A tolerance is a reflexive and symmetric, but not necessarily transitive, binary relation. Contrary what happens with equivalence relations, when dealing with tolerances one must distinguish between blocks (maximal subsets where the tolerance is a total relation) and classes (the class of an element is the set of those elements tolerable with it). Both blocks and classes of a tolerance on a set...

Based on the analysis of the rough set model on a tolerance relation and the fuzzy rough set, two types of fuzzy rough sets models on tolerance relations are constructed and researched. Then we propose the optimistic and pessimistic multi-granulation fuzzy rough sets models in a fuzzy tolerance approximation space with the point view of granular computing. In these models, the fuzzy lower and u...

It is well known that most of information systems are based on tolerance relation instead of the classical equivalence relation because of various factors in real-world. To acquire brief decision rules from the information systems, lower approximation reduction is needed. In this paper, the lower approximation reduction is proposed in inconsistent information systems based on tolerance relation...

OBJECTIVES: To investigate fasting glucose, glucose tolerance, insulin resistance and insulin–like growth factor 1 in patients with or without colorectal polyps. MATERIALS AND METHODS: In this cross-sectional study, we evaluated fasting glucose, insulin, insulin–like growth factor 1 (IGF-1), lipid profile and glucose tolerance test in 103 patients undergoing colonoscopy (52 normal and 53 wit...

The quotient space theory based on fuzzy tolerance relation is put forward to solve the problem of clustering in this paper. The similarity matrix does not always satisfy ultrametric inequality, theoretically and practically. We give the method to construct the hierarchical quotient space chain if the similarity matrix is only reflexive and symmetric. We consider not only the subset of data (cl...

objectives: to investigate fasting glucose, glucose tolerance, insulin resistance and insulin–like growth factor 1 in patients with or without colorectal polyps. materials and methods: in this cross-sectional study, we evaluated fasting glucose, insulin, insulin–like growth factor 1 (igf-1), lipid profile and glucose tolerance test in 103 patients undergoing colonoscopy (52 normal and 53 with a...

Tolerance design plays a major role in the quality of the product life cycle. Its purpose not only can ensure the products quality. At the same time, it monitors the product manufacturing costs. The traditional the tolerance design devotes to the optimization target of minimizing the manufacturing cost. But due to the manufacturing process of a product, there is a nonlinear relation between tol...

We generalize the notion of an approximation space introduced in 8]. In tolerance approximation spaces we deene the lower and upper set approximations. We investigate some attribute reduction problems for tolerance approximation spaces determined by tolerance information systems. The tolerance relation deened by the so called uncertainty function or the positive region of a given partition of o...

When designing mechanical assemblies, assembly tolerance design is an important issue which must be seriously considered by designers. Assembly tolerances reflect functional requirements of assembling, which can be used to control assembling qualities and production costs. This paper proposes a new method for designing assembly tolerance networks of mechanical assemblies. The method establishes...