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In this work, inspired by the concepts of cybernetics and viable system model (VSM), we present an Innovation road-map under the environment of cybernetic physical systems and their supporting digital ecosystems. The proposed road-map is defined as the Viable Cybernetic Innovation Ecosystems (VCIEs) composed of the Viable Cybernetic System, the Digital Ecosystem, the Innovation Ecosystem, the User/Consumer Ecosystem, the KM System, the Practice Ecosystem, and the Knowledge Ecosystem & Innovation Governance. We used Fuzzy Neutrosophic Multi-Criteria Models to assess the directions and efficiencies of influences resulting from the interactions between the aforementioned dimensions of the road-map so as to capture key leading influential dimensions and their criteria that can build up the innovation road-map under the environment of cybernetic physical systems and their underlying technologies of digitization that paves a way for innovation in smart manufacturing, smart cities, smart businesses, and smart technologies.