Single-valued neutrosophic Einstein interactive aggregation operators with applications for material selection in engineering design: case study of cryogenic storage tank

Single-valued neutrosophic sets (SVNSs) and their application to material selection in engineering design. Liquid hydrogen is a feasible ingredient for energy storage in a lightweight application due to its high gravimetric power density. Material selection is an essential component in engineering since it meets all of the functional criteria of the object. Materials selection is a time-consuming as well as a critical phase in the design process. Inadequate material(s) selection can have a detrimental impact on a manufacturer’s production, profitability, and credibility. Multi-criteria decision-making (MCDM) is an important tool in the engineering design process that deals with complexities in material selection. However, the existing MCDM techniques often produce conflicting results. To address such problems, an innovative aggregation technique is proposed for material selection in engineering design based on truthness, indeterminacy, and falsity indexes of SVNSs. Taking advantage of SVNSs and smooth approximation with interactive Einstein operations, single-valued neutrosophic Einstein interactive weighted averaging and geometric operators are proposed. Based on proposed AOs, a robust MCDM approach is proposed for material selection in engineering design. A practical application of the proposed MCDM approach for material selection of cryogenic storage containers is developed. Additionally, the authenticity analysis and comparison analysis are designed to discuss the validity and rationality of the optimal decision.

A further investigation on q-rung orthopair fuzzy Einstein aggregation operators

Aggregation of q-rung orthopair fuzzy information serves as an important branch of the q-rung orthopair fuzzy set theory, where operations on q-rung orthopair fuzzy values (q-ROFVs) play a crucial role. Recently, aggregation operators on q-ROFVs were established by employing the Einstein operations rather than the algebraic operations. In this paper, we give a further investigation on operations and aggregation operators for q-ROFVs based on the Einstein operational laws. We present the operational principles of Einstein operations over q-ROFVs and compare them with those built on the algebraic operations. The properties of the q-rung orthopair fuzzy Einstein weighted averaging (q-ROFEWA) operator and q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator are investigated in detail, such as idempotency, monotonicity, boundedness, shift-invariance and homogeneity. Then, the developed operators are applied to multiattribute decision making problems under the q-rung orthopair fuzzy environment. Finally, an example for selecting the design scheme for a blockchain-based agricultural product traceability system is presented to illustrate the feasibility and effectiveness of the proposed methods.

Power Improved Generalized Heronian Mean Operators Utilizing Hamacher Operations with Picture Fuzzy Information

In multiple attribute decision-making (MADM), to better denote complicated preference information of decision-makers (DMs), picture fuzzy set (PFS) as an expansion of intuitionistic fuzzy set (IFS) has become a powerful tool in the recent years. Meanwhile, to remove the impact of abnormal data and capture the correlations among attributes in MADM issue, we propose the power improved generalized Heronian mean (PIGHM) operators in this paper, which have the merits of both power average (PA) operator and improved generalized Heronian mean (IGHM) operator. Additionally, Hamacher operations as a generalization of Algebraic operations and Einstein operations demonstrate good smooth approximate. Motivated by these, the main purpose is to explore PIGHM operators utilizing Hamacher operations to cope with MADM issue with picture fuzzy information. First, we introduce the Hamacher operations, the normalized hamming distance, and similarity measure of picture fuzzy numbers (PHNs). Second, based on these, two new picture fuzzy aggregating operators (AOs), the picture fuzzy Hamacher weighted power improved generalized Heronian mean (PFHWPIGHM) operator and the picture fuzzy Hamacher weighted geometric power improved generalized Heronian mean (PFHWGPIGHM) operator, are put forward, and some properties and special instances of proposed AOs are also investigated. Third, a new MADM model in terms of the PIGHM AOs is developed. Eventually, a practical MADM example, together with sensitivity analysis and comparative analysis, is conducted to verify the credibility and superiority of the new MADM model.

A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management

A q-rung orthopair fuzzy set (q-ROFS), an extension of the Pythagorean fuzzy set (PFS) and intuitionistic fuzzy set (IFS), is very helpful in representing vague information that occurs in real-world circumstances. The intention of this article is to introduce several aggregation operators in the framework of q-rung orthopair fuzzy numbers (q-ROFNs). The key feature of q-ROFNs is to deal with the situation when the sum of the qth powers of membership and non-membership grades of each alternative in the universe is less than one. The Einstein operators with their operational laws have excellent flexibility. Due to the flexible nature of these Einstein operational laws, we introduce the q-rung orthopair fuzzy Einstein weighted averaging (q-ROFEWA) operator, q-rung orthopair fuzzy Einstein ordered weighted averaging (q-ROFEOWA) operator, q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator, and q-rung orthopair fuzzy Einstein ordered weighted geometric (q-ROFEOWG) operator. We discuss certain properties of these operators, inclusive of their ability that the aggregated value of a set of q-ROFNs is a unique q-ROFN. By utilizing the proposed Einstein operators, this article describes a robust multi-criteria decision making (MCDM) technique for solving real-world problems. Finally, a numerical example related to integrated energy modeling and sustainable energy planning is presented to justify the validity and feasibility of the proposed technique.

T-Spherical Fuzzy Einstein Hybrid Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

T-spherical fuzzy set is a recently developed model that copes with imprecise and uncertain events of real-life with the help of four functions having no restrictions. This article’s aim is to define some improved algebraic operations for T-SFSs known as Einstein sum, Einstein product and Einstein scalar multiplication based on Einstein t-norms and t-conorms. Then some geometric and averaging aggregation operators have been established based on defined Einstein operations. The validity of the defined aggregation operators has been investigated thoroughly. The multi-attribute decision-making method is described in the environment of T-SFSs and is supported by a comprehensive numerical example using the proposed Einstein aggregation tools. As consequences of the defined aggregation operators, the same concept of Einstein aggregation operators has been proposed for q-rung orthopair fuzzy sets, spherical fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and intuitionistic fuzzy sets. To signify the importance of proposed operators, a comparative analysis of proposed and existing studies is developed, and the results are analyzed numerically. The advantages of the proposed study are demonstrated numerically over the existing literature with the help of examples.

Linguistic Pythagorean Einstein Operators and Their Application to Decision Making

Linguistic Pythagorean fuzzy (LPF) set is an efficacious technique to comprehensively represent uncertain assessment information by combining the Pythagorean fuzzy numbers and linguistic variables. In this paper, we define several novel essential operations of LPF numbers based upon Einstein operations and discuss several relations between these operations. For solving the LPF numbers fusion problem, several LPF aggregation operators, including LPF Einstein weighted averaging (LPFEWA) operator, LPF Einstein weighted geometric (LPFEWG) operator and LPF Einstein hybrid operator, are propounded; the prominent characteristics of these operators are investigated as well. Furthermore, a multi-attribute group decision making (MAGDM) approach is presented on the basis of the developed operators under an LPF environment. Ultimately, two application cases are utilized to demonstrate the practicality and feasibility of the developed decision approach and the comparison analysis is provided to manifest the merits of it.