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Some Induced Averaging Aggregation Operators Based on Pythagorean Fuzzy Numbers

Received: 29 May 2017     Accepted: 10 August 2017     Published: 6 September 2017
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Abstract

In this paper we present two new types aggregation operators such as, induced Pythagorean fuzzy ordered weighted averaging aggregation operator and induced Pythagorean fuzzy hybrid averaging aggregation operator. We also discuss of important properties of these proposed operators and construct some examples to develop these operators.

Published in Mathematics Letters (Volume 3, Issue 4)
DOI 10.11648/j.ml.20170304.11
Page(s) 40-45
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), 2017. Published by Science Publishing Group

Keywords

Pythagorean Fuzzy Sets, I-PFOWA Operator, I-PFHA Operator

References
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[2] L. A. Zadeh, Fuzzy sets, Inf Control, (1965), 338-353.
[3] H. Bustine and P. Burillo, Vague sets are intuitionistic fuzzy sets. Fuzzy sets and systems, (1996), 79 (3), 403–405.
[4] C. H. Tan and X. H. Chen, Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making, Expert Syst Appl, (2010), 149.157.
[5] D. H. Hong, and C. H. Choi, Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy sets and systems, (2000) 114 (1), 103–113.
[6] H. Bustine and P. Burillo, Vague sets are intuitionistic fuzzy sets. Fuzzy sets and systems, (1996) 79 (3), 403–405.
[7] K. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets Syst, (1994), 137-142.
[8] K. Atanassov, Remarks on the intuitionistic fuzzy sets. III, Fuzzy Sets Syst, (1995), 401-402.
[9] K. Atanassov, equality between intuitionistic fuzzy sets, Fuzzy Sets Syst, (1996), 257-258.
[10] K. Atanassov, Intuitionistic fuzzy sets: theory and applications, Heidelberg, Germany: Physica-Verlag (1999).
[11] M. Xia and Z. S. Xu, Generalized point operators for aggregating intuitionistic fuzzy information, Int J Intell Syst (2010), 1061-1080.
[12] S. K. De, R. Biswas and A. R. Roy, Some operations on intuitionistic fuzzy sets, Fuzzy Set Syst, (2000), 477-484.
[13] Z. S. Xu, Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst, (2007), 1179- 1187.
[14] Z. S. Xu, R. R. Yager. Some geometric aggregation operators based on intuitionistic fuzzy sets, Int J Gen Syst (2006), 417-433.
[15] W. Wang and X. Liu, Intuitionistic Fuzzy Geometric Aggregation Operators Based on Einstein Operations, international journal of intelligent systems, (2011), 1049-1075.
[16] Weize Wang, Xinwang Liu, Intuitionistic Fuzzy Information Aggregation Using Einstein Operations, IEEE Trans. Fuzzy Systems, (2012) 923-938.
[17] X. Zhao and G. Wei, Some intuitionistic fuzzy Einstein hybrid aggregation operators And their application to multiple attribute decision making, Knowledge-Based Systems, (2013). 472-479.
[18] R. R. Yager, Pythagorean fuzzy subsets, In Proc. Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada (2013), 57-61.
[19] R. R. Yager, A. M. Abbasov, Pythagorean membership grades, complex numbers and decision making. Int J Intell Syst (2013), 28:436.452.
[20] K. Rahman, S. Abdullah, M. S. Ali Khan, A. Ali and F. Amin, Pythagorean fuzzy hybrid averaging aggregation operator and its application to multiple attribute decision making. Accepted.
[21] K. Rahman, M. S. Ali. Khan, Murad Ullah and A. Fahmi, Multiple attribute group decision making for plant location selection with Pythagorean fuzzy weighted geometric aggregation operator, The Nucleus (2017), 54, 66-74.
[22] K. Rahman, S. Abdullah, F. Husain M. S. Ali Khan, M. Shakeel, Pythagorean fuzzy ordered weighted geometric aggregation operator and their application to multiple attribute group decision making, J. Appl. Environ. Biol. Sci., (2017), 7(4) 67-83.
[23] K. Rahman, S. Abdullah, M. S. Ali Khan and M. Shakeel, Pythagorean fuzzy hybrid geometric aggregation operator and their applications to multiple attribute decision making, International Journal of Computer Science and Information Security (IJCSIS), (2016), 14, No. 6, 837-854.
[24] H. Garg, A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making, international journal of intelligent systems, (2016), 1-35.
Cite This Article
  • APA Style

    Khaista Rahman, Saleem Abdullah, Asad Ali, Fazli Amin. (2017). Some Induced Averaging Aggregation Operators Based on Pythagorean Fuzzy Numbers. Mathematics Letters, 3(4), 40-45. https://doi.org/10.11648/j.ml.20170304.11

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    ACS Style

    Khaista Rahman; Saleem Abdullah; Asad Ali; Fazli Amin. Some Induced Averaging Aggregation Operators Based on Pythagorean Fuzzy Numbers. Math. Lett. 2017, 3(4), 40-45. doi: 10.11648/j.ml.20170304.11

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    AMA Style

    Khaista Rahman, Saleem Abdullah, Asad Ali, Fazli Amin. Some Induced Averaging Aggregation Operators Based on Pythagorean Fuzzy Numbers. Math Lett. 2017;3(4):40-45. doi: 10.11648/j.ml.20170304.11

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  • @article{10.11648/j.ml.20170304.11,
      author = {Khaista Rahman and Saleem Abdullah and Asad Ali and Fazli Amin},
      title = {Some Induced Averaging Aggregation Operators Based on Pythagorean Fuzzy Numbers},
      journal = {Mathematics Letters},
      volume = {3},
      number = {4},
      pages = {40-45},
      doi = {10.11648/j.ml.20170304.11},
      url = {https://doi.org/10.11648/j.ml.20170304.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20170304.11},
      abstract = {In this paper we present two new types aggregation operators such as, induced Pythagorean fuzzy ordered weighted averaging aggregation operator and induced Pythagorean fuzzy hybrid averaging aggregation operator. We also discuss of important properties of these proposed operators and construct some examples to develop these operators.},
     year = {2017}
    }
    

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    AU  - Khaista Rahman
    AU  - Saleem Abdullah
    AU  - Asad Ali
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    N1  - https://doi.org/10.11648/j.ml.20170304.11
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    T2  - Mathematics Letters
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    AB  - In this paper we present two new types aggregation operators such as, induced Pythagorean fuzzy ordered weighted averaging aggregation operator and induced Pythagorean fuzzy hybrid averaging aggregation operator. We also discuss of important properties of these proposed operators and construct some examples to develop these operators.
    VL  - 3
    IS  - 4
    ER  - 

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Author Information
  • Department of Mathematics, Hazara University, Mansehra, Pakistan

  • Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan

  • Department of Mathematics, Hazara University, Mansehra, Pakistan

  • Department of Mathematics, Hazara University, Mansehra, Pakistan

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