A new modularization technique is used in Aspect-oriented software development for the separation of widely used functions such as logging, caching, synchronization, and exception handling from the core business logic functions. Aspects are identified using the mathematical modeling tool, Colored Petri nets. During the software development process, dependencies may arise as a result of using operators such as Before, After, Around, and Replace; such dependencies are consumed by our framework. Using the specification of aspects, we generate a composition rule for every match point, which directs the composition process at the initial requirements phase of software development. The proposed FTS approach, incorporating a feedback edge set, topological ordering, and second valid ordering, is efficient in resolving conflicts and dependencies among the aspects. To analyze the second valid ordering, grey relational analysis is used to rank the aspects, while analysis of variance method is used for the verification thereof. The proposed approach is illustrated by a case study. © 2014, King Fahd University of Petroleum and Minerals.