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), 2024. Published by Science Publishing Group

Keywords

Pythagorean Fuzzy Sets, PFWA Operator, PFOWA Operator

References

[1]	Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986, K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst, (1986), 87-96.
[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.

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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
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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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