Some methods for strategic decision-making
problems with immediate probabilities in
Pythagorean fuzzy environment
School of Mathematics, Thapar University,
Harish Garg, School of Mathematics, Thapar
University, Patiala 147 004, India.
In this article, a new decision-making model with prob-
abilistic information and using the concept of immediate
probabilities has been developed to aggregate the infor-
mation under the Pythagorean fuzzy set environment.
In it, the existing probabilities have been modiﬁed by
introducing the attitudinal character of the decision maker
by using an ordered weighted average operator. Based on
it, we have developed some new probabilistic aggregation
operator with Pythagorean fuzzy information, namely
probabilistic Pythagorean fuzzy weighted average oper-
ator, immediate probability Pythagorean fuzzy ordered
weighted average operator, probabilistic Pythagorean
fuzzy ordered weighted average, probabilistic Pythagorean
fuzzy weighted geometric operator, immediate probability
Pythagorean fuzzy ordered weighted geometric operator,
probabilistic Pythagorean fuzzy ordered weighted geo-
metric, etc. Furthermore, we extended these operators by
taking interval-valued Pythagorean fuzzy information and
developed their corresponding aggregation operators. Few
properties of these operators have also been investigated.
Finally, an illustrative example about the selection of the
optimal production strategy has been given to show the
utility of the developed method.
decision making, Pythagorean fuzzy sets, interval-valued Pythagorean
fuzzy set, probabilistic aggregation operators
Int J Intell Syst. 2018;33:687–712. wileyonlinelibrary.com/journal/int © 2018 Wiley Periodicals, Inc. 687