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Due to the complexity of objective world, as well as the ambiguity of human thinking, the practical decision-making issues become more and more difficult. Pythagorean fuzzy set is an effective tool for depicting uncertainty of the multi-criteria decision-making problems. This study aims to develop a Pythagorean fuzzy multi-criteria decision-making approach to deal with decision-making problem under uncertainty circumstance. Firstly, the concept, representation and related properties of Spearman rank correlation coefficient (SRCC) originated from statistical theory between two PFSs are introduced, which is used to measure the closeness degree between ideal alternative and each alternative. Then, a multi-criteria decision-making approach with Pythagorean fuzzy environment is developed based on the proposed SRCC. Finally, to illustrate the applicability and effectiveness of the proposed method, a real-world infrastructure project decision-making was demonstrated. The result shows that the main advantage of the proposed decision rule would reduce the complexity of the decision-making problem both in theory and practice. [ABSTRACT FROM AUTHOR]

To provide theoretical reference for owners to identify unbalanced bids, this paper aims to construct an identification method based on grey relational and fuzzy set theory. Firstly, to measure the closeness degree between bidding unit price from engineering's estimated price, grey relational analysis theory is used to express the relationship between them. Secondly, a combined weight method determining all line items is calculated through integrating analytic hierarchy model and maximizing deviation method. Thirdly, based on fuzzy set theory, the membership degree and the fuzzy relation matrix are constructed, and then a fuzzy comprehensive identification method is established to identify unbalanced bidding. Fourthly, on the basis of fuzzy comprehensive identification method, the scoring set and total score vector are designed, and the rank of unbalanced bids is obtained by total score vector. Finally, a practical construction project bidding is stated to illustrate the effectiveness and practicability of the proposed method. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy sets (PFSs), as an extension of intuitionistic fuzzy sets (IFSs) for dealing with uncertainty information, have attracted considerable attention in the decision-making area. The Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method is one of the most popular decision-making approaches. In the TOPSIS method, the desired alternative should have not only the shortest distance from the positive ideal solution, but also the farthest distance from the negative ideal solution. Similarity measures play an important role in assessing the degree between ideal and proposal alternatives in decision-making. Thus, this paper aims to provide an extended TOPSIS by developing new similarity measures with PFSs and applying it to multi-criteria decision-making (MCDM) problems. The main contributions of this paper are as follows: (1) development of three new similarity measures with PFSs, and investigation of their properties; (2) extension of the TOPSIS method based on the proposed similarity measures; and (3) establishment of a Pythagorean fuzzy decision-making method using the improved TOPSIS method. A case study on the selection of a project delivery system is conducted to show the applicability of the presented approach. [ABSTRACT FROM AUTHOR]

An appropriate project delivery system plays an essential role in sustainable construction project management. Due to the complexity of practical problems and the ambiguity of human thinking, selecting an appropriate project delivery system (PDS) is an enormous challenge for owners. This paper aims to develop a PDS selection method to deal with the related-indicators case by combining the advantages of Pythagorean fuzzy sets (PFSs) and Pythagorean fuzzy weighted Muirhead mean (PFWMM) operators. The contributions of this paper are as follows: (1) This study innovatively introduced the PFWMM operator to deal with PDS selection problems for the case of the relevance among all indicators affecting PDSs selection in a complex environment. (2) A new method of solving indicators' weights was proposed to adapt to the related-indicators PDS selection problem, through investigating the differences between the ideal PDS and the alternative PDS under all indicators. (3) A decision-making framework for PDS selection was constructed by comprehensive use of the advantages of PFSs and the PFWMM operator in dealing with related-indicators PDS decision-making problems. An example of selecting a PDS is exhibited to illustrate the effectiveness and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

Interval Pythagorean fuzzy set (IPFS), which can handle imprecise and ambiguous information, has attracted considerable attention in both theory and practice. However, one of the main difficulties under IPFSs is the comparison between interval numbers. To overcome this shortcoming, connection number theory is first introduced, and interval numbers are transformed into connection numbers in the operating process. Considering that similarity measures play an important role in assessing the degree between ideal and proposal alternatives in the decision making process, this paper aims to develop new similarity measures with IPFSs and apply them to multi-criteria decision making (MCDM) problems. The main contributions of this paper are as follows: (1) introduction of a comparison method through transforming interval numbers into connection numbers; (2) development of three new similarity measures with IPFSs based on the minimum and maximum operators, and investigation of their properties; (3) calculation of the similarity measures considering weights of membership and non-membership degrees; (4) establishment of an interval Pythagorean fuzzy decision making method applying the presented similarity measures. A case study on selecting a project delivery system is made to show the applicability of the proposed approach. [ABSTRACT FROM AUTHOR]