Why when a cationic surfactant such as C16TAC when interacting with an anionic dye (Indigo carmine) above the CMC, the absorbance of dye increases with increasing the concentration of C16TAC but no blue or red shift was observed ?
If "absorbance of dye increases with increasing the concentration of C16TAC but no blue or red shift was observed" it is probably not really absorbance but reflection. Your mixture is probably producing a colloidal solution. Verify Tyndall effect. If this is the case the incident light is being reflected and not reaching the detector what makes the equipment interpret as absorbed light.
Have you verified Tyndall effect? Air is transparent but it has dust and small particles, water vapor, etc. Colloidal solutions may look very much as true solutions.
But if you did, then another possibility can be that when mixing C16TAC with indigo carmine they react and form a substance that absorbs another light color which is not red or blue complementary. I mean that maybe there's a new wavelength of absorbance which is not complementary of red and blue together with red and blue complementary.
But as "Surfactants are compounds that lower the surface tension (or interfacial tension) between two liquids, between a gas and a liquid, or between a liquid and a solid. Surfactants may act as detergents, wetting agents, emulsifiers, foaming agents, and dispersants" I still think you have a problem with formation of colloids.
Normally when some interaction occurs between a chromophore (dye) and some species, this will affect the energy levels in chromophore and leads to red or blue shift. Sometimes, the absorption intensity increases (hyperchromic) or decreases (hypochromic). There are various factors that can cause these changes. One of them is due to solvatochromism (the behavior of a molecule changing its color as a result of the solvent polarity).
With dyes and surfactants, i think the increasing in dye absorbance is due to its solubility in surfactants which plays as a solvent and there are not a strong binding between them