Natural disasters have always been difficult to manage because of their spatio-temporal scale. Although the use of GIS and RS has made this process somewhat simpler, there are still serious challenges in managing and smart allocating human resources, increasing operational power and cost savings, continuous monitoring, and ensuring the effectiveness of the relief activities. The development of VGI and the studies of big data have provided the prerequisite for the introduction of the crowdsourcing service into the GIS. In this research, we tried to solve some of the problems and challenges of crisis management by relying on the characteristics of the crowdsourcing service and its integration with the GIS. Dividing complex emergency processes into atomic crowdsourcing services in a wireless mobile environment is regarded as an appropriate solution. Proposed atomic crowdsourcing services include an informative, content, and confirmative segment. Composing such services can manage sophisticated crisis fields. But, the use of services necessitates a robust and operational framework. This framework must also be capable of simulating the environment in addition to executing, managing, and communicating with the environment. However, current crisis management frameworks cannot cover all these issues at the same time. The present study aims to design a crisis crowdsourcing mathematical framework, which has been constructed upon vector space elements, tensors, and geometrical products. Vectors simulate crisis environment for main objects in a multi-dimensional space. In addition, operations are coincided with possible actions among crisis objects. Framework introduces tools to compose and arrange services in optimum mode to conquer complex aiding process. Since low-speed and high processing load are among the fundamental problems of existing software frameworks, the use of tensors and matrices in frameworks increase the speed and decrease the processing load due to cumulative integrated computing. Further, it offers a mathematical intelligible documentation method, which is able to record the processing details as well as the object status in space. On the other hand, although tensors are widely used in other fields of engineering, there is little record of their use in GIS or crisis management. Thus, with the designed framework, it is possible to use the experiences gained from other disciplines. Different scenarios have confirmed the accuracy and efficiency of the framework in deploying potential of crowds. It offers an environment to easily incorporate people in a wireless mobile application, to tackle emergency process. Indeed, rather than the social aspects of research in providing a new IT-based methodology for employing crowd’s ability, this research has implemented a special math framework for managing new proposed crowdsourcing services that is easily implemented through a mobile GIS system in a wireless network.
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