This study addresses the inherent uncertainty in human decision-making by leveraging fuzzy sets, which were introduced to better capture the imprecision associated with human thoughts and judgments. As an extension to traditional fuzzy sets, the Linear Diophantine Fuzzy Set (LDFS) was developed, offering a more flexible approach by relaxing existing limitations on grade values. The LDFS has found applications across various fields, demonstrating its versatility and effectiveness. In this study, we explore the application of the Linear Diophantine Fuzzy Set within the framework of the Combinative Distance-based Assessment (CODAS) method. The CODAS method stands out because it incorporates Euclidean and Taxicab distances. Decision-making should consider not only the direct distances between ideal solutions and alternatives but also the indirect distances. The foremost objective of this research is to propose a novel approach by integrating the CODAS method with the LDFS to address complex decision-making problems characterized by uncertainty and imprecision. To illustrate the practical utility of the proposed method, we apply it to a numerical example involving the selection of a logistics specialist, a critical decision in emergency logistics optimization. The research also includes a case study on a logistics specialist, highlighting the practical application of the methods discussed. Furthermore, this study provides a comprehensive sensitivity analysis of the parameters' weights to evaluate the robustness and reliability of the proposed method. The results highlight the effectiveness of the LDF CODAS method in making informed and reliable decisions under conditions of uncertainty, paving the way for future applications in other decision-making scenarios.

Many effective tools in fuzzy soft set theory have been proposed to handle various complicated problems in different fields of our real life, especially in decision making. Molodtsov’s soft set theory has been regarded as a newly emerging mathematical tool to deal with uncertainty and vagueness. Lattice ordered multi-fuzzy soft set ($\mathcal{L}\mathcal{M}\mathcal{F}\mathcal{S}\mathcal{S}$) has been applied in forecasting process. However, similarity measure is not used in this application. In our research, similarity measure of $\mathcal{L}\mathcal{M}\mathcal{F}\mathcal{S}\mathcal{S}$ is proposed to calculate the similarity between two $\mathcal{L}\mathcal{M}\mathcal{F}\mathcal{S}\mathcal{S}s$. Moreover, some of its properties are introduced and proved. Finally, an application of $\mathcal{L}\mathcal{M}\mathcal{F}\mathcal{S}\mathcal{S}$ in decision making using similarity measure is analysed.

In a dynamic world of technological advances, the Internet of Things (IoT) is a transformational and widespread force that has revolutionized the way we communicate with our surroundings and regulate our environments. It offers several advantages but also introduces inherent risks. In this study, we provide a comprehensive analysis of the risks associated with IoT and employ the effectiveness of a Linear Diophantine Fuzzy Set to rank the risk factors. Because of the significant uncertainties frequently present in IoT contexts, the use of a fuzzy framework is invaluable in discerning and addressing these risks. The primary contribution is to employ the Measurement of Alternatives and Ranking according to the Compromise Solution (MARCOS) method and linear diophantine fuzzy sets to propose a multi-criteria group decision-making method (MCGDM) for ranking attributes to facilitate risk prioritization, enabling consumers to determine the crucial hazards in their IoT systems. Furthermore, we implement a comparative study and a sensitivity analysis to demonstrate the robustness of our proposed methodology. The insights obtained from our research not only improve the awareness of IoT hazards but also enable organizations and individuals to make informed decisions when navigating IoT fields. By proactively addressing these risks, we endorse the development and secure deployment of IoT technology.

The global agricultural sector is responsible for fulfilling the food requirements of the increasing population around the globe, alongside contributing to 28% of global employment. Drones are used for effective and efficient spray of fertilizers to reduce labor and the associated costs. Various drones are available in the market, each with pros and cons. The main aim of this paper is to select a suitable drone for spraying fertilizers in agri-land among the various attributes using a novel Complex Linear Diophantine Fuzzy Soft set algorithm. This novel concept is first introduced alongside its fundamental operations like ⊕ and ⊗. This hybrid structure has the properties of the Complex Linear Diophantine Fuzzy set and soft set. A decision-support system based on Complex Linear Diophantine Fuzzy Soft set was designed and applied on the multi-attribute decision making problem of selecting the best drone for spraying fertilizer on crops.

Molodtsov instigated the concept of soft set theory as a generic mathematical tool for dealing with uncertainty. Yong Yang et.al propounded the idea of multi-fuzzy soft set and investigated its application in decision making problems. The main objec