Research On Extensions And Applications Of Pythagorean Fuzzy Set Theory

In this paper, combing Pythagorean fuzzy set with interval-valued theory, soft set theory, linguistic set theory, we propose three kinds of extended models, i.e.,interval-valued Pythagorean fuzzy set, Pythagorean fuzzy soft set, Pythagorean fuzzy linguistic set, and have a deep going and systematic study on every kind of model. It includes:(1) In view of the Pythagorean fuzzy sets, two new operators are suggested, and their properties are also discussed in detail. Combined the existing Pythagorean fuzzy aggregation operators, a series of inequalities are developed, and their correctness is proved. Based on the adjustable characteristic of the point operators, we investigate Pythagorean fuzzy point operators which describe the fuzziness more stronger.Meanwhile, to aggregate the information of the Pythagorean fuzzy point operators, the Pythagorean fuzzy point weighted average(PFPWA) operator. Two Pythagorean fuzzy multiple attribute group decision making methods based on SIR method and MABAC are explored, respectively. Meanwhile, some Pythagorean fuzzy information measures are proposed, and their transformation relationships are discussed in detail.Also, we apply it to medical diagnosis and pattern recognition to state the effectiveness and superiority of the proposed similarity measure.(2) In order to more accurately describe the uncertainty of the objective world,we propose the interval-valued Pythagorean fuzzy sets, define the corresponding operational laws, score function and accuracy function. According to operational laws,two kinds of interval-valued fuzzy aggregation operators are studied. An interval-valued Pythagorean fuzzy multiple attribute group decision making method based on ELECTRE is established.(3) In order to solve the problem that intuitionistic fuzzy soft sets can't deal with the situation that the sum of membership degree and non-membership degree of the parameter is bigger than 1, combine the characteristics of Pythagorean fuzzy set with the parameterization of soft set, and construct a new mathematical model, namely Pythagorean fuzzy soft set. Some basic operations are defined. The axiomatic definitions of Pythagorean fuzzy soft information measures(distance measure,similarity measure, entropy measure,inclusion measure) are shown, and corresponding formulae are designed, meanwhile, their transformation relationships are analysed. A Pythagorean fuzzy soft clustering method based on similarity measure is established.(4) Aiming at the problem of Pythagorean fuzzy linguistic information aggregation, the operational law, accurate function and score function of Pythagorean fuzzy linguistic numbers are defined, Pythagorean fuzzy linguistic aggregation operators are presented, and their corresponding properties are discussed in detail.Two Pythagorean fuzzy linguistic multiple attribute group decision making methods based on combination weight are introduced.