Çok Kriterli Karar Verme Üzerine Dayalı Yamuksal Bulanık Çoklu Sayıların Yeni Bir Benzerlik Fonksiyonu

Öz

Bu çalışmanın temel amacı, çok kriterli karar vermeye dayalı yamuksal bulanık çoklu sayıları üzerinde yeni bir yöntem sunmaktır. Bu nedenle, yamuksal bulanık çoklu sayıların geliştirilmesi için yamuksal bulanık çoklu sayılar üzerine yeni bir benzerlik fonksiyonu, ağırlıklı yeni bir benzerlik fonksiyonu tanımlanmış ve bu benzerlik fonksiyonlarının temel özellikleri incelenmiştir. Buna ek olarak, sunulan yöntemin pratikliğini ve doğruluğunu teyit etmek için metot sayısal bir örneğe uygulanmaktadır.

Anahtar Kelimeler

• Bulanık küme,Yamuksal bulanık çoklu sayılar,Benzerlik fonksiyonu,Çok kriterli karar verme

A New Similarity Function of Trapezoidal Fuzzy Multi-Numbers Based On Multi-Criteria Decision Making

Öz

The main aim of this study is to introduce a novel method based on multi-criteria decision making trapezoidal fuzzy multi-number. Therefore, in order to develop trapezoidal fuzzy multi-numbers, a new similarity function and weighted new similarity function on trapezoidal fuzzy multi-numbers have been defined and the basic properties of these similarity functions have been examined. In addition, the method is applied to a numerical example in order to confirm the practicality and accuracy of the submitted method.

Anahtar Kelimeler

• Fuzzy set,Trapezoidal Fuzzy Multi-Numbers,Similarity function

Kaynakça

1. Alim A, Johora F T, Babu S, Sultana A, 2015. Elementary operations on LR fuzzy number. Adv Pure Math 5(03):131
2. Bakbak D, Uluçay V, Şahin M, 2019a. Neutrosophic soft expert multiset and their application to multiple criteria decision making. Mathematics, 7(1), 50.
3. Bakbak D, Uluçay V, 2019a. Chapter Eight Multiple Criteria Decision Making in Architecture Based on Q-Neutrosophic Soft Expert Multiset. NEUTROSOPHIC TRIPLET STRUCTURES, 90.
4. Bakbak D, Uluçay V, 2019b. Multicriteria Decision-Making Method Using the Cosine Vector Similarity Measure Under Intuitionistic Trapezoidal Fuzzy Multi-Numbers in Architecture. 6th International Multidisciplinary Studies Congress (Multicongress’19) Gaziantep, Türkiye.
5. Bakbak D, Uluçay V, and Şahin, M, 2019b. Intuitionistic Trapezoidal Fuzzy Multi-Numbers and Some Arithmetic Averaging Operators with Their Application in Architecture. 6th International Multidisciplinary Studies Congress (Multicongress’19) Gaziantep, Türkiye.
6. Ban AI, Coroianu L, 2015.Existence, uniqueness, calculus and properties of triangular approximations of fuzzy numbers under a general condition. Int. J ApproxReason 62:1–26
7. Chandra S, Aggarwal A, 2015. On solving matrix games with pay-offs of triangular fuzzy numbers: certain observations and generalizations. Eur. J.Oper. Res. 246(2):575–581
8. Chakraborty D, Guha D, 2010. Addition two generalized fuzzy numbers. Int. J Ind. Math 2(1):9–20

9. Hassan N, Uluçay V, Şahin M, 2018. Q-neutrosophic soft expert set and its application in decision making. International Journal of Fuzzy System Applications (IJFSA), 7(4), 37-61.
10. Kaufmann A, Gupta MM, 1988. Fuzzy mathematical models in engineering and management science. Elsevier Science Publishers ,Amsterdam
11. Miyamoto S, 2001. Fuzzy multi-sets and their generalizations. Multi-set processing, Lecture notes in computer science, vol 2235.Springer,Berlin, pp 225–235
12. Miyamoto S, 2004. Data structure and operations for fuzzy multi-sets. Transactions on rough sets II, Lecture notes in computer science, vol 3135. Springer, Berlin, pp 189–200
13. Maturo A, 2009. On some structures of fuzzy numbers. Iran J Fuzzy Syst 6(4):49–59
14. Meng Y, Zhou Q, Jiao J, Zheng J, Gao D, 2015. The ordered weighted geometric averaging algorithm to multiple attribute decision making with in triangular fuzzy numbers based on the mean area measurement method1. Appl. Math Sci., 9(43):2147–2151
15. Wang YJ, 2015. Ranking triangle and trapezoidal fuzzy numbers based on the relative preference relation. Appl. Math model, 39(2):586–599
16. Rouhparvar H, Panahi A, 2015. A new definition for defuzzification of Generalized fuzzy numbers and its application. Appl Soft Comput., 30:577–584
17. Rezvani S., 2015. Ranking generalized exponential trapezoidal fuzzy numbers based on variance. Appl Math Comput., 262:191–198
18. Riera JV, Massanet S, Herrera-Viedma , Torrens J, 2015. Some interesting properties of The fuzzy linguistic model based on discrete fuzzy number stoma age hesitant fuzzy linguistic information. Appl. Soft Comput., 36:383–391
19. Riera JV, Torrens J, 2015. Using discrete fuzzy numbers in the aggregation of İn complete qualitative information. Fuzzy Sets Syst. 264:121–137
20. Roseline S, Amirtharaj S, 2015. Improved ranking of generalized trapezoidal fuzzy numbers. Int. J Innov. Res Sci. Eng. Techno l4:6106–6113
21. Roseline S, Amirtharaj S, 2014. Generalized fuzzy hungarian method for eneralized trapezoidal fuzzy transportation problem with ranking of Generalized fuzzy numbers. Int. J Appl. Math Stat. Sci. (IJAMSS) 1(3):5–12
22. Ruan J, Shi P, Lim CC, Wang X, 2015. Relief supplies allocation and optimization by interval and fuzzy number approaches. Inf.Sci.,303:15–32.
23. Surapati P, Biswas P , 2012. Multi-objective assignment Problem with generalized trapezoidal fuzzy numbers. Int J Appl Inf Syst 2(6):13–20
24. Sebastian S, Ramakrishnan TV, 2010. Multi-fuzzy sets. Int Math Forum 5(50):2471–2476
25. Syropoulos A, 2012. On generalized fuzzy multisets and their use in computation. Iranian Journal of Fuzzy Systems Vol. 9, No. 2, pp. 113-125.
26. Syropoulos A, 2010. On non-symmetric multi-fuzzy sets. Crit. Rev IV:35–41
27. Saeidifar A, 2015. Possibilistic characteristic functions. Fuzzy Inf. Eng. 7(1):61–72
28. Sinova B, Casals MR, Gil M A, Lubiano MA , 2015. The fuzzy characterizing function of The distribution of a random fuzzy number. Appl. Math Model 39(14):4044–4056
29. Stupnanova A, 2015. A probabilistic approach to the arithmetics of fuzzy numbers. Fuzzy Sets Syst 264:64–75
30. Şahin M, Uluçay V, Acıoglu H, 2018. Some weighted arithmetic operators and geometric operators with SVNSs and their application to multi-criteria decision making problems. Infinite Study.
31. Şahin M, Alkhazaleh S, Ulucay V, 2015. Neutrosophic soft expert sets. Applied Mathematics, 6(1), 116.
32. Thowhida A, Ahmad SU, 2009. A computational method for fuzzy arithmetic operations. Daffodil Int. Univ. J SciTechnol.,4(1):18–22
33. Uluçay V, Deli I, Şahin M, 2018a. Trapezoidal fuzzy multi-number and its application to multi-criteria decision-making problems. Neural Computing and Applications, 1-10.
34. Uluçay V, Deli I, Şahin M, 2018b. Similarity measures of bipolar neutrosophic sets and their application to multiple criteria decision making. Neural Computing and Applications, 29(3), 739-748.
35. Ulucay V, Sahin M, Olgun N, 2018c. Time-neutrosophic soft expert sets and its decision making problem. Matematika, Volume 34, Number 2, 245–260.
36. Uluçay V, Şahin M, Hassan N, 2018d. Generalized neutrosophic soft expert set for multiple-criteria decision-making. Symmetry, 10(10), 437.
37. Ulucay V, Kılıç A, Şahin M, Deniz H, 2019a. A New Hybrid Distance-Based Similarity Measure for Refined Neutrosophic sets and its Application in Medical Diagnosis. MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics, 35(1), 83-94.
38. Uluçay V, Deli I, Şahin M, 2019b. Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems. Complex & Intelligent Systems, 5(1), 65-78.
39. Wei SH, Chen SM, 2009. A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. Expert Syst. Appl. 36, 589-598.
40. Ye J, 2012a, Multi criteria decision-making method using the Dice similarity measure based on the reduce intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets, Applied Mathematical Modelling, 36, 4466–4472.
41. Ye J, 2012b. Multi-criteria group decision-making method using vector similarity measures for trapezoidal intuitionistic fuzzy numbers, Group Decision and Negotiation, 21, 519–530.
42. Yager RR, 1986. On the theory of bags. Int J Gen Syst. 13:23–37
43. Zadeh LA, 1965 Fuzzy sets. Inf Control 8:338–353
44. Zimmermann HJ, 1993. Fuzzy set theory and its applications. Kluwer Academic Publishers, Berlin.