In this paper, a novel multi-attribute decision-making method using Advanced Pythagorean fuzzy weighted geometric operator in a Pythagorean fuzzy environment is developed. Pythagorean fuzzy aggregation operators have drawbacks that they give indeterminate results in some special cases when membership value or nonmembership value gets 0 value or 1 value and the weight vector is of type (1, 0) or (0, 1) . The Advanced Pythagorean fuzzy geometric operator, the proposed operator can overcome the drawbacks. In some situations, for example, where the sum of squares of membership degree and non-membership degree gets unit value of a Pythagorean fuzzy number, multi-attribute decision making (MADM) methods using some existing aggregation operators give unreasonable ranking orders (ROs) of alternatives or can't discriminate the ROs of alternatives. But the present MADM method can get over the drawbacks of the existing MADM methods. The present MADM method is devoted to eliminate the drawbacks of the existing MADM methods and to select the best real estate company for investment.

The popularity of mutual funds, which are necessarily portfolios, has been drawing more attention from the people of India over the last three decades. In a mutual fund, one can invest his or her money in the securities of different sectors traded mainly in the stock exchange markets to get expected return bearing tolerable risks. A mutual fund other than the passive mutual funds is directed by an active fund manager. The performance of a mutual fund depends on the shares and securities of different companies it contains and the fund manager's performance also. Risk and return can be measured based on different criteria. Before investment, one should select such a mutual fund that can fulfill his or her anticipation as much as possible within the risk–return skeleton. Therefore the selection of a mutual fund is rigorously a multicriteria decision making. This paper has considered five open‐ended, large‐cap, direct, suspended sales mutual funds for the research work. In the first stage, we have shortlisted the more crucial criteria comparatively from a list of criteria with the help of the Fuzzy Analytic Hierarchy Process. In the second stage, we have applied the Pythagorean fuzzy Gray Relation Analysis approach to determine the weights of shortlisted criteria as well as the rank of those mutual funds. Finally, a comparison has been drawn between the present model and the Pythagorean fuzzy Interactive Multicriteria Decision‐Making model, to show the effectiveness of the present model.

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