Abstract
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 non-membership value gets 0 value or 1 value and the weight vector is of type (1,0)T or (0,1)T. 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.
Highlights
Human behaviours and their opinions are not always crisp in nature
We have developed a novel multi-attribute decision making (MADM) approach with the help of a novel aggregation operators (AOs) advanced Pythagorean fuzzy weighted geometric (APyFWG)
We have shown the superiority of the proposed AO as well as the corresponding MADM method
Summary
Human behaviours and their opinions are not always crisp in nature. The mathematical interpretations of their opinion can’t be expressed only in real numbers rather, the members of the fuzzy set in most of the cases. Intuitionistic fuzzy set (IFS) [2], the extension of FS introduced by Attanassov is superior to the FS. It uses MD and nonmembership degree (NMD) to express the degree of belongingness of an element. Pythagorean fuzzy set (PyFS) [3] introduced by Yager is another crucial extension of FS where the sum of the squares of MD and NMD of an element is less than or equal to 1. Garg [21] developed generalized Pythagorean fuzzy information aggregation using Einstein operations.
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