# Indetermsoft-Set-Based D* Extra Lie Framework for Resource Provisioning in Cloud Computing
## 1 Introduction  
Cloud computing is a highly expansive platform that supports a broad spectrum of applications, catering to diverse needs across various domains. Its vast infrastructure allows for the scalable deployment of both resource-intensive scientific simulations and lightweight personal applications. By offering on-demand access to computing resources, cloud computing enables flexibility and efficiency, accommodating everything from large-scale data processing to everyday tasks. This adaptability makes it an invaluable tool for organizations and individuals alike, providing the necessary resources to handle complex workloads and drive innovation across different fields. Effective resource management is composed of several activities, which include the provisioning of resources, the reporting of provisioning, task scheduling, and thermal management. The resource management system must be capable of dealing with the huge size, heterogeneity, and changing workload demands of cloud users. The main aim of the resource-provisioning scheme is to achieve the maximum data transfer rate with the minimum incurred cost of transfer. For applications utilizing the cloud, their Quality of Service (QoS) must be upgraded without violating the Service-Level Agreement (SLA). While the resources are provisioned, resource availability must be ensured, deployment must be optimized, and interdependency between the user tasks must be managed very well. The improper provisioning of resources leads to an increase in the host machine downtime, compromised service, the inefficient functioning of the application, energy wastage, prolonged time to scale up/down, inability to satisfy the cost goal of users, etc. [1; 2; 3]. Modern cloud computing structures are utilized to serve computation-intensive applications with large datasets. Resource provisioning is an important aspect of accommodating this use. Potential sources that cause interruption to effective resource provisioning are uncertain operating conditions, performance fluctuations, the improper positioning of the cloud, and the complex infrastructure of a multi-cloud environment. Several forms of uncertainty in the cloud include dynamic elasticity, rapid performance change, large-scale virtualization, loosely coupled applications, the elastic escalation of user demands, etc. These uncertainties make resource provisioning a difficult activity. It is also impossible to determine the workload demands and to obtain the exact knowledge of system parameters like processor speed and bandwidth. Hence, there is a need to develop an intelligent framework with a self-learning ability to make resource-provisioning decisions by properly handling these uncertainties [4; 5]. The classical soft set deals only with the determinate form of data, whose values are obviously certain and precise. However, in real-world scenarios, there are several sources that generate uncertainty, which include a lack of information and ignorance. The Indetermsoft set is an extension of the traditional soft set that is designed to handle the uncertain form of data. The word \"indeterm\" represents indeterminate, reflecting the conflicting and unique form of output. The mathematical definition of the Indetermsoft set is as follows: Let U be the universe of discourse, H be the non-empty subset of U, and P(H) be the power set of H. The Indetermsoft set function \(ISSF:A\to P(H)\) satisfies three properties: the set A has indeterminacy, P(H) has some indeterminacy, and there exists an attribute value \(v\in A\) such that F(v) is indeterminate [6; 7; 8]. D* lite is exactly the reverse of the A* algorithm and is much simpler. The trivial A* algorithm is executed in reverse order; i.e., it begins from the goal state and traverses to the start state. It first determines the current solution and goes into the waiting state until an obstacle occurs. Then, D* lite performs re-planning and incrementally repairs the path by keeping the modifications around the robot's current pose [9; 10].