Abstract
Bulanık küme teorisi, araştırmacıların ölçüm hatası, belirsizlik ve insan düşüncelerinden kaynaklanan belirsizlikleri tespit etmelerini sağlar. Bulanık küme teorisi birçok araştırmacı tarafından pek çok farklı türe genişletilmiştir. Sezgisel bulanık kümeler, bu türlerden biridir. Sezgisel bulanık kümelerde iki fonksiyon vardır. Bunlar üyelik fonksiyonu ve üye olmama fonksiyonlarıdır. Sezgisel bulanık sayıların sıralanması birçok gerçek yaşam probleminin modellenmesinde temel bir rol oynamaktadır. Literatürde, sezgisel bulanık sayıları sıralamak için çeşitli yöntemler pek çok araştırmacı tarafından önerilmiştir. Üçgenin iç teğet çemberinin kenarlara değme noktalarını karşı köşe noktalarıyla birleştiren doğru parçalarının kesişim noktası, Gergonne noktasıdır. Bu çalışmada, üçgen sezgisel bulanık sayıyı sıralamak için Gergonne noktasına dayanan yeni bir yöntem önerilmiştir. Önerilen yöntemi diğer yöntemlerle karşılaştırmak için farklı üçgen sezgisel bulanık sayılar kullanılarak bir çalışma yapılmıştır. Elde edilen sonuçlar yorumlanmıştır.
Keywords
Sezgisel bulanık kümeler Gergonne noktası bulanık sayıyı sıralamak üçgen sezgisel bulanık sayılar
References
- Zadeh L. A.(1965), Fuzzy Sets, Information and Control,8(3), 338 - 353.
- Grzegorzewski P.(1993), Distances and orderings in a family of intuitionistic fuzzy numbers, Proceedings of the 3rd Conference of the European Society for Fuzzy Logic and Technology, 10- 12.
- Mithcell H.B.(2004), Ranking – Intuitionistic Fuzzy numbers, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,12,377-386.
- Nayagam V. L.D, Venkateshwari G. and Sivaraman G.(2008), Ranking of Intuitionistic Fuzzy Numbers, Proceeding of International Conference on Fuzzy Systems(Fuzz – IEEE), 1971-1974.
- Chen S.J. and Hwang C.L.(1992), Fuzzy Multiple Attribute Decision Making, Springer Verlag: New York
- Whang J. and Zhang Z.(2009), Aggregation operators on intuitionistic trapezoidal fuzzy numbers and its application to multi-criteria decision making problems, Journals of System Engineering and Electronics, 20(2),321-326.
- Li D.F. (2010a), A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems, Computers and Mathematics with Applications, 60,1557-1570.
- Li D.F., Nan J. X. and Zhang M. J (2010b), A Ranking Method of Triangular Intuitionistic Fuzzy Numbers and Application to Decision Making, International Journal of Computational Intelligence Systems, 3(5), 522-530.
- Nehi H. M.(2010), A New Ranking Method for Intuitionistic Fuzzy Numbers, International Journal of Fuzzy Systems, 12(1),80-86.
- Wei C-P. and Tang X.(2010), Possibility Degree Method for Ranking Intuitionistic Fuzzy Numbers, Proceedings of International Conference on Web Intelligence and Intelligent Agent Technology,142-145.
- Nayagam V. L.D, Venkateshwari G. and Sivaraman G.(2011), Modified ranking of intuitionistic fuzzy numbers, Notes on Intuitionistic Fuzzy Sets, 17(2);5-22.
- Salahsour S., Shekari G. A. and Hakimzadeh A. (2012), A novel approach for ranking triangular intuitionistic fuzzy numbers, AWER Procedia Information Technology and Computer Science, 1, 442-446.
- Seikh M.R, Nayak P.K. and Pal M.(2012), Generalized Triangular Fuzzy Numbers in Intuitionistic Fuzzy Environment, International Journal of Engineering Research and Development, 5(1), 8-13.
- Nagoorgani A. and Ponnalagu K.(2012), A New Approach on Solving Intuitionistic Fuzzy Linear Programming Problem, Applied Mathematical Sciences, 6(70),3467-3474.
- Das S. and Guha D.(2013), Ranking of Intuitionistic Fuzzy Number by Centroid Point, Journal of Industrial and Information, 1(2),107-110.Kumar A. and Kaur M.(2013), A Ranking Approach for Intuitionistic Fuzzy Numbers and Its Application, Journal of Applied Research and Technology,11(3), 381-396.
- Rezvani S.(2013), Ranking method of trapezoidal intuitionistic fuzzy numbers, Annals of Fuzzy Mathematics and Informatics,5(3),515-523.
- Roseline S.S. and Amirtharaj E.C.H.(2013), A New Method for Ranking of Intuitionistic Fuzzy Numbers, Indian Journal of Applied Research, 3(6),1-2.
- Peng Z. and Chen Q.(2013), A New Method for Ranking Canonical Intuitionistic Fuzzy Numbers, Proceedings of the International Conference on Information and Engineering and Applications (IEA) 2012, 1, 609-618.
- Zang M.J. and Nan J. X. (2013), A compromise ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems, Iranian Journal of Fuzzy Systems, 10- 21-37.
- Seikh M. R., Nayak P. K. and Pal M. (2013), Notes on triangular intuitionistic fuzzy numbers, International Journal of Mathematics in Operational Research, 5(4), 446-465.
- Prakash K.A., Suresh M. and Vengataasalam S. (2016), A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept, Mathematical Sciences,10(4), 177-184.
- Bharati S. K.(2017), Ranking Method of Intuitionistic Fuzzy Numbers, Global Journal of Pure and Applied Mathematics,13(9),4595-4608.
- Garg H. (2017), A Robust Ranking Method for Intuitionistic Multiplicative Set Under Crisp, Interval Enviroments and Its Applications, IEEE Transactions on Emerging Topics on Computational Intelligence, 1(5),366-374.
- Nayagam L.G., Selveraj J. and Ponnialagan D.(2017) A New Ranking Principle for Ordering Trapezoidal Intuitionistic Fuzzy Numbers, Complexity,1-24.
- Tao Z., Liu X., Chen H. and Zhou L.(2017), Ranking Internal – Valued Fuzzy Numbers with Intuitionistic Fuzzy Possibility Degree and Its Application to Fuzzy Multi – Attribute Decision Making, International Journal of Fuzzy Systems, 19(3),646-658.
- Uthra G. Thangavelu K. and Shunmugapriya S.(2017), Ranking Generalized Intutionistic Pentagonal Fuzzy Number by Centroidal Approach, International Journal of Mathematics and its Applications, 5(4),589-593.
- Garg H. and Kumar K.(2018), Improved possibility degree method for ranking intuitionistic fuzzy numbers and their application in multiattribute decision – making, Granular Computing, 4(2),237-247.
- Hao Y. and Chen X.(2018), Study on the ranking problems in multiple attribute decision making based on interval - valued intuitionistic fuzzy numbers, International Journal of Intelligent Systems,33(3),560-572.
- Uthra G. Thangavelu K. and Shunmugapriya S.(2018), Ranking Generalized Intuitionistic Fuzzy Numbers, International Journal of Mathematics Trends and Technology,56(7),530-538.
- Xing Z., Xiong W. and Liu H.(2018), A Euclidian Approach for Ranking Intuitionistic Fuzzy Values, IEEE Transactions on Fuzzy Systems, 26(1),353-365.
- Atanassov K. T. (1986), Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, (20)1, 1-87.
- Nehi H.M. and Maleki H.R.(2005), Intuitionistic Fuzzy Numbers and It’s Applications in Fuzzy Optimization Problem, Proceeding of the 9th WSEAS Internatipnal Conference on Sysyems,1-5.
- Kahraman C., Cevik Onar S., Cebi S. and Oztaysi B.(2017), Extension of information axiom from ordinary to intuitionistic fuzzy sets: an application to search algorithm selection, Computers and Industrial Engineering, 105, 348-361.
- Akyar H. and Akyar E.(2016), Üşgenin Gergonne Noktası yardımıyla üçgensel fuzzy sayıları sıralama yöntemi, Anadolu Universitesi Bilim ve Teknoloji Dergisi – B Teorik Bilimler, 4(1),29-38.
Abstract
Fuzzy sets theory allows researchers to identify the uncertainties that arise from measurement error, vagueness and human thoughts. Fuzzy sets theory has been extended into various
different types by many researchers. Intuitionistic fuzzy sets are one of these types. There are two functions in intuitionistic fuzzy sets. These are membership function and non - membership
function. The ranking of intuitionistic fuzzy numbers plays the main role in modeling many real life problems. Several methods for ranking intuitionistic fuzzy numbers have been well
discussed in the literature. In a triangle, the lines from the vertices to the points of contact of the opposite sides of the inscribed circle meet at a point. That point is the Gergonne point. In this paper, a new method based on the Gergonne point is proposed to rank triangular intuitionistic fuzzy numbers. An illustrative example and comparison study is performed with the existing methods by using different triangular intuitionistic fuzzy numbers. The results are interpreted as a conclusion.
Keywords
Intuitionistic fuzzy sets Gergonne point ranking fuzzy number triangular intuitionistic fuzzy numbers
References
- Zadeh L. A.(1965), Fuzzy Sets, Information and Control,8(3), 338 - 353.
- Grzegorzewski P.(1993), Distances and orderings in a family of intuitionistic fuzzy numbers, Proceedings of the 3rd Conference of the European Society for Fuzzy Logic and Technology, 10- 12.
- Mithcell H.B.(2004), Ranking – Intuitionistic Fuzzy numbers, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,12,377-386.
- Nayagam V. L.D, Venkateshwari G. and Sivaraman G.(2008), Ranking of Intuitionistic Fuzzy Numbers, Proceeding of International Conference on Fuzzy Systems(Fuzz – IEEE), 1971-1974.
- Chen S.J. and Hwang C.L.(1992), Fuzzy Multiple Attribute Decision Making, Springer Verlag: New York
- Whang J. and Zhang Z.(2009), Aggregation operators on intuitionistic trapezoidal fuzzy numbers and its application to multi-criteria decision making problems, Journals of System Engineering and Electronics, 20(2),321-326.
- Li D.F. (2010a), A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems, Computers and Mathematics with Applications, 60,1557-1570.
- Li D.F., Nan J. X. and Zhang M. J (2010b), A Ranking Method of Triangular Intuitionistic Fuzzy Numbers and Application to Decision Making, International Journal of Computational Intelligence Systems, 3(5), 522-530.
- Nehi H. M.(2010), A New Ranking Method for Intuitionistic Fuzzy Numbers, International Journal of Fuzzy Systems, 12(1),80-86.
- Wei C-P. and Tang X.(2010), Possibility Degree Method for Ranking Intuitionistic Fuzzy Numbers, Proceedings of International Conference on Web Intelligence and Intelligent Agent Technology,142-145.
- Nayagam V. L.D, Venkateshwari G. and Sivaraman G.(2011), Modified ranking of intuitionistic fuzzy numbers, Notes on Intuitionistic Fuzzy Sets, 17(2);5-22.
- Salahsour S., Shekari G. A. and Hakimzadeh A. (2012), A novel approach for ranking triangular intuitionistic fuzzy numbers, AWER Procedia Information Technology and Computer Science, 1, 442-446.
- Seikh M.R, Nayak P.K. and Pal M.(2012), Generalized Triangular Fuzzy Numbers in Intuitionistic Fuzzy Environment, International Journal of Engineering Research and Development, 5(1), 8-13.
- Nagoorgani A. and Ponnalagu K.(2012), A New Approach on Solving Intuitionistic Fuzzy Linear Programming Problem, Applied Mathematical Sciences, 6(70),3467-3474.
- Das S. and Guha D.(2013), Ranking of Intuitionistic Fuzzy Number by Centroid Point, Journal of Industrial and Information, 1(2),107-110.Kumar A. and Kaur M.(2013), A Ranking Approach for Intuitionistic Fuzzy Numbers and Its Application, Journal of Applied Research and Technology,11(3), 381-396.
- Rezvani S.(2013), Ranking method of trapezoidal intuitionistic fuzzy numbers, Annals of Fuzzy Mathematics and Informatics,5(3),515-523.
- Roseline S.S. and Amirtharaj E.C.H.(2013), A New Method for Ranking of Intuitionistic Fuzzy Numbers, Indian Journal of Applied Research, 3(6),1-2.
- Peng Z. and Chen Q.(2013), A New Method for Ranking Canonical Intuitionistic Fuzzy Numbers, Proceedings of the International Conference on Information and Engineering and Applications (IEA) 2012, 1, 609-618.
- Zang M.J. and Nan J. X. (2013), A compromise ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems, Iranian Journal of Fuzzy Systems, 10- 21-37.
- Seikh M. R., Nayak P. K. and Pal M. (2013), Notes on triangular intuitionistic fuzzy numbers, International Journal of Mathematics in Operational Research, 5(4), 446-465.
- Prakash K.A., Suresh M. and Vengataasalam S. (2016), A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept, Mathematical Sciences,10(4), 177-184.
- Bharati S. K.(2017), Ranking Method of Intuitionistic Fuzzy Numbers, Global Journal of Pure and Applied Mathematics,13(9),4595-4608.
- Garg H. (2017), A Robust Ranking Method for Intuitionistic Multiplicative Set Under Crisp, Interval Enviroments and Its Applications, IEEE Transactions on Emerging Topics on Computational Intelligence, 1(5),366-374.
- Nayagam L.G., Selveraj J. and Ponnialagan D.(2017) A New Ranking Principle for Ordering Trapezoidal Intuitionistic Fuzzy Numbers, Complexity,1-24.
- Tao Z., Liu X., Chen H. and Zhou L.(2017), Ranking Internal – Valued Fuzzy Numbers with Intuitionistic Fuzzy Possibility Degree and Its Application to Fuzzy Multi – Attribute Decision Making, International Journal of Fuzzy Systems, 19(3),646-658.
- Uthra G. Thangavelu K. and Shunmugapriya S.(2017), Ranking Generalized Intutionistic Pentagonal Fuzzy Number by Centroidal Approach, International Journal of Mathematics and its Applications, 5(4),589-593.
- Garg H. and Kumar K.(2018), Improved possibility degree method for ranking intuitionistic fuzzy numbers and their application in multiattribute decision – making, Granular Computing, 4(2),237-247.
- Hao Y. and Chen X.(2018), Study on the ranking problems in multiple attribute decision making based on interval - valued intuitionistic fuzzy numbers, International Journal of Intelligent Systems,33(3),560-572.
- Uthra G. Thangavelu K. and Shunmugapriya S.(2018), Ranking Generalized Intuitionistic Fuzzy Numbers, International Journal of Mathematics Trends and Technology,56(7),530-538.
- Xing Z., Xiong W. and Liu H.(2018), A Euclidian Approach for Ranking Intuitionistic Fuzzy Values, IEEE Transactions on Fuzzy Systems, 26(1),353-365.
- Atanassov K. T. (1986), Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, (20)1, 1-87.
- Nehi H.M. and Maleki H.R.(2005), Intuitionistic Fuzzy Numbers and It’s Applications in Fuzzy Optimization Problem, Proceeding of the 9th WSEAS Internatipnal Conference on Sysyems,1-5.
- Kahraman C., Cevik Onar S., Cebi S. and Oztaysi B.(2017), Extension of information axiom from ordinary to intuitionistic fuzzy sets: an application to search algorithm selection, Computers and Industrial Engineering, 105, 348-361.
- Akyar H. and Akyar E.(2016), Üşgenin Gergonne Noktası yardımıyla üçgensel fuzzy sayıları sıralama yöntemi, Anadolu Universitesi Bilim ve Teknoloji Dergisi – B Teorik Bilimler, 4(1),29-38.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Articles |
| Authors | |
| Publication Date | June 30, 2019 |
| Published in Issue | Year 2019 Volume: 1 Issue: 1 |
