This doctoral dissertation research aims to develop a comprehensive definition of urban open spaces and to determine the extent of environmental, social and economic impacts of open spaces on cities and the people living there. The approach I take to define urban open space is to apply fuzzy set theory to conceptualize the physical characteristics of open spaces. In addition, a 'W-green index' is developed to quantify the scope of greenness in urban open spaces. Finally, I characterize the environmental impact of open spaces' greenness on the surface temperature, explore the social benefits through observing recreation and relaxation, and identify the relationship between housing price and open space be creating a hedonic model on nearby housing to quantify the economic impact. Fuzzy open space mapping helps to investigate the landscape characteristics of existing-recognized open spaces as well as other areas that can serve as open spaces. Research findings indicated that two fuzzy open space values are effective to the variability in different land-use types and between arid and humid cities. W-Green index quantifies the greenness for various types of open spaces. Most parks in Tempe, Arizona are grass-dominant with higher W-Green index, while natural landscapes are shrub-dominant with lower index. W-Green index has the advantage to explain vegetation composition and structural characteristics in open spaces. The outputs of comprehensive analyses show that the different qualities and types of open spaces, including size, greenness, equipment (facility), and surrounding areas, have different patterns in the reduction of surface temperature and the number of physical activities. The variance in housing prices through the distance to park was, however, not clear in this research. This dissertation project provides better insight into how to describe, plan, and prioritize the functions and types of urban open spaces need for sustainable living. This project builds a comprehensive framework for analyzing urban open spaces in an arid city. This dissertation helps expand the view for urban environment and play a key role in establishing a strategy and finding decision-makings.