A syllogism is a formal logical scheme used to infer a conclusion from a set of premises. In a categorical syllogism, there are only two premises and each premise and conclusion is given in form a of quantity-quantified relationship between two objects. Different order of objects in premises produce a classification known as syllogistic figures. Ordered combinations of 3 quantifiers with a certain figure, known as moods, provide 256 combinations in total. However, only 25 of them are valid, i.e. conclusion follows from premises. The classical syllogistic system allows to model human thought as reasoning with syllogistic structures. However, a major lack is that there is still no systems that allow to arrive at a decision of syllogisms automatically. This work is an attempt to design a fully algorithmic approach that allows to calculate properties of a whole syllogistic system and provide automated reasoning for given data sets. Since there is a limitation of the classical syllogistic system such as fixed number of crisp quantifiers, advanced fuzzy-quantifiers were introduced to bypass this restriction. Based on the classical syllogistic concept extended by fuzzy-quantifiers, an algorithm for fuzzy-syllogistic reasoning was proposed and integrated into a software system developed for this purpose. Possible applications of syllogistic reasoning, in particular, ontology-based fuzzy-syllogistic reasoning were also discussed.