Cut topology generated by generalized triangular fuzzy numbers
Sigma Journal of Engineering and Natural Sciences 2025, Vol. 43, Issue 1, pp. 213-221; doi.org/10.14744/sigma.2025.00016
Abstract
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 analyzed with examples
Keywords: Cut Topology; Fuzzy Set; Generalized Triangular Fuzzy Number
References
- Zadeh LA. Fuzzy sets. Inform Control 1965;8:338353. and [CrossRef]
- Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets Syst 1986;20:8796. [CrossRef]
- Zadeh LA. Fuzzy logic. IEEE Comput 1988;21:8393. [CrossRef]
- Chang SSL, Zadeh LA. On fuzzy mapping and con- trol. IEEE Trans Syst Man Cybern 1972;2:3034. [CrossRef] By Theorem 3.30 and 𝛾 = 2𝛼/3, 𝑓−1(2𝛼/3𝐵̃0.4) = 𝛼𝐴̃0.6 [5] Buckley JJ. Eslami, E. An Introduction to Fuzzy for each 𝛼 ∈ [0,0.6]. Since 𝑓−1(𝛾𝐵̃0.4) ∈ 𝑇(𝛽𝐴̃0.6) for Logic and Fuzzy Sets. New York: Physica-Verlag each 𝛾𝐵̃0.4 ∈ 𝑇(𝛽𝐵̃0.4), 𝑓−1 is a continuous function. Hence, Heidelberg; 2002. [CrossRef] the function 𝑓 is homeomorphism from 𝐴 to 𝐵 and [6] Chen CT. Extensions of the TOPSIS for group deci- (𝐴, 𝑇(𝛽𝐴̃0.6)) ≅ (𝐵, 𝑇(𝛽𝐵̃0.4)). sion-making under fuzzy environment. Fuzzy Sets Syst 2000;114:19. [CrossRef]
- Zhang DA. Natural topology for fuzzy numbers. J [18] Sutherland WA. Introduction to Metric and Math Anal Appl 2001;264:344353. [CrossRef] Topological Spaces. Oxford: Clarendon Press; 1975.
- Font JJ, Miralles, A, Sanchis M. On the fuzzy num- [19] Munkers JR. Topology. 2nd ed. Upper Saddle River, ber space with the level convergence topology. J NJ; Prentice Hall; 2000. Funct Spaces Appl 2012;2012;326417. [CrossRef] [20] Chen S. Ranking fuzzy numbers with maximizing set
- Padmapriya R, Thangavelu P. Topologies gener- and minimizing set. Fuzzy Sets Syst 1985;17:113129. ated by the cuts of a fuzzy set. Int J Math Arch [CrossRef] 2014;5:156165.
- Padmapriya R, Thangavelu P. Topologies generated by the fuzzy numbers. Int J Eng Trends Technol ranking generalized fuzzy numbers with differ- 2017;43:243246. ent heights and different spreads. Expert Sys Appl
- Yanardağ Y. Cut topology generated by generalized 2009;36:68336842. [CrossRef] triangular fuzzy numbers. [In Turkish]. Master’s [22] Dutta P, Dash SR. Medical decision making via the Thesis. Kilis: Kilis 7 Aralık University, Graduate arithmetic of generalized triangular fuzzy numbers. School of Natural and Applied Science; 2020. Open Cybern Syst J 2018;12:119. [CrossRef]
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YANARDAĞ, Y.; KULE, M. Cut topology generated by generalized triangular fuzzy numbers. Sigma Journal of Engineering and Natural Sciences 2025, Vol. 43, pp. 213-221. https://doi.org/10.14744/sigma.2025.00016
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