New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators

Khaista Rahman; Muhammad Sajjad Ali Khan; Murad Ullah

doi:doi:10.11648/j.ml.20170302.12

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New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators

Khaista Rahman, Muhammad Sajjad Ali Khan, Murad Ullah

Published in Mathematics Letters (Volume 3, Issue 2)

Received: 13 April 2017 Accepted: 21 April 2017 Published: 22 May 2017

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Abstract

In this paper, we present two Pythagorean fuzzy averaging aggregation operators such as, Pythagorean fuzzy weighted averaging (PFWA) operator, Pythagorean fuzzy ordered weighted averaging (PFOWA) operator and also introduce some of their basic properties.

Published in	Mathematics Letters (Volume 3, Issue 2)
DOI	10.11648/j.ml.20170302.12
Page(s)	29-36
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, PFWA Operator, PFOWA Operator

References

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[13]	Z. S. Xu, Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst, (2007), 1179-1187.
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[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.
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[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.
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APA Style

Khaista Rahman, Muhammad Sajjad Ali Khan, Murad Ullah. (2017). New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators. Mathematics Letters, 3(2), 29-36. https://doi.org/10.11648/j.ml.20170302.12

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ACS Style

Khaista Rahman; Muhammad Sajjad Ali Khan; Murad Ullah. New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators. Math. Lett. 2017, 3(2), 29-36. doi: 10.11648/j.ml.20170302.12

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AMA Style

Khaista Rahman, Muhammad Sajjad Ali Khan, Murad Ullah. New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators. Math Lett. 2017;3(2):29-36. doi: 10.11648/j.ml.20170302.12

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@article{10.11648/j.ml.20170302.12,
  author = {Khaista Rahman and Muhammad Sajjad Ali Khan and Murad Ullah},
  title = {New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators},
  journal = {Mathematics Letters},
  volume = {3},
  number = {2},
  pages = {29-36},
  doi = {10.11648/j.ml.20170302.12},
  url = {https://doi.org/10.11648/j.ml.20170302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20170302.12},
  abstract = {In this paper, we present two Pythagorean fuzzy averaging aggregation operators such as, Pythagorean fuzzy weighted averaging (PFWA) operator, Pythagorean fuzzy ordered weighted averaging (PFOWA) operator and also introduce some of their basic properties.},
 year = {2017}
}

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TY  - JOUR
T1  - New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators
AU  - Khaista Rahman
AU  - Muhammad Sajjad Ali Khan
AU  - Murad Ullah
Y1  - 2017/05/22
PY  - 2017
N1  - https://doi.org/10.11648/j.ml.20170302.12
DO  - 10.11648/j.ml.20170302.12
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 29
EP  - 36
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20170302.12
AB  - In this paper, we present two Pythagorean fuzzy averaging aggregation operators such as, Pythagorean fuzzy weighted averaging (PFWA) operator, Pythagorean fuzzy ordered weighted averaging (PFOWA) operator and also introduce some of their basic properties.
VL  - 3
IS  - 2
ER  -

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Author Information

Khaista Rahman

Department of Mathematics, Hazara University, Mansehra, Pakistan
Muhammad Sajjad Ali Khan

Department of Mathematics, Hazara University, Mansehra, Pakistan
Murad Ullah

Department of Mathematics, Islamia College University Peshawar, Pakistan

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APA Style

Khaista Rahman, Muhammad Sajjad Ali Khan, Murad Ullah. (2017). New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators. Mathematics Letters, 3(2), 29-36. https://doi.org/10.11648/j.ml.20170302.12

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ACS Style

Khaista Rahman; Muhammad Sajjad Ali Khan; Murad Ullah. New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators. Math. Lett. 2017, 3(2), 29-36. doi: 10.11648/j.ml.20170302.12

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AMA Style

Khaista Rahman, Muhammad Sajjad Ali Khan, Murad Ullah. New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators. Math Lett. 2017;3(2):29-36. doi: 10.11648/j.ml.20170302.12

Copy | Download

@article{10.11648/j.ml.20170302.12,
  author = {Khaista Rahman and Muhammad Sajjad Ali Khan and Murad Ullah},
  title = {New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators},
  journal = {Mathematics Letters},
  volume = {3},
  number = {2},
  pages = {29-36},
  doi = {10.11648/j.ml.20170302.12},
  url = {https://doi.org/10.11648/j.ml.20170302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20170302.12},
  abstract = {In this paper, we present two Pythagorean fuzzy averaging aggregation operators such as, Pythagorean fuzzy weighted averaging (PFWA) operator, Pythagorean fuzzy ordered weighted averaging (PFOWA) operator and also introduce some of their basic properties.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - New Approaches to Pythagorean Fuzzy Averaging Aggregation Operators
AU  - Khaista Rahman
AU  - Muhammad Sajjad Ali Khan
AU  - Murad Ullah
Y1  - 2017/05/22
PY  - 2017
N1  - https://doi.org/10.11648/j.ml.20170302.12
DO  - 10.11648/j.ml.20170302.12
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 29
EP  - 36
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20170302.12
AB  - In this paper, we present two Pythagorean fuzzy averaging aggregation operators such as, Pythagorean fuzzy weighted averaging (PFWA) operator, Pythagorean fuzzy ordered weighted averaging (PFOWA) operator and also introduce some of their basic properties.
VL  - 3
IS  - 2
ER  -

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