Not sure exactly what you are looking for in your question. If you are looking for a single formula that will give a simple yes/no answer for whether any given three lengths can compose a triangle, I suppose you could have a brute force solution such as:
$(a + b - c) + (b + c - a) + (a + c - b) - (|a+b-c| + |b+c-a| + |a+c-b|)$
Which simplifies to:
$(a + b + c) - (|a+b-c|+|b+c-a|+|a+c-b|)$
If your result is less than 0, then the three sides cannot compose a triangle. The logic is that all three variations of the inequality need to be greater than zero. If they all are, then their absolute values are equivalent and the expression above would yield 0 as the result. If any of the inequalities are negative, then subtracting the absolute value will leave an even more negative number in your result.