Certain types of M-fuzzifying matroids: A fundamental look at the security protocols in RFID and IoT

Security protocols for RFID and IoT are often built on NP-hard problems. The greedy algorithm is an effective method to solve some NP-hard problems. However, the greedy algorithm can get the optimal solution if and only if the structure of the solutions is a matroid. This paper focuses on M-fuzzifying matroids. The notions of acyclic matroids, simple matroids, paving matroids and uniform matroids are generalized to fuzzy setting, which are called M-fuzzifying acyclic matroids, M-fuzzifying simple matroids, fuzzifying paving matroids and fuzzifying uniform matroids, respectively. From the sense of categorical, the relationships between M-fuzzifying matroids, M-fuzzifying acyclic matroids and M-fuzzifying simple matroids are investigated.