Interval-Valued Pythagorean Fuzzy Power Heronian/Power Geometric-Geometric Heronian Means Operators And Their Application In Decision Making

Interval-valued Pythagorean fuzzy multiple attribute(group)decision making is based on Interval-valued Pythagorean fuzzy set and multiple attribute(group)decision making.From the existing literature,it can be seen that the theory is mainly focused on aggregation operators,and these operators can only process the overall information from a single dimension.In this case,based on Interval-valued Pythagorean fuzzy environment,this paper targetedly investigates two kinds of operators with good properties——power average operator and Heronian means operator,and tries to integrate the two kinds of operators to improve the accuracy of decision making.The specific work is as follow:(1)The related knowledge of Interval-valued Pythagorean fuzzy set is introduced.The completeness and separability of Interval-valued Pythagorean fuzzy number space under the normalized Hamming distance is discussed.(2)Power average operator and power geometric operator are extended to interval-valued Pythagorean fuzzy environment,and interval-valued Pythagorean fuzzy power average(IVPFPA)operator,interval-valued Pythagorean fuzzy power weighted average(IVPFPWA)operator,interval-valued Pythagorean fuzzy power geometric(IVPFPG)operator and interval-valued Pythagorean fuzzy power weighted geometric(IVPFPWG)operator are developed.Moreover,the special properties of these operators are also studied.Finally,a multiple attribute decision making model based on IVPFPWA operator / IVPFPWG operator is presented,and a practical example is given to illustrate its rationality.(3)Heronian means operator and geometric Heronian means operator are extended to interval-valued Pythagorean fuzzy environment,and interval-valued Pythagorean fuzzy Heronian means(IVPFHM)operator,interval-valued Pythagorean fuzzy weighted Heronian means(IVPFWHM)operator,interval-valued Pythagorean fuzzy geometric Heronian means(IVPFGHM)operator and interval-valued Pythagorean fuzzy geometric weighted Heronian means(IVPFGWHM)operator are developed.At the same time,some basic properties and special cases of these operators are also studied.Finally,a multiple attribute decision making model based on IVPFWHM operator / IVPFGWHM operator is established,and a practical example is given to illustrate its rationality and superiority.(4)Under the interval-valued Pythagorean fuzzy environment,power average operator and Heronian means operator are combined,and interval-valued Pythagorean fuzzy power Heronian means(IVPFPHM)operator and interval-valued Pythagorean fuzzy power weighted Heronian means(IVPFPWHM)operator are proposed;power geometric operator and geometric Heronian means operator are combined,and interval-valued Pythagorean fuzzy power geometric-geometric Heronian means(IVPFPG-GHM)operator and interval-valued Pythagorean fuzzy power weighted geometric-geometric Heronian means(IVPFPWG-GHM)operator are proposed.The new operators consider the initial information from a high-dimension perspective.That is,not only the correlation between attributes is reflected by the cross operation of(geometric)Heronian means operator,but also the influence of ‘singular value'(unduly large or unduly small)is greatly eliminated by assigning the credibility to a single variable.In addition,some desirable properties and special cases of new operators are also studied.Finally,a multiple attribute group decision making model based on IVPFPWHM operator / IVPFPWG-GHM operator is presented,and a practical example is given to illustrate its feasibility and rationality.