New Chebyshev distance measures for Pythagorean fuzzy sets with applications to multiple criteria decision analysis using an extended ELECTRE approach

This paper aims to propose novel Chebyshev distance measures for Pythagorean membership grades and establish their based elimination and choice translating reality method (ELECTRE) for addressing multiple criteria decision-making problems under uncertainty of Pythagorean fuzziness. Pythagorean fuzzy (PF) sets have a significant effect on fuzzy modeling for intelligent informatics and decision support because the degrees of membership, non-membership, and indeterminacy, strength of commitment, and direction of commitment featured by PF information are extended for a wider coverage of information span. The theory of PF sets is a powerful tool in dealing with imprecise and ambiguous evaluations for realistic problems and modeling intelligent decision making for complex systems. This paper focuses on both theory and applications of the Chebyshev metric for PF contexts, and special attention is devoted to the theoretical development of Chebyshev distances in connection with Pythagorean membership grades based on various types of representations. To surmount the difficulties confronted by the existing measures, such as low comprehensivity, incomparability in scaling, ignorance of square degrees in metric specification, double weighting, and inappropriate normalization, this paper makes a comprehensive comparison to validate the effectiveness and superiority of the proposed Chebyshev distance measures. To support decision making within complicated PF environments, this paper develops an extended ELECTRE approach based on the Chebyshev distance measure to conduct multiple criteria decision analysis involving PF information for determining partial and complete rankings of candidate alternatives. In particular, this paper constructs novel Chebyshev metric-based preference functions depending on the individual characteristics of the criteria. The developed PF ELECTRE approach leads to using all the information that characterizes a PF set via the concepts of the scalar function and various Chebyshev metric-based comparison indices, such as (net) concordance indices, (net) discordance indices, and the overall precedence index. Practical applications with a comparative analysis in the field of bridge-superstructure construction are conducted to examine the usefulness and advantages of the proposed methodology in the real world.