Technology roadmaps have already been widely adopted as an important management tool during the past three decades after the invention of the management tool by Motorola in the 1980s. The technology road-mapping processes which can be integrated with firms' competence sets are very important for strategy definitions. However, how the uncertainties being associated with the costs, time, quality, etc. for technology road mapping were seldom discussed, not to mention how various objectives can be considered at the same time. Thus, this research aims to propose a fuzzy multiple objective programming based competence set expansion technique to resolve the above mentioned technology road-mapping problem. An empirical study based on the road-mapping of novel compressors for air conditioners will be used to demonstrate the feasibility of the proposed framework. The well-verified analytic framework can serve as a basis for research and development (R&D) strategy definitions by practitioners.