Generalized Interval-Valued Neutrosophic Set and Its Application
Anjan Mukherjee
1
(
Department of Mathematics, Tripura University Agartala, Agartala, India, Pin-977022.
)
Rakhal Das
2
(
Department of Mathematics, The ICFAI University Tripura, Agartala, India, Pin-977210.
)
کلید واژه: Neutrosophic Set, Neutrosophic Topology, Interval-Valued Neutrosophic set, Generalized Neutrosophic set, Generalized Interval-Valued Neutrosophic Set, Generalized Interval-Valued Neutrosophic Topological Space.,
چکیده مقاله :
In this work, we introduce the idea of generalized interval-valued neutrosophic sets. After providing the fundamental definitions of operations related to these sets, we establish several key properties and explore the relationships between generalized interval-valued neutrosophic sets and other related concepts. Finally, we extend the notion of generalized neutrosophic topological spaces to incorporate generalized interval-valued neutrosophic topological spaces. We define the concept of generalized interval-valued neutrosophic g-continuous function between two generalized interval-valued neutrosophic topological spaces. Lastly, an application has been shown in decision making problem.
چکیده انگلیسی :
In this work, we introduce the idea of generalized interval-valued neutrosophic sets. After providing the fundamental definitions of operations related to these sets, we establish several key properties and explore the relationships between generalized interval-valued neutrosophic sets and other related concepts. Finally, we extend the notion of generalized neutrosophic topological spaces to incorporate generalized interval-valued neutrosophic topological spaces. We define the concept of generalized interval-valued neutrosophic g-continuous function between two generalized interval-valued neutrosophic topological spaces. Lastly, an application has been shown in decision making problem.
[1] Zadeh LA. Fuzzy sets. Information and Control. 1965; 8(3): 338-353.
[2] Atanassov K. Intuitionistic fuzzy sets. International journal bioautomation. 2016; 20(1): 1-6.
[3] Smarandache F. Neutrosophy and neutrosophic logic. In First international conference on neutrosophy, neutrosophic logic, set, probability, and statistics university of New Mexico, Gallup, NM. 2002; 87301: 338-353.
[4] Smarandache, F. A unifying field in Logics: Neutrosophic Logic. In Philosophy. American Research Press. 1999; 1: 1-141.
[5] Salama AA, Alblowi SA. Neutrosophic set and Netrosophic topological spaces. IOSR Journal of Mathematics (IOSR-JM). 2012; 3(4): 31-35.
[6] Saha A, Broumi S. New operators on interval valued Neutrosophic sets. Neutrosophic Sets and Systems. 2019; 28: 128-137. DOI: https://doi.org/10.5281/zenodo.3382525
[7] Salama AA, Alblowi SA. Generalized Neutrosophic set and generalized Neutrosophic topological spaces. Computer Science and Engineering. 2012; 2(7): 129-132. DOI: https://doi.org/10.5923/j.computer.20120207.01
[8] Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 1986; 20(1): 87-96. DOI: https://doi.org/10.1016/S0165-0114(86)80034-3
[9] Atanassov K. Two variants of intuitionistic fuzzy propositional calculus. IM-MFAIS-5-88, sofia.1988; 4: 9-12.
[10] Chang CL. Fuzzy topological spaces. Journal of Mathematical Analysis and Applications. 1968; 24(1): 182-190. DOI: https://doi.org/10.1016/0022-247X(68)90057-7
[11] Coker D. An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems. 1997; 88(1): 81-89. DOI: https://doi.org/10.1016/S0165-0114(96)00076-0
[12] Das R, Tripathy BC. Neutrosophic multiset topological space. Neutrosophic Sets and Systems. 2020; 35(1): 142-152. DOI: https://doi.org/10.5281/zenodo.3951651
[13] Das S, Das R, Granados C. Topology on quadripartitioned neutrosophic sets. Neutrosophic Sets and Systems. 2021; 45: 54-61. DOI: https://doi.org/10.5281/zenodo.5485442
[14] Mukherjee A, Das R. Neutrosophic bipolar vague soft set and its application to decision making problems. Neutrosophic Sets and Systems. 2020; 32: 409-424. DOI: https://doi.org/10.5281/zenodo.3723198
[15] Pramanik S, Das S, Das R, Tripathy BC. Neutrosophic BWM-TOPSIS strategy under SVNS environment. Neutrosophic Sets and Systems. 2023; 56: 178-189. DOI: https://doi.org/10.5281/zenodo.8194759
[16] Saadati R, Park JH. On the intuitionistic fuzzy topological spaces. Chaos, Solitons & Fractals. 2006; 27(2): 331-344. DOI: https://doi.org/10.1016/j.chaos.2005.03.019
