Bulanık Esnek Maks-Min Karar Verme Metodunun Bir Genelleştirmesi ve Gürültü Kaldırmada Performans Temelli Değer Atamaya Uygulaması

Öz

Son zamanlarda, FSMmDM ile gösterilen ve [Çağman, N., Enginoǧlu, S., Fuzzy soft matrix theory and its application in decision making, Iranian Journal of Fuzzy Systems, 2012, 9(1), 109-119] çalışmasında verilen bulanık esnek maks-min karar verme metodu, Enginoğlu ve Memiş [A configuration of some soft decision-making algorithms via -matrices, Cumhuriyet Science Journal, 2018, 39(4), 871-881] tarafından bulanık parametreli bulanık esnek matrisler ( -matrisler) yoluyla orijinaline sadık kalacak biçimde yapılandırıldı. CE12 ile gösterilen ve ve-çarpım/veya-çarpım (CE12a/CE12o) yoluyla inşa edilen bu yapılandırılmış metot karar vermede kullanışlı olmasına rağmen, yüksek sayıda veri işlenirken zaman ve karmaşıklık bakımından daha cazip hale getirilmesi gerekmektedir. Bu çalışmada, FSMmDM’nin genelleştirmeleri olan ve EMC19a ve EMC19o ile gösterilen iki algoritma öneriyoruz. Ayrıca, EMC19a’nın -matrislerin ilk satırlarındaki bileşenlerin 0 ya da 1 olduğunda CE12a’yı özel bir durum olarak kabul ettiğini gösteriyoruz. Ardından, bu algoritmaların çalışma sürelerini karşılaştırıyoruz. Sonuçlar herhangi bir veri sayısında EMC19a ve EMC19o’nun sırasıyla CE12a ve CE12o’dan daha iyi bir performans sergilediğini göstermektedir. Daha sonra, EMC19o’yu gürültü kaldırmada bir karar verme problemine uyguluyoruz. Son olarak, sonraki çalışmalar hakkında bir tartışmaya yer veriyoruz.

Anahtar Kelimeler

• Bulanık kümeler

A Generalization of Fuzzy Soft Max-Min Decision-Making Method and Its Application to a Performance-Based Value Assignment in Image Denoising

Öz

Latterly, the fuzzy soft max-min decision-making method denoted by FSMmDM and provided in [Çağman, N., Enginoǧlu, S., Fuzzy soft matrix theory and its application in decision making, Iranian Journal of Fuzzy Systems, 2012, 9(1), 109-119] has been configured via fuzzy parameterized fuzzy soft matrices (fpfs-matrices) by Enginoğlu and Memiş [A configuration of some soft decision-making algorithms via fpfs-matrices, Cumhuriyet Science Journal, 2018, 39(4), 871-881], faithfully to the original. Although this configured method denoted by CE12 and constructed by and-product/or-product (CE12a/CE12o) is useful in decision-making, the method should be made more attractive in terms of time and complexity in the event that a large amount of data is processed. In this paper, we propose two algorithms EMC19a and EMC19o that accept CE12a and CE12o as a special case, respectively, in the event that the first rows of the fpfs-matrices are binary. That is, EMC19a and EMC19o are new generalized forms of FSMmDM. Afterwards, we compare the running times of these algorithms. The results show that EMC19a and EMC19o outperform CE12a and CE12o, respectively, in any number of data. We then apply EMC19o to a decision-making problem in image denoising. Finally, we discuss the need for further research

Anahtar Kelimeler

• Fuzzy sets,soft sets

Kaynakça

1. Molodtsov, D., Soft set theory-first results, Computers and Mathematics with Applications, 1999, 37(4-5), 19-31.
2. Tunçay, M., Sezgin, A., Soft union ring and its applications to ring theory, International Journal of Computer Applications, 2016, 151(9), 7-13.
3. Ullah, A., Karaaslan, F., Ahmad, I., Soft uni-Abel-Grassmann’s groups, European Journal of Pure and Applied Mathematics, 2018, 11(2), 517-536.
4. Maji, P. K., Biswas, R., Roy, A. R., Soft set theory, Computer and Mathematics with Applications, 2003, 45, 555-562.
5. Çağman, N., Enginoğlu, S., Çıtak, F., Fuzzy soft set theory and its applications, Iranian Journal of Fuzzy Systems, 2011, 8(3), 137-147.
6. Çıtak, F., Çağman, N., Soft k-int-ideals of semirings and its algebraic structures, Annals of Fuzzy Mathematics and Informatics, 2017, 13(4), 531-538.
7. Atmaca, S., Zorlutuna, İ., On topological structures of fuzzy parametrized soft sets, The Scientific World Journal, 2014, Article ID 164176, 8 pages.
8. Enginoğlu, S., Çağman, N., Karataş, S., Aydın, T., On soft topology, El-Cezerî Journal of Science and Engineering, 2015, 2(3), 23-38.

9. Maji, P. K., Roy, A. R., Biswas, R., An application of soft sets in a decision making problem, Computer and Mathematics with Applications, 2002, 44, 1077-1083.
10. Çıtak, F., Çağman, N., Soft int-rings and its algebraic applications, Journal of Intelligent and Fuzzy Systems, 2015, 28, 1225-1233.
11. Çağman, N., Enginoǧlu, S., Fuzzy soft matrix theory and its application in decision making, Iranian Journal of Fuzzy Systems, 2012, 9(1), 109-119.
12. Muştuoğlu, E., Sezgin, A., Türk, Z. K., Some characterizations on soft uni-groups and normal soft uni-groups, International Journal of Computer Applications, 2016, 155(10), 1-8.
13. Sezgin, A., A new approach to semigroup theory I: Soft union semigroups, ideals and bi-ideals, Algebra Letters, 2016, 2016(3), 1-46.
14. Çağman, N., Çıtak, F., Enginoğlu, S., Fuzzy parameterized fuzzy soft set theory and its applications, Turkish Journal of Fuzzy Systems, 2010, 1(1), 21-35.
15. Çaǧman, N., Enginoǧlu, S., Soft matrix theory and its decision making, Computer and Mathematics with Applications, 2010, 59, 3308-3314.
16. Bera, S., Roy, S. K., Karaaslan, F., Çağman, N., Soft congruence relation over lattice, Hacettepe Journal of Mathematics and Statistics, 2017, 46(6), 1035-1042.
17. Maji, P. K., Biswas, R., Roy, A. R., Fuzzy soft sets, The Journal of Fuzzy Mathematics, 2001, 9(3), 589-602.
18. Atmaca, S., Relationship between fuzzy soft topological spaces and (X,τ_e) parameter spaces, Cumhuriyet Science Journal, 2017, 38(4), Supplement, 813-821.
19. Karaaslan, F., Soft classes and soft rough classes with applications in decision making, Mathematical Problems in Engineering, 2016, 2016, 1-11.
20. Sezgin, A., Çağman, N., Çıtak, F., α-Inclusions applied to group theory via soft set and logic, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 2019, 68(1), 334-352.
21. Enginoǧlu, S., Soft matrices, Doctoral Dissertation, Gaziosmanpaşa University, Tokat, Turkey 2012.
22. Çağman, N., Enginoğlu, S., Soft set theory and uni-int decision making, European Journal of Operational Research, 2010, 207(2), 848-855.
23. Çağman, N., Çıtak, F., Enginoğlu, S., FP-soft set theory and its applications, Annals of Fuzzy Mathematics and Informatics, 2011, 2(2), 219-226.
24. Zorlutuna, İ., Atmaca, S., Fuzzy parametrized fuzzy soft topology, New Trends in Mathematical Sciences, 2016, 4(1), 142-152.
25. Enginoğlu, S., Memiş, S. A configuration of some soft decision-making algorithms via fpfs-matrices, Cumhuriyet Science Journal, 2018, 39(4), 871-881.
26. Enginoglu, S., Memiş, S., Comment on “Fuzzy soft sets” [The Journal of Fuzzy Mathematics, 9(3), 2001, 589–602], International Journal of Latest Engineering Research and Applications, 2018, 3(9), 1-9.
27. Enginoglu, S., Memiş, S., Öngel, T., Comment on soft set theory and uni-int decision making [European Journal of Operational Research, (2010) 207, 848-855], Journal of New Results in Science, 2018, 7(3), 28-43.
28. Enginoglu, S., Memiş, S., Arslan, B., Comment (2) on soft set theory and uni-int decision making [European Journal of Operational Research, (2010) 207, 848-855], Journal of New Theory, 2018, 25, 85-102.
29. Enginoğlu, S., Memiş, S., A Review on an application of fuzzy soft set in multicriteria decision making problem [P.K. Das, R. Borgohain, International Journal of Computer Applications 38 (12) (2012) 33-37]. In: Akgül, M., Yılmaz, İ., İpek, A. (eds.) Proceeding of International Conference on Mathematical Studies and Applications 2018, pp. 173-178, Karaman, Turkey (2018).
30. Enginoğlu, S., Memiş, S., A review on some soft decision-making methods. In: Akgül, M., Yılmaz, İ., İpek, A. (eds.) Proceeding of International Conference on Mathematical Studies and Applications 2018, pp. 437-442, Karaman, Turkey (2018).
31. Enginoğlu, S., Çağman, N., Fuzzy parameterized fuzzy soft matrices and their application in decision-making, TWMS Journal of Applied and Engineering Mathematics, In Press.
32. Erkan, U., Gökrem, L., Enginoğlu, S., Different applied median filter in salt and pepper noise, Computers and Electrical Engineering, 2018, 70, 789-798.