Some Induced Averaging Aggregation Operators Based on Pythagorean Fuzzy Numbers
Mathematics Letters
Volume 3, Issue 4, August 2017, Pages: 40-45
Received: May 29, 2017; Accepted: Aug. 10, 2017; Published: Sep. 6, 2017
Views 1168      Downloads 72
Authors
Khaista Rahman, Department of Mathematics, Hazara University, Mansehra, Pakistan
Saleem Abdullah, Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan
Asad Ali, Department of Mathematics, Hazara University, Mansehra, Pakistan
Fazli Amin, Department of Mathematics, Hazara University, Mansehra, Pakistan
Article Tools
Follow on us
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.
Keywords
Pythagorean Fuzzy Sets, I-PFOWA Operator, I-PFHA Operator
To cite this article
Khaista Rahman, Saleem Abdullah, Asad Ali, Fazli Amin, Some Induced Averaging Aggregation Operators Based on Pythagorean Fuzzy Numbers, Mathematics Letters. Vol. 3, No. 4, 2017, pp. 40-45. doi: 10.11648/j.ml.20170304.11
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186