Nowadays, the importance of solving urban problems from the smallest unit, the neighborhood, has been obvious for planners. Gaining knowledge of sustainability and moving towards sustainable development have been in focus for decades. Sustainable neighborhood is introduced as the foundation of sustainable urban development. Neighborhoods attempt to appropriate their structure according to the needs of today's residents, and approach again the components missing since previous times. Historical neighborhoods that suited the needs of their residents were formed and became responsive to most of the needs of their residents. The present study aims to measure and assess sustainability indicators on the neighborhood scale, in neighborhoods of the historical texture of Yazd city (Iran). To achieve the above objective, fuzzy logic was used to measure the sustainability of neighborhoods. The results showed that neighborhoods of the historical texture are not appropriate in terms of sustainability conditions because these conditions are poor and below average. Among the nine historical neighborhoods, Godal-mosalla neighborhood, with a value of 0.474 as compared to others, is in a better condition. The next ranks belong to Sheikhdad, Fahadan, Shessh-dadgiri, Poshte-bagh, Gazargah, Gonbade-sabz, Dolat-abad, and Zartoshtiha. It is obvious that the current situation is not confirmed by the sustainable neighborhood criteria and sustainable city approach, and the city managers have a long way toward achieving those approaches. Therefore, improving the unsustainability of historical neighborhoods in four dimensions, namely economic, environmental, physical and social, with an emphasis on "justice" particularly in unstable neighborhoods should be of priority for promotion.