Sustainable development implies establishing principles, objectives and strategies within organizations that impact the organizational culture in innovation. However, a method needs to be defined in order to know the critical factors that allow the strengthening of the organizational culture in innovation with emphasis on Industry 4.0 and sustainable development in a highly changing environment for a specific organization. In this sense, the paper identifies the set of factors that are documented through reviews and analysis of the literature, subsequently proposes a Multi-Criteria Decision Making (MCDM) methodology using hesitant fuzzy linguistic term sets (HFLTS) and combinative distance-based assessment (CODAS), where factors are evaluated to obtain a score and hierarchy value. Weight values were calculated using the ambiguity reduction method, which incorporates the knowledge acquired by researchers in organizational culture of innovation and expert judgment under the Saaty scale used in analytic hierarchy process (AHP). Finally, a model of organizational culture in innovation is proposed that can be used by organizations to focus strategies on the factors of greater hierarchy and thereby optimize their resources considering the sustainable development and the Industry 4.0 approach.