Interval-valued Pythagorean Hesitant Fuzzy Theory And Its Application To Group Decision Making

As an extension of intuitionistic fuzzy set theory,we can see that intervalvalued intuitionistic fuzzy sets,Pythagorean hesitant fuzzy sets and intervalvalued Pythagorean hesitant fuzzy sets have stronger ability to express uncertainty and which can objectively and accurately reflect the real thoughts of decision makers in dealing with incomplete information.The aim of this paper is to research theory and develop multi-attribute group decision approaches with interval-valued Pythagorean hesitant fuzzy information.The structure of this paper is arranged as follows:1.Multiple-attribute decision making method based on interval-valued intuitionistic fuzzy entropy is discussed.This paper proposes the definition of core interval based on Hukuhara difference of interval numbers,and refines the uncertainty measurement axiomatic principles of interval-valued intuitionistic fuzzy sets.Considering the uncertainty of interval-valued intuitionistic fuzzy sets is decided by the fuzziness and hesitancy,then a new interval-valued intuitionistic fuzzy entropy based on the exponential weighted is presented and the new entropy model can be applied effectively in multiple attributes decision making analysis with unknown information of attribute weights.2.Based on hesitant fuzzy sets and interval-valued Pythagorean fuzzy sets,the concept of interval-valued Pythagorean hesitant fuzzy set is addressed and some basic operational laws are discussed.Then some operators for aggregating interval-valued Pythagorean hesitant fuzzy information are studied and applied to the multi-attributes group decision making problems.On this basis,some ideal properties of interval-valued Pythagorean hesitant fuzzy set are studied.To solve the problem of priority selection of alternatives in the decision environment of interval value Pythagoras hesitant fuzzy group and to retain as much fuzzy information as possible,we construct the score function and the accuracy function models with the form of interval numbers.Then the relations between these aggregation operators are discussed by comparing the interval numbers.Finally,the multi-attribute decision making arithmetic and case analysis based on interval-valued Pythagorean hesitant fuzzy environments are presented.3.Considering the importance of similarity degree to the research of fuzzy decision,then four kinds of correlation coefficients of Pythagorean hesitant fuzzy sets are proposed and generalized,and the weighted correlation coefficients and properties are discussed in detail.Especially,the concepts of local correlation and local information energy are proposed respectively based on the membership degree interval,non-membership degree interval and indeterminacy degree interval,which can depict the similarity between two interval-valued Pythagorean hesitant fuzzy sets more meticulously and completely.We use the least common multiple method to make the cardinality of different intervalvalued Pythagorean fuzzy Numbers consistent,and through the construction of the score function and the accuracy function with the form of interval number,we realize the correlation comparison of different interval-valued Pythagorean fuzzy sets.Finally,these new correlation coefficient methods are applied to the multi-attributes decision making problems under the interval value Pythagoras fuzzy environment,the empirical analysis shows that the model is feasible and effective.