Compared to Fermatean fuzzy sets, Pythagorean fuzzy sets, and intuitionistic fuzzy sets, (p, q)-rung orthopair fuzzy sets ((p, q)-ROFSs) can display membership grades over a wider range, allowing them to present more confusing circumstances. This article elaborates the use of (p, q)-ROFS in engineering design for material selection. Material selection is a crucial part of engineering because it satisfies all of the object’s functional requirements. The design process’s crucial and time-consuming phase of material selection. The output, profitability, and reputation of a manufacturer can suffer from the choice of the incorrect material(s). An essential tool in the engineering design process for handling the complexity of material selection is multi-attribute decision-making (MADM). However, the outcomes of using the current MADM approaches are frequently inconsistent. To solve these issues, a novel aggregation method based on the truthness and falsity indices of (p, q)-ROFS is suggested for material selection in engineering design. We present (p, q)-rung orthopair fuzzy Hamacher interactive aggregation operators (AOs) that take advantage of (p, q)-ROFS and smooth approximation with interactive Hamacher operations. Based on the indicated AOs, in engineering design, a trustworthy MADM method is advised for material selection (MS). The main contributions of this article are as follows: (1) The aggregation operators for (p, q)-rung orthopair fuzzy numbers and their attributes have been studied using Hamacher norms. (2) MADM is established under (p, q)-rung orthopair fuzzy sets. A step-by-step explanation of the proposed method is given using an algorithm. (3) The developed method is then applied as a case study in the selection of materials for cryogenic storage tanks. (4) The results have been contrasted with the rankings obtained by several currently employed techniques. The authenticity analysis and comparison analysis are also intended to talk about the reliability and sanity of the best choice.
In this paper, we propose a novel multi-attribute group decision making (MAGDM) approach under the p, q-quasirung orthopair fuzzy number (p, q-QOFN) environment. For this, we propose new multiplication operation and scalar power operation for p, q-QOFNs based on Yager’s norm. Then, by using the proposed multiplication operation and scalar power operation of p, q-QOFNs and the concept of prioritized geometric aggregation operator (AO), we propose the p, q-quasirung orthopair fuzzy Yager prioritized weighted geometric (p, q-QOFYPWG) AO for aggregating p, q-QOFNs. We also prove the different properties of the proposed p, q-QOFYPWG AO of p, q-QOFNs. However, based on the proposed p, q-QOFYPWG AO, we propose a new MAGDM approach in the context of p, q-QOFNs environment. Afterwards, we utilize the proposed MAGDM approach to solve the different MAGDM problems, and compare the preference orders (POs) obtained from the proposed MAGDM approach to POs obtained from other existing MAGDM approaches. The proposed MAGDM approach can overcome the shortcomings of the existing MAGDM approaches, where they cannot distinguish the POs of the alternatives in some cases. The proposed MAGDM approach provides a very useful approach to deal with MAGDM problems in the p, q-QOFNs environment.
The correlation coefficient is a powerful tool to measure the relationship between two variables and is very useful in decision-making. In this paper, we propose a new multiattribute decision-making (MADM) method for q-rung orthopair fuzzy number (q-ROFN) environment. For this, we propose a novel correlation coefficient for q-rung orthopair fuzzy sets (q-ROFSs), which measures the strength of the relationship between two q-ROFSs. We also present the various properties of the proposed correlation coefficient of q-ROFSs. Moreover, we also develop the weighted correlation coefficient of q-ROFSs. Afterward, we propose a new MADM method under the q-ROFNs environment based on the proposed weighted correlation coefficient of q-ROFSs and the “Technique for Order Preference by Similarity to Ideal Solution” (TOPSIS) method. The proposed MADM method can overcome the shortcomings of the existing MADM methods of the q-ROFNs environment, where they cannot distinguish the ranking orders (ROs) of the alternatives. The proposed MADM method provides a very useful method to deal with MADM problems in the q-ROFNs environment.
This paper introduces an enhanced fuzzy k-nearest neighbor (FKNN) approach called the feature-weighted Minkowski distance and local means-based fuzzy k-nearest neighbor (FWM-LMFKNN). This method improves classification accuracy by incorporating feature weights, Minkowski distance, and class representative local mean vectors. The feature weighting process is developed based on feature relevance and complementarity. We improve the distance calculations between instances by utilizing feature information-based weighting and Minkowski distance, resulting in a more precise set of nearest neighbors. Furthermore, the FWM-LMFKNN classifier considers the local structure of class subsets by using local mean vectors instead of individual neighbors, which improves its classification performance. Empirical results using twenty different real-world data sets demonstrate that the proposed method achieves statistically significantly higher classification performance than traditional KNN, FKNN, and six other related state-of-the-art methods.
Probabilistic linguistic term sets (PLTSs), a form of fuzzy language, are capable of effectively expressing the evaluation information of decision-makers (DMs) in emergency decision-making (EDM) for disasters. Thus, an EDM method based on PLTSs and regret theory is proposed, addressing the uncertainty of decision-making information and the incomplete rationality of DMs in disaster scenarios. First, a novel distance measure method for PLTSs is established, integrating Euclidean distance, Jensen–Shannon (JS) divergence and Jousselme distance. Next, expert weights are determined based on the trust in each expert and the similarity of viewpoints. During consensus reaching, a feedback adjustment coefficient is introduced to maintain the integrity of the original evaluation information provided by the experts. Furthermore, a combined weighting method is developed, incorporating both objective and subjective attribute weights to derive comprehensive attribute weights. Taking into account the incomplete rationality of DMs, an EDM method is formulated using PLTSs and regret theory to prioritize alternatives. Finally, the effectiveness of the proposed method is validated through a case study using the selection of a transportation plan for relief supplies during the Yushu earthquake as an example, along with sensitivity analysis and a comparison with other existing approaches.
