Strain-hardening cement-based composites (SHCCs) are high-performance fibre-reinforced composites characterised by their high ductility under tensile load. To utilise their advantageous properties fully, a performance-based durability concept is required. Probabilistic approaches developed for crack-free ordinary concrete provide a rational basis for this. However, the approaches currently available require extension due to a lack of data required to quantify the input variables and the need to adapt the underlying analytical formulas describing chloride ingress. These formulas need to account for material-specific conditions and resultant behaviour, such as multiple cracking in the case of SHCC. In this first part of a two-part treatise, a fuzzy-probabilistic concept to assess the durability of SHCC exposed to chlorides is presented. The analytical solution for chloride ingress used in the DuraCrete approach has been adapted to allow for a mathematically correct description of the influence of aging and to reflect clearly the contribution of cracks to chloride ingress. Furthermore, the considerable non-stochastic uncertainty associated with most variables in a new material is accounted for with the help of fuzzy-probability theory. In the second part, the durability of a SHCC member exposed to a marine environment will be assessed using this new concept.