Araştırma Makalesi
Yıl 2025,
Cilt: 43 Sayı: 1, 213 - 221, 28.02.2025
Öz
Kaynakça
- References
- Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets Syst 1986;20:8796. Buckley JJ. Eslami, E. An Introduction to Fuzzy Logic and Fuzzy Sets. New York: Physica-Verlag Heidelberg; 2002.
- Chang CL. Fuzzy topological spaces. J Math Anal Appl 1968;24:182190.
- Chang SSL, Zadeh LA. On fuzzy mapping and control. IEEE Trans Syst Man Cybern 1972;2:3034.
- Chen S. Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets Syst 1985;17:113129.
- Chen CT. Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst 2000;114:19.
- Chen SM, Chen JH. Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Sys Appl 2009;36:68336842.
- Chen SH, Hsieh CH. Representation, ranking, distance, and similarity of L-R type fuzzy number and application. Aust J Intell Process Syst 2000;6:217229.
- Dutta P, Dash SR. Medical decision making via the arithmetic of generalized triangular fuzzy numbers. Open Cybern Syst J 2018;12:119.
- Font JJ, Miralles, A, Sanchis M. On the fuzzy number space with the level convergence topology. J Funct Spaces Appl 2012;2012;326417.
- Klir GJ, Yuan B. Fuzzy Set and Fuzzy Logic: Theory and Applications. New Jersey: Upper Saddle River, Prentice Hall Publishers; 1995.
- Lowen. R. Fuzzy topological spaces and fuzzy compactness. J Math Anal Appl 1979;56:621633.
- Manes EG, Dubois D, Prade H. Review: Didier Dubois and Henri Prade, Fuzzy sets and systems: Theory and applications. Bullet Am Math Soc 1982;7:603612.
- Munkers JR. Topology. 2nd ed. Upper Saddle River, NJ; Prentice Hall; 2000.
- Onasanya BO, Hoshoka-Mayerova S. Some Topological and algebraic properties of alpha level subsets’ topology of a fuzzy subset. An Sti Univ Ovid Co-Mat 2018;26:213227.
- Padmapriya R, Thangavelu P. Topologies generated by the α cuts of a fuzzy set. Int J Math Arch 2014;5:156165.
- Padmapriya R, Thangavelu P. Topologies generated by the fuzzy numbers. Int J Eng Trends Technol 2017;43:243246.
- Sutherland WA. Introduction to Metric and Topological Spaces. Oxford: Clarendon Press; 1975.
- Yanardağ Y. Cut topology generated by generalized triangular fuzzy numbers. [In Turkish]. Master’s Thesis. Kilis: Kilis 7 Aralık University, Graduate School of Natural and Applied Science; 2020.
- Zadeh LA. Fuzzy sets. Inform Control 1965;8:338353.
- Zadeh LA. Fuzzy logic. IEEE Comput 1988;21:8393.
- Zhang DA. Natural topology for fuzzy numbers. J Math Anal Appl 2001;264:344353.
Yıl 2025,
Cilt: 43 Sayı: 1, 213 - 221, 28.02.2025
Öz
In this study, we propose a new topology called the cut topology. We first develop a synthetic base by using the 𝛼 cut family of the generalized triangular fuzzy number. Then, we generate the cut topology by the synthetic base and give subspace cut topology on a subset of any set. Moreover, the fundamental concepts such as interior, closure, and limit points of a set in the cut topology are discussed. Finally, neighborhood, continuity, and homeomorphism are ana-lyzed with examples.
Anahtar Kelimeler
Kaynakça
- References
- Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets Syst 1986;20:8796. Buckley JJ. Eslami, E. An Introduction to Fuzzy Logic and Fuzzy Sets. New York: Physica-Verlag Heidelberg; 2002.
- Chang CL. Fuzzy topological spaces. J Math Anal Appl 1968;24:182190.
- Chang SSL, Zadeh LA. On fuzzy mapping and control. IEEE Trans Syst Man Cybern 1972;2:3034.
- Chen S. Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets Syst 1985;17:113129.
- Chen CT. Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst 2000;114:19.
- Chen SM, Chen JH. Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Sys Appl 2009;36:68336842.
- Chen SH, Hsieh CH. Representation, ranking, distance, and similarity of L-R type fuzzy number and application. Aust J Intell Process Syst 2000;6:217229.
- Dutta P, Dash SR. Medical decision making via the arithmetic of generalized triangular fuzzy numbers. Open Cybern Syst J 2018;12:119.
- Font JJ, Miralles, A, Sanchis M. On the fuzzy number space with the level convergence topology. J Funct Spaces Appl 2012;2012;326417.
- Klir GJ, Yuan B. Fuzzy Set and Fuzzy Logic: Theory and Applications. New Jersey: Upper Saddle River, Prentice Hall Publishers; 1995.
- Lowen. R. Fuzzy topological spaces and fuzzy compactness. J Math Anal Appl 1979;56:621633.
- Manes EG, Dubois D, Prade H. Review: Didier Dubois and Henri Prade, Fuzzy sets and systems: Theory and applications. Bullet Am Math Soc 1982;7:603612.
- Munkers JR. Topology. 2nd ed. Upper Saddle River, NJ; Prentice Hall; 2000.
- Onasanya BO, Hoshoka-Mayerova S. Some Topological and algebraic properties of alpha level subsets’ topology of a fuzzy subset. An Sti Univ Ovid Co-Mat 2018;26:213227.
- Padmapriya R, Thangavelu P. Topologies generated by the α cuts of a fuzzy set. Int J Math Arch 2014;5:156165.
- Padmapriya R, Thangavelu P. Topologies generated by the fuzzy numbers. Int J Eng Trends Technol 2017;43:243246.
- Sutherland WA. Introduction to Metric and Topological Spaces. Oxford: Clarendon Press; 1975.
- Yanardağ Y. Cut topology generated by generalized triangular fuzzy numbers. [In Turkish]. Master’s Thesis. Kilis: Kilis 7 Aralık University, Graduate School of Natural and Applied Science; 2020.
- Zadeh LA. Fuzzy sets. Inform Control 1965;8:338353.
- Zadeh LA. Fuzzy logic. IEEE Comput 1988;21:8393.
- Zhang DA. Natural topology for fuzzy numbers. J Math Anal Appl 2001;264:344353.
Toplam 22 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Klinik Tıp Bilimleri (Diğer) |
| Bölüm | Research Articles |
| Yazarlar | |
| Yayımlanma Tarihi | 28 Şubat 2025 |
| Gönderilme Tarihi | 5 Ekim 2023 |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 43 Sayı: 1 |
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