We introduce the concept of Diophantine spherical vague set approach to multiple-attribute decision-making. The Spherical vague set is a novel expansion of the vague set and interval valued spherical fuzzy set. Three new concepts have been introduce such as Diophantine spherical vague weighted averaging operator, Diophantine spherical vague weighted geometric operator, generalized Diophantine spherical vague weighted averaging operator and generalized Diophantine spherical vague weighted geometric operator. We provide a numerical example to show how Euclidean distance and Hamming distance interact. Applications of the Diophantine spherical vague number include idempotency, boundedness, commutativity and monotonicity in algebraic operations. They can determine the optimal option and are more well-known and reasonable. Our goal was to identify the optimal choice by comparing expert opinions with the criteria. As a result, the model’s output was more accurate as well as in the range of the natural number . The weighted averaging distance and weighted geometric distance operators are distance measure that is based on aggregating model. By comparing the models under discussion with those suggested in the literature, we hoped to show their worth and reliability. It is possible to find a better solution more quickly, simply, and practically. Our objective was to compare the expert evaluations with the criteria and determine which option was the most suitable. Because they yield more precise solutions, these models are more accurate and more related to models with . To show the superiority and the validity of the proposed aggregation operations, we compared it with the existing method and concluded from the comparison and sensitivity analysis that our proposed technique is more effective and reliable. This investigation yielded some intriguing results.

The increase in traffic caused by new development affects the change in traffic conditions on the surrounding roads, and shopping centres are significant traffic generators. The development of local travel generation rates and their characteristics for individual land uses from the aspect of traffic demand is a reliable way to plan traffic in order to come up with preventive solutions to traffic problems, that is, prevention of possible negative consequences on traffic conditions in the street network occurring due to the construction of shopping centres. One of the main aims of this paper is to develop a model for objective assessment of the generated traffic demand for significant changes in land use, such as the construction of shopping centres in medium-sized towns. All these would be steps in the right direction for the promotion of reliable traffic planning and adoption of TIA for every new development before a decision regarding the change in land purpose has been made. This kind of process still has not been established systematically in either Bosnia and Herzegovina and the Republic of Serbia, or in surrounding countries. This paper focuses on the formulation of a model for determining the volume of traffic generated by shopping centres in medium-sized towns in two countries of the Southeast Europe region. The survey was conducted in eight different locations (cities) where there are shopping centres with common facilities. The analysis showed that the number of visitors and vehicles attracted by the shopping centre zone can be determined by a model based on a linear regression analysis. The analysis included exploring several different factors of trip generation in shopping centres, including the relationship between trip generation and combinations of several independent variables. The verification of the model was conducted in real conditions of the traffic flow generated by a shopping centre which was not the analysis subject when forming the forecasting model. In this way, the validity of the proposed model is credibly assessed. The developed model can be applied in the procedures of planning the construction of shopping centres in medium-sized cities in the Republic of Serbia and Bosnia and Herzegovina, and wider, in the region of Southeast Europe, in order to estimate the volume of generated traffic demand, that is, its impact on the conditions of traffic on the surrounding traffic network.

In this manuscript, we delve into the realm of lattice ordered complex linear diophantine fuzzy soft set, which constitutes an invaluable extension to the existing Fuzzy set theories. Within this exploration, we investigate basic operations such as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\oplus$\end{document}⊕ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\otimes$\end{document}⊗, together with their properties and theorems. This manuscript is more amenable in two ways, i.e., it enables real-life problems involving parametrization tool and applications with an existing order between the components of the parameter set based on the preference in the complex frame of reference. Adaptive cruise control (ACC) is a system designed for maintaining distance between two vehicles and to sustain a manually provided input speed. The purpose of cars with ACC is to avoid a collision that frequently happens nowadays, thereby improving road safety regulations amidst rising collision rates. The fundamental aim of this manuscript is to prefer an applicable car with ACC together with its latest model by defining a peculiar postulation of lattice ordered complex linear diophantine fuzzy soft set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\rm ( \widehat{LOCLDFSS} )$\end{document}(LOCLDFSS^). Emphasizing real-life applicability, we illustrate the effectiveness and validity of our suggested methodology in tackling current automotive safety concerns, providing useful guidance on reducing challenges related to contemporary driving conditions.

This paper addresses the concept of the vendor-managed inventory (VMI) problem, focusing on the replenishment policy and the vehicle routing problem (VRP) model. These components are integrated to tackle a three-echelon distribution issue comprising a single plant, multiple depots, and multiple retailers, with the primary objective of minimizing transportation and inventory costs within this complex distribution network. A three-phase methodology is proposed to optimize the entire supply chain, from the plant to the final retailer, and its performance is evaluated through computational experiments. This research is motivated by a real-life supply network, highlighting its practical relevance and applicability. To extend the capabilities of existing methods for solving the combined inventory and routing problem, an insertion heuristic is incorporated to enhance vehicle utilization, thereby reducing total costs. Computational results demonstrate the effectiveness of the improved algorithm, indicating that it is sufficiently robust for practical application. Significant cost savings can be achieved with the proposed approach, making it a valuable contribution to the field of supply chain optimization.

The eternal 1-secure set, strategically protects graphical structures against attacks by placing sentinels within dominating sets. This study adapts this concept to real-world scenarios, like emergency response systems, by addressing challenges such as roadblocks and traffic congestion. We introduce the secure set and the eternal 1-secure set for fuzzy graphs based on edge membership levels J. Our analysis examines the relationship between the security number of a fuzzy graph G at level J and the domination number of its spanning subgraph at level J, demonstrating the potential of the eternal 1-secure set to enhance security measures in dynamic environments.

Enterprise resource planning (ERP) is widely used to boost the total market power of businesses. The wrong selection is one of the key reasons why ERP installations fail. Due to the complexity of the business environment and the range of ERP systems, choosing an ERP system is a complex and time-consuming procedure. ERP alternatives may be assessed using several criteria, so the ERP selection process may be considered a multi-criteria decision-making (MCDM) problem. In this study, the rough best worst method (BWM) was used to determine criteria weights, while the newly developed rough integrated simple weighted sum product (WISP) was used to rank ERP alternatives. Results suggest that the SFT-4 coded software is regarded as the best option, followed by SFT-5, SFT-6, SFT-2, SFT-3, and SFT-1. Results of the newly developed rough WISP method are compared to those of existing rough techniques in the sensitivity analysis. The differences between them have been found to be negligible. The outcomes show how effectively developed rough BWM and WISP integrated method performs in terms of ERP selection with usability, accuracy, ease of use, and consistency. This study will help decision-makers in a context where ERP is implemented choose the best ERP software for different sectors.