Due　to　the　complexity　of　society　and　the　high　degree　of　uncertainty　of　the　issues　faced,　precise　numbers　are,　in　many　cases,　difficult　to　describe　their　nature.　And　to　deal　with　the　problem　that　the　existing　interval　grey　number　distance　method　does　not　reflect　the　characteristics　of　interval　grey　number　well.　This　paper　introduces　a　distance　entropy　to　assign　different　weights　to　the　upper　and　lower　bounds　and　the　kernel.　To　prevent　the　extreme　value　bias　of　the　grey　correlation　coefficients,　we　propose　a　relative　weight　to　constrain　the　extreme　values.　Considering　the　loss　aversion　of　decision-makers,　an　extended　TODIM　is　proposed,　which　combines　the　corresponding　gains　and　losses　to　obtain　the　perceived　dominance　degree.　From　the　method　proposed　in　this　paper,　the　perceived　dominance　degree　is　established　to　provide　the　ranking　of　the　decision　alternatives.　A　case　of　selecting　an　artillery　weapon　for　a　certain　unit　is　used　to　validate　the　proposed　method,　followed　by　a　comparative　analysis.