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It is very difficult and important to construct Bell inequalities forn-partite, k-settings of measurement, and d-dimensional (n,k,d) systems.Inspired by the iteration formula form of theMermin-Ardehali-Belinski{\u{\i}}-Klyshko (MABK) inequality, we generalize themulti-component correlation functions for bipartite d-dimensional systems ton-partite ones, and construct the corresponding Bell inequality. TheCollins-Gisin-Linden-Massar-Popescu inequality can be reproduced by this way.The most important result is that for prime d the general Bell function infull-correlated multi-component correlation function form for (n,2,d) systemscan be reformulated in iteration formula by two full-correlated multi-componentBell functions for (n-1,2,d) systems. As applications, we recover the MABKinequality and the most robust coincidence Bell inequalities for(3,2,3),(4,2,3),(5,2,3), and (3,2,5) Bell scenarios with this iterationformula. This implies that the iteration formula is an efficient way ofconstructing multi-partite Bell inequalities. In addition, we also give somenew Bell inequalities with the same robustness but inequivalent to the knownones.

The Iteration Formula of (n,2,d) Full-correlated Multi-component Bell Function and Its Applications