Informatica

In order to better solve the multi-attribute decision-making (MADM) issues in real life, this paper proposes the probabilistic spherical hesitant fuzzy set (PSHFS) theory based on spherical HFS (SHFS) and probabilistic HFS (PHFS). Firstly, PSHFS is developed, and its basic operations of PHSF element (PSHFE) are proposed. Secondly, generalized PSHF weighted averaging (GPSHFWA) and generalized PSHF weighted geometric (GPSHFWG) operators are constructed, and their excellent properties and some special forms are investigated. Thirdly, for MADM problems with different priorities of related evaluation criteria, we propose generalized PSHF prioritized weighted averaging (GPSHFPWA) and geometric (GPSHFPWG) operators, and investigate their excellent properties and some special operators. Fourthly, two new MADM techniques are constructed dependent on the proposed two types of operators in practical MADM problems. Finally, the effectiveness of the two MADM techniques constructed is tested through an application example of the green enterprise credit selection (GECS). The sensitivity analysis of parameter shows the influence on different values of parameter on the optimal alternatives by setting different parameter values, and shows the flexibility of the proposed MADM techniques. Meanwhile, the two MADM techniques are compared with several existing MADM techniques to prove the advantages of the two MADM techniques.

Quality Function Deployment (QFD) is a technique used to collect Customer Requirements (CRs) for the product to be designed before the start of the manufacturing processes, and also used to determine whether CRs will be met with correlated or uncorrelated Design Requirements (DRs). In QFD technique, customers tend to explain their expectations from the product by using linguistic expressions instead of using exact numbers. Vagueness and impreciseness in linguistic expressions can be captured perfectly using fuzzy set theory. Pythagorean fuzzy (PF) sets as one of the extensions of ordinary fuzzy sets offer the decision maker a larger membership and non-membership assignment region than ordinary intuitionistic fuzzy sets. In this paper, customer requirements in QFD analysis are prioritized by Best-Worst Method (BWM), which has become a very popular optimization-based weighting method in recent years. In the proposed BWM and QFD methodology, interval-valued Pythagorean fuzzy (IVPF) sets are used for the first time in order to handle the uncertainties in the linguistic judgments. In the application, the two-phase IVPF methodology is proposed to a real life e-scooter design problem addressing 12 customer & 12 design requirements. The proposed PF methodology could determine the weights of customer requirements, and identify which of the design requirements is stronger, and make a competitive analysis to reveal the position of our company in the market under fuzzy environment. Besides, the sensitivity and comparative analyses have demonstrated the dominance of our company over the other competitors.