Please make the question clearer. Do you need a mathematical relationship or what?
These 3 analyses are very different but they can all be carried out off-line (ex-situ)for the liquid (fuel) sample; Fourier Transform Infrared (FT-IR) spectroscopy tells more about the functional groups present in the sample (eg. OH, C=0 etc), Gas chromatography–mass spectrometry (GC-MS) gives you a break down of the fatty acid (the dominant group in the oil) composition (eg. Stearic acid- 20%, oleic acid- 11% etc) while heating value tells more about energy dissipation capacity of the fuel. FT-IR.
While GC-MS and Heating value analyses are destructive (consuming the sample), FT-IR analysis may not be destructive if the exposure of the oil to IR radiation would not impair its qualities.
I hope this would be helpful, if not, try and be specific.
Again,I could have suggested that you carry out experiments to determine the relationship but FT-IR and GC-MS are analysis techniques not properties of the oil.
Virtually all oils have the same functional groups present with just few variations. The higher the molecular weight (as obtainable from GC-MS fatty acid profile), the higher the high-heating value. Higher unsaturation (as obtainable from FT-IR analysis) favors the higher heating value.