Finite Dimensional Convex Fuzzy Normed Space and Its Basic Properties

Authors

  • Hawraa Yousif Daher Branch of Mathematics and Computer Applications, Department of Applied Sciences, University of Technology, Baghdad, Iraq.
  • Jehad R. Kider Branch of Mathematics and Computer Applications, Department of Applied Sciences, University of Technology, Baghdad, Iraq. https://orcid.org/0000-0002-3173-5654

DOI:

https://doi.org/10.21123/bsj.2024.10530

Keywords:

Convex Fuzzy Absolute Value Space, Convex Fuzzy Complete Space, Convex Fuzzy Compact Space, Convex Fuzzy Equivalent Norms, Convex Fuzzy Normed Space

Abstract

Here the notion of convex fuzzy absolute value space is represented with an example which shows that the existence of such space. The reason behind introducing the definition of convex fuzzy absolute value and does not using the ordinary absolute value is the main definition in this paper will be not correct with ordinary absolute value. After that the main definition of convex fuzzy normed space is recalled with example which shows that the existence of such space. Then other definitions and theorems is recalled that will be used later in the section of main results such as the convex fuzzy norm is convex fuzzy continuous function. So our goal in the section of results and discussion is to prove some properties of finite dimensional convex fuzzy normed space which not true ingeneral for convex fuzzy normed space. Thus the last section contains the following results with proofs if  is a subspace of the convex fuzzy normed space  with dim  then  is convex fuzzy complete subspace of . Moreover when  is a convex fuzzy bounded as well as convex fuzzy closed subspace of the c-FNS,  also dim   then  is convex fuzzy compact. As well as if dim  for a linear space   then there is a unique convex fuzzy norm on . Finally if ={: the convex fuzzy norm of  belongs to I } a convex fuzzy closed subset of  as well as convex fuzzy compact this implies that dim where   is convex fuzzy normed space.

References

Bag T, Samanta SK. A comparative study of fuzzy norms on a linear space. Fuzzy Sets Syst. 2008; 159: 670–684. https://doi.org/10.1016/j.fss.2007.09.011

Sadeqi IF, Kia S. Fuzzy normed linear space and its topological structure. Chaos Soli. Fract. 2009; 40(5): 2576-2589. https://doi.org/10.1016/j.chaos.2007.10.051

Golet I. On generalized fuzzy normed spaces and coincidence theorems. Fuzzy Sets Syst. 2010; 161: 1138-1144. https://doi.org/10.1016/j.fss.2009.10.004

Janfada M, Baghani H, Baghani O. On Felbin’s-type fuzzy normed linear spaces and fuzzy bounded operators. Iran J Fuzzy Syst. 2011; 8: 117–130.

Na ̃da ̃ban S, Dzitac S, Dziyac I. Fuzzy normed linear spaces. Book. Fuzzy Logic and Fuzzy Sets. 2020; 391: 153-174.

Dzitac S, Oros H, Deac D, Na ̃da ̃ban S. Fixed Point Theory in Fuzzy Normed Linear Spaces. Int. J Comput commun conrol. 2021;16(6): 1-11. https://doi.org/10.15837/ijccc.2021.6.4587.

Sabre RI. Fuzzy Convergence Sequence in Fuzzy Compact Operators on Standard Normed Spaces. Baghdad Sci J. 2021; 18(4): 1204-1211. http://dx.doi.org/10.21123/bsj.2021.18.4.1204

Sabre RI, Ahmed BA. Best Proximity Point Theorem for −Contractive Type Mapping in Fuzzy Normed Space. Baghdad Sci. J. 2023; 20(5): 1722-1730. https://doi.org/10.21123/bsj.2023.7509

Daher HY, Kider JR. Some properties of convex fuzzy normed space. Int J appl Math and Comput Sci. 2024; 19(2): 354-355.

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Finite Dimensional Convex Fuzzy Normed Space and Its Basic Properties. Baghdad Sci.J [Internet]. [cited 2024 Dec. 4];22(6). Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/10530