Data envelopment analysis (DEA) is a linear programming approach used to determine the relative efficiencies of multiple decision-making units (DMUs). A transportation problem (TP) is a special type of linear programming problem (LPP) which is used to minimize the total transportation cost or maximize the total transportation profit of transporting a product from multiple sources to multiple destinations. Because of the connection between the multi-objective TP (MOTP) and DEA, DEA-based techniques are more often used to handle practical TPs. The objective of this work is to investigate the TP with Fermatean fuzzy costs in the presence of numerous conflicting objectives. In particular, a Fermatean fuzzy DEA (FFDEA) method is proposed to solve the Fermatean fuzzy MOTP (FFMOTP). In this regard, every arc in FFMOTP is considered a DMU. Additionally, those objective functions that should be maximized will be used to define the outputs of DMUs, while those that should be minimized will be used to define the inputs of DMUs. As a consequence, two different Fermatean fuzzy effciency scores (FFESs) will be obtained for every arc by solving the FFDEA models. Therefore, unique FFESs will be obtained for every arc by finding the mean of these FFESs. Finally, the FFMOTP will be transformed into a single objective Fermatean fuzzy TP (FFTP) that can be solved by applying standard algorithms. A numerical example is illustrated to support the proposed method, and the results obtained by using the proposed method are compared to those of existing techniques. Moreover, the advantages of the proposed method are also discussed.

Aggregation operators are useful tools for approaching situations in the realm of multiattribute decision-making (MADM). Among the most valuable aggregation strategies, the Hamy mean (HM) operator is designed to capture the correlations among integral parameters. In this article, a series of Hamy-inspired operators are used to combine 2-tuple linguistic Fermatean fuzzy (2TLFF) information. The new 2TLFF aggregation operators that are born from this adaptation include the 2-tuple linguistic Fermatean fuzzy Hamy mean (2TLFFHM) operator, 2-tuple linguistic Fermatean fuzzy weighted Hamy mean (2TFFWHM) operator, 2-tuple linguistic Fermatean fuzzy dual Hamy mean (2TLFFDHM) operator, and 2-tuple linguistic Fermatean fuzzy weighted Hamy mean (2TLFFWDHM) operator. Furthermore, various essential theorems are stated, and special cases of these operators are thoroughly examined. Then, a renewed multiattribute group decision-making (MAGDM) technique based on the suggested aggregation operators is provided. A practical example corroborates the usefulness and implementability of this technique. Finally, the merits of the proposed MAGDM method are demonstrated by comparing it with existing approaches, namely, it can deal with MAGDM problems by considering interactions among multiple attributes based on the 2TLFFWHM operator.

This paper aims to introduce the novel concept of neutrosophic crisp soft set (NCSS), including various types of neutrosophic crisp soft sets (NCSSs) and their fundamental operations. We define NCS-mapping and its inverse NCS-mapping between two NCS-classes. We develop a robust mathematical modeling with the help of NCS-mapping to analyze the emerging trends in social networking systems (SNSs) for our various generations. We investigate the advantages, disadvantages, and natural aspects of SNSs for five generations. With the changing of the generations, it is analyzed that emerging trends and the benefits of SNSs are increasing day by day. The suggested modeling with NCS-mapping is applicable in solving various decision-making problems.

In recent years, network security has become a major concern. Using the Internet to store and analyze data has become an integral aspect of the production and operation of many new and traditional enterprises. However, many enterprises lack the necessary resources to secure information security, and selecting the best network security service provider has become a real issue for many enterprises. This research introduces a novel decision‐making method utilizing the 2‐tuple linguistic complex q‐rung orthopair fuzzy numbers (2TLCq‐ROFNs) to tackle this issue. We propose the 2TLCq‐ROF concept by combining the complex q‐rung orthopair fuzzy set with 2‐tuple linguistic terms, including the fundamental definition, operational rules, scoring, and accuracy functions. Aggregation operators are the fundamental mathematical approach used to combine various inputs into a single output. Taking into account the interaction between the attributes, we develop the 2TLCq‐ROF Hamacher (2TLCq‐ROFH) operators by using the innovative operational rules. These operators include the 2TLCq‐ROFH weighted average (2TLCq‐ROFHWA), 2TLCq‐ROFH ordered weighted average (2TLCq‐ROFHOWA), 2TLCq‐ROFH hybrid average (2TLCq‐ROFHHA), 2TLCq‐ROFH weighted geometric (2TLCq‐ROFHWG), 2TLCq‐ROFH ordered weighted geometric (2TLCq‐ROFHOWG), and 2TLCq‐ROFH hybrid geometric (2TLCq‐ROFHHG) operators. In addition, we talk about the properties of 2TLCq‐ROFH operators such as idempotency, commutativity, monotonicity, and boundedness and also examine their spatial cases. To tackle the problems of the 2TLCq‐ROF multiattribute group decision‐making (MAGDM) environment, we develop a novel approach according to the COPRAS (complex proportional assessment) model. Finally, to validate the feasibility of the given strategy, we employ a quantitative example related to select the best network security service provider. In comparison with existing approaches, the developed decision‐making algorithm is most extensively used and reduces the loss of information.

The intelligent manufacturing system (IMS) is a framework that improves productivity by organizing the logical features involved in manufacturing. The procedure of intelligent manufacturing owns the capability to self-control the manufacturing of the products according to the specifications of design. Different IMSs are designed to deal with continuous changes in market which can adjust to make the modified environment easier. The central idea of this research article is to select an IMS that can adapt the updated situations faster than the existing competing systems and provide higher benefits in utilizing new possibilities. To select such IMS, the applicability of multiobjective optimization on the basis of the ratio analysis (MOORA) method has been explored using Fermatean fuzzy sets. The Fermatean fuzzy aggregated weighted operators are used to construct the decision matrices. Then, the ratio analysis-based MOORA method is developed to accomplish the ranking of under consideration IMSs. Furthermore, the conversion of qualitative attributes into quantitative attributes has been performed using Fermatean fuzzy numbers (FFNs). Finally, a brief comparative analysis of the developed technique with existing models is narrated to reveal the flexibility of the Fermatean fuzzy MOORA method.