Decisions involved in process synthesis are often more complex than those involved in other disciplines. This arises from the fact that such decisions are concerned with specification or identification of highly interconnected systems, e.g. process structures, which may contain a multitude of recycling loops. It appears that no rigorous technique is available. which is capable of representing exactly and organizing efficiently the system of decisions for a process synthesis problem. A novel mathematical notion, decision-mapping, has been introduced in this work to render the complex decisions in process design and synthesis consistent and complete. The basic terminologies of decision-mapping, including extension, equivalence, completeness, complementariness, and active domain, have been defined based on rigorous set-theoretic formalism, and the most important properties of decision-mappings have been identified and proved. Decision-mapping, as a rigorously established technique, is directly applicable in developing efficient and exact process synthesis methods or improving existing methods. The applicability and meritorious features of this new technique are illustrated by synthesizing a large scale process.