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Topological Structure of Fuzzy PU-new Ideal in PU-algebra

Received: 6 November 2021     Accepted: 17 December 2021     Published: 31 December 2021
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Abstract

In this manuscript, we consider the fuzzification of the notion PU-new ideal of PU-algebra and define the fuzzy topological terms such that fuzzy topology, τ-open fuzzy set, fuzzy neighborhood, fuzzy interior, sequence of fuzzy sets, fuzzy neighborhood system, fuzzy continuity of a function with respect to PU-new ideal of PU-algebra. We explore the new theorems and related properties of above mention notions with respect to PU-new ideal on PU-algebras. Such that for (Ⱬ, τ) to be a TSFP on Ⱬ and the set Ḟ is a fuzzy in Ⱬ and N be a fuzzy neighborhood system of Ḟ then the finite intersection of elements of ‘N’ is also an element of ‘N’ also any fuzzy set of Ⱬ which contains an element of “N” is also an element of “N”. Furthermore we prove the conditions with respect to fuzzy neighborhood, convergence of a sequence of fuzzy sets, fuzzy interior set of a fuzzy set under which a fuzzy set is τ-open. We show that how the function Ψ from (Ⱬ1,τ) to (Ⱬ2,ω) is fuzzy continuous. We prove that if Ψ is a fuzzy continuous function then for every fuzzy set in Ⱬ1, inverse of each neighborhood of Ψ() is a neighborhood of a fuzzy set .

Published in International Journal of Systems Science and Applied Mathematics (Volume 6, Issue 4)
DOI 10.11648/j.ijssam.20210604.13
Page(s) 125-130
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

PU-algebra, Fuzzy PU-new Ideal, Fuzzy Topology, Topology of Fuzzy PU-new Ideal, Fuzzy Continuity

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  • APA Style

    Muhammad Shafiq, Naveed Sheikh, Dawood Khan. (2021). Topological Structure of Fuzzy PU-new Ideal in PU-algebra. International Journal of Systems Science and Applied Mathematics, 6(4), 125-130. https://doi.org/10.11648/j.ijssam.20210604.13

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    ACS Style

    Muhammad Shafiq; Naveed Sheikh; Dawood Khan. Topological Structure of Fuzzy PU-new Ideal in PU-algebra. Int. J. Syst. Sci. Appl. Math. 2021, 6(4), 125-130. doi: 10.11648/j.ijssam.20210604.13

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    AMA Style

    Muhammad Shafiq, Naveed Sheikh, Dawood Khan. Topological Structure of Fuzzy PU-new Ideal in PU-algebra. Int J Syst Sci Appl Math. 2021;6(4):125-130. doi: 10.11648/j.ijssam.20210604.13

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  • @article{10.11648/j.ijssam.20210604.13,
      author = {Muhammad Shafiq and Naveed Sheikh and Dawood Khan},
      title = {Topological Structure of Fuzzy PU-new Ideal in PU-algebra},
      journal = {International Journal of Systems Science and Applied Mathematics},
      volume = {6},
      number = {4},
      pages = {125-130},
      doi = {10.11648/j.ijssam.20210604.13},
      url = {https://doi.org/10.11648/j.ijssam.20210604.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20210604.13},
      abstract = {In this manuscript, we consider the fuzzification of the notion PU-new ideal of PU-algebra and define the fuzzy topological terms such that fuzzy topology, τ-open fuzzy set, fuzzy neighborhood, fuzzy interior, sequence of fuzzy sets, fuzzy neighborhood system, fuzzy continuity of a function with respect to PU-new ideal of PU-algebra. We explore the new theorems and related properties of above mention notions with respect to PU-new ideal on PU-algebras. Such that for (Ⱬ, τ) to be a TSFP on Ⱬ and the set Ḟ is a fuzzy in Ⱬ and NḞ be a fuzzy neighborhood system of Ḟ then the finite intersection of elements of ‘NḞ’ is also an element of ‘NḞ’ also any fuzzy set of Ⱬ which contains an element of “NḞ” is also an element of “NḞ”. Furthermore we prove the conditions with respect to fuzzy neighborhood, convergence of a sequence of fuzzy sets, fuzzy interior set of a fuzzy set under which a fuzzy set Ḟ is τ-open. We show that how the function Ψ from (Ⱬ1,τ) to (Ⱬ2,ω) is fuzzy continuous. We prove that if Ψ is a fuzzy continuous function then for every fuzzy set Ḟ in Ⱬ1, inverse of each neighborhood of Ψ(Ḟ) is a neighborhood of a fuzzy set Ḟ.},
     year = {2021}
    }
    

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  • TY  - JOUR
    T1  - Topological Structure of Fuzzy PU-new Ideal in PU-algebra
    AU  - Muhammad Shafiq
    AU  - Naveed Sheikh
    AU  - Dawood Khan
    Y1  - 2021/12/31
    PY  - 2021
    N1  - https://doi.org/10.11648/j.ijssam.20210604.13
    DO  - 10.11648/j.ijssam.20210604.13
    T2  - International Journal of Systems Science and Applied Mathematics
    JF  - International Journal of Systems Science and Applied Mathematics
    JO  - International Journal of Systems Science and Applied Mathematics
    SP  - 125
    EP  - 130
    PB  - Science Publishing Group
    SN  - 2575-5803
    UR  - https://doi.org/10.11648/j.ijssam.20210604.13
    AB  - In this manuscript, we consider the fuzzification of the notion PU-new ideal of PU-algebra and define the fuzzy topological terms such that fuzzy topology, τ-open fuzzy set, fuzzy neighborhood, fuzzy interior, sequence of fuzzy sets, fuzzy neighborhood system, fuzzy continuity of a function with respect to PU-new ideal of PU-algebra. We explore the new theorems and related properties of above mention notions with respect to PU-new ideal on PU-algebras. Such that for (Ⱬ, τ) to be a TSFP on Ⱬ and the set Ḟ is a fuzzy in Ⱬ and NḞ be a fuzzy neighborhood system of Ḟ then the finite intersection of elements of ‘NḞ’ is also an element of ‘NḞ’ also any fuzzy set of Ⱬ which contains an element of “NḞ” is also an element of “NḞ”. Furthermore we prove the conditions with respect to fuzzy neighborhood, convergence of a sequence of fuzzy sets, fuzzy interior set of a fuzzy set under which a fuzzy set Ḟ is τ-open. We show that how the function Ψ from (Ⱬ1,τ) to (Ⱬ2,ω) is fuzzy continuous. We prove that if Ψ is a fuzzy continuous function then for every fuzzy set Ḟ in Ⱬ1, inverse of each neighborhood of Ψ(Ḟ) is a neighborhood of a fuzzy set Ḟ.
    VL  - 6
    IS  - 4
    ER  - 

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Author Information
  • Mathematics Department, Faculty of Mathematics Department, University of Balochistan, Quetta, Pakistan

  • Mathematics Department, Faculty of Mathematics Department, University of Balochistan, Quetta, Pakistan

  • Mathematics Department, Faculty of Mathematics Department, University of Balochistan, Quetta, Pakistan

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