Arithmetic operator hierarchy

Parentheses are used in the usual algebraic fashion to prevent errors caused by the hierarchy of arithmetic operations (multiplication or division is performed before addition or subtraction, for example). 

Table 2.2 Hierarchy of arithmetic operations (in order from high to low) ...

This grammar defines simple expressions consisting of numbers and the two arithmetic operators plus and times, obeying the usual hierarchy of operators used in mathematics. The second group of rules (or productions), for example, define a term. A term is a number, followed by a times symbol, followed by a term or a term is simply a number. Generally, a rule like... 

Operation nodes These nodes represent operations like arithmetic operations (-h, X, -r), boolean operations (A, V, <, >), or more complex operations. The complex operation nodes provide hierarchy within the graph semantics as used in description languages (procedures, functions). 

A basic requirement for the correct calculation of arithmetic and algebraic expressions is the adherence to the correct hierarchy, or order, of operations. Table 2.2 shows that parentheses have the... 

ABSTRACT By analyzing the hierarchy of safety factors in purification plant of natural gas, they are divided into personnel, equipment, environment and management. After the study of safety index, evaluation methods and fuzzy arithmetic method for each hierarchy, its fuzzy evaluation flow is given. During the evaluation, the weight of the factors and each hierarchy is decided by analytical hierarchical process, and the operational criterion adapts maximum membership degree. And this model is exemplified in purification plant of natural gas. The results show that the second fuzzy evaluation is effective to assess purification plant of natural gas. 

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