With the incorporation of fuzzy set theory into Multi-criteria decision-making (MCDM), the engineers have modified how they make decisions in consideration of uncertainty and imprecision. Where emotional considerations come into play together with numerical considerations in a given real life problem, a conventional decision making process does not apply well. At the time when Zadeh invented the fuzzy set theory, fuzzy set could handle vague and incomplete data and hence it is highly applicable in engineering. When we do not know what will happen, Fuzzy Analytic Hierarchy Process (FAHP) and the Fuzzy Technique of Order Preference by Similarity to Ideal Solution (Fuzzy TOPSIS) simplify the process of comparison and ranking of options. The paper examines such approaches and provides an explanation and examples mathematically and in the field of engineering.