An Interval‐Valued Pythagorean Fuzzy Compromise Approach with Correlation‐Based Closeness Indices for Multiple‐Criteria Decision Analysis of Bridge Construction Methods

Abstract

The purpose of this paper is to develop a novel compromise approach using correlation-based closeness indices for addressing multiple-criteria decision analysis (MCDA) problems of bridge construction methods under complex uncertainty based on interval-valued Pythagorean fuzzy (IVPF) sets. The assessment of bridge construction methods requires the consideration of multiple alternatives and conflicting tangible and intangible criteria in intricate and varied circumstances. The concept of IVPF sets is capable of handling imprecise and ambiguous information and managing complex uncertainty in real-world applications. Inspired by useful ideas concerning information energies, correlations, and correlation coefficients, this paper constructs new concepts of correlation-based closeness indices for IVPF characteristics and investigates their desirable properties. These indices can be utilized to achieve anchored judgments in decision-making processes and to reflect a certain balance between connections with positive and negative ideal points of reference. Moreover, these indices can fully consider the amount of information associated with higher degrees of uncertainty and effectively fuse imprecise and ambiguous evaluative ratings to construct a meaningful comparison approach. By using the correlation-based closeness index, this paper establishes effective algorithmic procedures of the proposed IVPF compromise approach for conducting multiple-criteria evaluation tasks within IVPF environments. The proposed methodology is implemented in a practical problem of selecting a suitable bridge construction method to demonstrate its feasibility and applicability. The practicality and effectiveness of the proposed methodology are verified through a comparative analysis with well-known compromise methods and other relevant nonstandard fuzzy models.

Pythagorean fuzzy likelihood function based on beta distributions and its based dominance ordering model in an uncertain multiple criteria decision support framework

“…On the basis of the optimal permutation matrix (see Appendix B for details), one obtains by means of Equation (22). Consequently, the ultimate dominance ranking of the five alternatives was obtained as , which is in agreement with the results obtained by using the correlation‐based compromise approach in relation to fixed ideals by Chen 47 and the interval‐valued PF compromise method via correlation‐based closeness indices by Chen 48 . The application findings exhibit the practicability and reasonableness of the initiated dominance ordering methodology in treating an MCDA issue within PF environments.…”

“…This section develops an inquiry into a selection issue involving financing policies for fulfilling working capital requirements. This real‐world financing decision for working capital policies was originated by Chen 46 within the interval‐valued PF environments and then modified to adapt to PF decision environments in Chen's studies 47,48 . The implementation process of the illustrative application can reveal that the dominance ordering methodology is reasonably practicable.…”

“…This subsection presents the algorithmic procedure implemented in addressing a financing decision‐making issue to scrutinize the conceivability of the developed techniques and validate the pragmatic effectiveness in MCDA issues in PF contexts. The investigated case contains decision information of PF evaluative ratings with normalized weights and was originally formulated and described in Chen 47,48 . Figure 5 briefly overviews the financing problem for working capital policies, consisting of five plans that encompass the working capital financing policy and six evaluative criteria for carefully assessing these five types of plans.…”

“…In Step 2, in conformity with the normalized weights provided by Chen, 47,48 the vector of criterion weights (0.10, 0.05, 0.20, 0.10, 0.25, 0.30), where . In Step 3, in conformity with the PF evaluative rating, as presented in Chen, 47,48 and the PF characteristics of each alternative were devised as follows: …”

A Novel Multiple Attribute Group Decision-Making Approach Based on Interval-Valued Pythagorean Fuzzy Linguistic Sets

“…Yang et al [18] proposed novel operations of interval-valued Pythagorean fuzzy numbers (IVPFNs) under Frank t-norm and t-conorm and based on which the authors further proposed a set of interval-valued Pythagorean fuzzy (IVPFS) power average operators. Cheng [19] proposed an IVPF compromise decision-making approach and applied it in bridge construction analysis. Wei et al [20] proposed an IVPF Maclaurin symmetric mean AO based decision-making method, which is powerful for its ability of capturing the interrelationship among multiple attributes.…”