# Pythagorean Fuzzy Weighted Averaging Aggregation Operator and its Application to Decision Making Theory

## Abstract

*The objective of the present work is divided into two folds. Firstly, Pythagorean fuzzy weighted averaging aggregation operator has been introduced along with their several properties, namely idem potency, boundedness and monotonicity. Secondly, we apply this proposed operator to deal with multiple attribute group decision making problems under Pythagorean fuzzy information. For this we construct an algorithm for multiple attribute group decision making problems. At the last we also construct a numerical example for multiple attribute group decision making.*

## References

L. A. Zadeh, “Fuzzy sets”, Information and Control. 1965.

K. Atanassov, “Intuitionistic fuzzy sets”, Fuzzy Sets Syst., vol. 20, pp. 87-96, 1986.

D. H. Hong and C. H. Choi, “Multicriteria fuzzy decision-making problems based on vague set theory”, Fuzzy Sets Syst., vol. 114, pp.103-113, 2000.

K. Atanassov, “More on intuitionistic fuzzy sets”, Fuzzy Sets Syst., vol. 33, pp. 37-46, 1989.

K. Atanassov and G. Gargov, “Interval valued intuitionistic fuzzy sets”, Fuzzy Sets Syst., vol. 31, pp. 343-349, 1989.

K. Atanassov, “New operations defined over the intuitionistic fuzzy sets”, Fuzzy Sets Syst., vol. 61, pp.137-142, 1994a.

K. Atanassov, “Operators over interval valued intuitionistic fuzzy sets”, Fuzzy Sets Syst., vol. 64, 159-174, 1994b.

K. Atanassov, “Intuitionistic Fuzzy Sets”, Theory and Applications, Heidelberg: Physica-Verlag, 1999.

K. Atanassov, “Two theorems for intuitionistic fuzzy sets”, Fuzzy Sets Syst., vol. 110, pp. 267-269, 2000.

S.K. De, R. Biswas and A. R. Roy, “Some operations on intuitionistic fuzzy sets” Fuzzy Sets Syst., vol. 114, pp. 477-484, 2000.

K. Atanassov, “New operations defined over the intuitionistic fuzzy sets”, Fuzzy Sets Syst., vol. 61, pp. 137-142, 1994a.

H. Bustince and P. Burillo, “Vague sets are intuitionistic fuzzy sets”, Fuzzy Sets Syst., vol. 79, pp. 403-405, 1996.

H. Bustince, J. Kacprzyk and V. Mohedano, “Intuitionistic fuzzy generators: application to intuitionistic fuzzy complementation”, Fuzzy Sets Syst., vol. 114, pp. 485-504, 2000.

R. R. Yager, “Pythagorean membership grades in multi-criteria decision making”, IEEE Trans Fuzzy Syst., vol. 22, pp. 958-965, 2014.

S. M. Chen and J. M. Tan, “Handling multicriteria fuzzy decision-making problems based on vague set theory”, Fuzzy Sets Syst., vol. 67, pp. 163-172, 1994.

Z. S. Xu, “Intuitionistic fuzzy aggregation operators”, IEEE Transactions on Fuzzy Systems, vol. 15, no. 6, pp. 1179-1187, 2007.

Z. S. Xu and R. R. Yager, “Intuitionistic fuzzy aggregation operators”, IEEE Trans. Fuzzy Syst., vol. 15, pp.1179-1187, 2007.

G. W. Wei, “Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making”, Applied. Soft. Computing, vol. 10, pp. 423-431, 2010.

W. Wang and X. Liu, “Intuitionistic Fuzzy Geometric Aggregation Operators Based on Einstein Operations” vol. 26, pp.1049-1075, 2011.

X. Zhang and Z. S. Xu, “Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean”, Fuzzy Sets., vol. 29, pp. 1061-1078, 2014.

R. E. Bellman and L. A. Zadeh, “Decision-making in a fuzzy environment”, Manage Sci, vol. 17, pp. B-141-B R. Yager, “OWA aggregation of intuitionistic fuzzy sets”, Int. J. Gen Syst., vol. 38, pp. 617-641, 2009.

K. Atanassov, G. Pasi and R.R. Yager, “Intuitionistic fuzzy interpretations of multi-criteria militiaperson and multi-measurement tool decision making”, Int. J. Syst Sci, vol. 36, pp. 859-868, 2005.

R. R. Yager, “Level sets and the representation theorem for intuitionistic fuzzy sets”, Soft Compute., vol. 14, pp.1-7, 2010.

R. R. Yager, “Pythagorean fuzzy subsets”, In Proc. Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, pp. 57-61, 2013.

Z. S. Xu and R. R. Yager, “Some geometric aggregation operators based on intuitionistic fuzzy sets”, Int. J. Gen. Syst., vol. 35, pp. 417-433, 2006.

Z. S. Xu and R. R. Yager, “Dynamic intuitionistic fuzzy multi-attribute decision making”, Int J Approx. Reason., vol. 48, pp. 246-262, 2008

Z. S. Xu and R. R. Yager, “Intuitionistic fuzzy Bonferroni means”, IEEE Trans Syst Man Cybern., vol. 41, pp. 568-578, 2011.

K. Rahman, M.S.A. Khan, Murad Ullah and A. Fahmi, “Multiple Attribute Group Decision Making for Plant Location Selection with Pythagorean Fuzzy Weighted Geometric Aggregation Operator”, The Nucleus, 54, No. 1 pp. 66-74, 2017.

K. Rahman, S. Abdullah, F. Husain, M. S. Ali Khan and M. Shakeel, “Pythagorean fuzzy ordered weighted geometric aggregation operator and their application to multiple attribute group decision making”, J. Appl. Environ. Biol. Sci., vol. 7, no. 4, pp. 67-83, 2017.

K. Rahman, S. Abdullah, R. Ahmed and Murad Ullah, “Pythagorean fuzzy Einstein weighted geometric aggregation operator and their application to multiple attribute group decision making” J. Intelligent & Fuzzy Systems, vol. 33, pp. 635–647, 2017.

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## How to Cite

*The Nucleus*, vol. 54, no. 3, pp. 190–196, Sep. 2017.