.99~137 (2019)
  52. G. Beliakov, "On averaging operators for Atanassov’s intuitionistic fuzzy sets", Inform. Sci, 181, pp.1116~1124 (2011)
  53. Z. Xu, "Some geometric aggregation operators based on intuitionistic fuzzy sets", Int. J. General Syst, 35, pp.417~433 (2006)
  54. J. Wu, "Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers", Applied Mathematical Modelling, 37(1-2), pp.318~327 (2013)
  55. M. Xia, "Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm", Knowledge-Based Systems, 31, pp.78~88 (2012)

관련 논문AI추천

Multiple attribute group decision making based on intuitionistic fuzzy neutral geometric operators induced by interaction coefficientsWei Yang, Xin Mei Wang, Zi Wen Jiang기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2017 · 제14권 제5호Power aggregation operators on trapezoidal fuzzy multi-numbers and their applications to a zero-waste problemDavut Kesen, Nuh Okumus기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2024 · 제27권 제2호Generalized hesitant fuzzy geometric aggregation operators and their applications in multicriteria decision makingJie Yang기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2017 · 제13권 제1호Dual hesitant fuzzy aggregation operators based on Bonferroni means and their applications to multiple attribute decision makingChunyong Wang, Huonian Tu, Shengda Tao, Xiaoqiang Zhou기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2017 · 제14권 제3호Aggregation operators of cubic picture fuzzy quantities and their application in decision support systemsSaleem Abdullah, Shahzaib Ashraf, Tahir Mahmood강원경기수학회 · 한국수학논문집2020 · 제28권 제2호An approach for decision making using intuitionistic trapezoidal fuzzy soft setMohuya B. Kar, Samarjit Kar, Sujit Das, Tandra Pal기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2018 · 제16권 제1호

이 간행물의 다른 논문 (4건)

$\Gamma$-$KU$-algebrasS. H. Han, Fatema. F. Kareem, J. I. Baek, Samy M. Mostafa, K.Hurpp. 1-27Prime ideals and maximal ideals on commutative $L$-algebrasXiao Fei Yang, Xiao Long Xin, Huan Yun, Ling Ling Maopp. 29-51Ideals in unital cycloids based on fuzzy pointsYoung Bae Junpp. 53-65α-b-regularity in a fuzzy topological spaceAnjana Bhattacharyyapp. 67-80
원문 보기