Dempster-Shafer theory nowadays is used to model the epistemic (subjective) uncertainty as an alternative to the traditional probabilistic approach. Few decades back, Bayesian probability theory was used for this purpose as to handle problems encountered in different engineering disciplines. Since bayesian theory primarily needs precise measurements from experiments, this requirement restricted its application for problems having weak and sparse information and urged for further research to explore new techniques. In the meanwhile concept of imprecise probability came to light ensued different formalism, among them Dempster-Shafer theory is a prominent frame work. In this thesis Dempster-Shafer theory (D-S Theory) a data fusion technique is discussed along with subsequent improvements for combining conflicting information in D-S structure. In mining engineering during underground extraction of minerals (coal particularly) chances of occurrence of natural hazards like mine fires, gas outbursts, flooding with water and subsidence of overlying strata etc are although rare but with high uncertainty thus provides weak information about the system. Their history having detailed records is short. To wrestle with such problems, Dempster-Shafer formalism is a strong and effective tool. Here in this thesis complete modus operandi of the Dempster-Shafer formalism has been narrated with the help of illustrative examples. And by using this technique, quality of mine air in a coal fire zone is ascertained and a Mine Fire Index (MFI) is developed which is easy to use even for the lower hierarchy of the mine management and is helpful in making decision.