Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values

Abstract

Moore's interval arithmetic always provides the same results of arithmetic operations, e.g. [1, 3]+ [5, 9]= [6, 12]. But in real life problems, the operation result can be different, e.g. equal to [4, 7]. Therefore, real problems require more advanced arithmetic. The paper presents (on example of the division) an arithmetic of intervally-precisiated values (IPV-arithmetic) and its main advantages. Thanks to it, it is possible to process different tasks that people solve intuitively. The most important advantages are: existence of inverse elements of addition and multiplication, holding the distributivity law and the cancellation law of multiplication, possibility of achieving not only the solution span [x̲, x̄] but also the full, multidimensional solution and its cardinality distribution without using Monte Carlo method, possibility of achieving unique and complete solution sets of equations with unknowns, possibility of calculations with uncorrelated IPVs, possibility of calculations with fully correlated and partly correlated IPVs, possibility of uncertainty decreasing of original data items occurring in problems. All these advantages are illustrated and visualised by examples.

Keywords

• Interval arithmetic
• Interval-precisiation arithmetic
• Granular computing
• Interval equations
• Computing with words