Volatile compounds, physicochemical and sensory attributes of four sweet cherry cultivars (Canada giant, Ferrovia, Lapins and Skeena) grown in Northern Greece were determined. Eighteen volatile compounds were identified and semi-quantified in cherries using solid phase micro extraction in combination with gas chromatography/mass spectrometry (SPME-GC/MS). Carbonyl compounds were the most abundant in sweet cherry aroma, followed by alcohols, esters and hydrocarbons/terpenes. Cherry cultivars in order of increasing amounts of volatiles were: Lapins < Canada giant < Ferrovia < Skeena. Physicochemical parameters determined included: titratable acidity (TA), pH, total soluble solids (TSS), maturity index (MI) and total phenolic content (TPC). TA ranged between 0.21 and 0.28 g malic acid/100 g fresh weight (FW). The pH ranged between 3.81 and 3.96. TSS ranged between 13.00 and 16.00 °Brix. MI ranged between 51.8 and 75.0. TPC ranged between 95.14 and 170.35 mg gallic acid equivalents (GAE)/100 g FW. Sensory evaluation showed that cherry colour, in order of increasing intensity, was: Canada giant < Ferrovia < Lapins < Skeena. Respective order for cherry firmness was: Canada giant < Lapins ≤ Ferrovia < Skeena and for flavour: Lapins < Canada giant < Skeena ≤ Ferrovia. Correlation of volatiles to physicochemical and sensory attributes showed varying trends.

We consider a finite, irreducible, aperiodic, time homogenous Markov chain on a fuzzy partition and for the resulting aggregated process we study two aspects emerging from the classical theory on hard partitions. The first aspect is lumpability, a technique for recovering from the large state space of a stochastic system. We provide necessary and sufficient conditions for strong lumpability on the transition probabilities of the original chain for the lumped process to have the Markov property. The second aspect is the asymptotic behavior of the lumped chain The results are compared with those existing in the classical theory of hard partitions.