Abstract- This paper shows that maintaining logical consistency of an iris recognition system is a matter of finding a suitable partitioning of the input space in enrollable and unenrollable pairs by negotiating the user comfort and the safety of the biometric system. In other words, consistent enrollment is mandatory in order to preserve system consistency. A fuzzy 3-valent disambiguated model of iris recognition is proposed and analyzed in terms of completeness, consistency, user comfort and biometric safety. It is also shown here that the fuzzy 3-valent model of iris recognition is hosted by an 8-valent Boolean algebra of modulo 8 integers that represents the computational formalization in which a biometric system (a software agent) can achieve the artificial understanding of iris recognition in a logically consistent manner.

I. INTRODUCTION Because the visual acuity of the human agent is doubled by its intelligence – both of them together ensuring an excellent quality in indentifying the (dis)similarity of iris images, the geometry that illustrates the binary decisions given by the human agent during a Turing test [11] of iris recognition is very simple (Fig. 1.a): it consists of one collection of crisp points (0 and 1) and one histogram that counts how many times a decision of unitary score (1 - for the case of similar irides) or a null decision (0 - for the pairs of non-similar irides) was given by the human agent. Still, the geometry that illustrates the fuzzy binary decisions given by a software agent ([6]-[8]) during a Turing test of iris recognition is not that simple: in this case, the fuzzy biometric decisions given by the software agent define (draw) a f-geometry [13] in which the intra- and inter-class score distributions could be a little bit confused (Fig. 1.c, Fig. 2.a, Fig. 2.b), or confused much stronger (Fig. 1.b, Fig. 1.c in [6], Fig. 10 in [4]), or not confused at all. (Fig. 1.b from here, and Fig. 4.a, Fig. 4.b, Fig. 4.c in [6]).