Quantitative Logic and Soft Computing

Admittedly, the notion "intelligence or intelligent computing" has been around us for several decades, implicitly indicating any non-conventional methods of solving complex system problems such as expert systems and intelligent control techniques that mimic human skill and replace human operators for automation. Various kinds of intelligent methods have been suggested, phenomenological or ontological, and we have been witnessing quite successful applications. On the other hand, "Soft Computing Techniques" is the concept coined by Lot? Zadeh, referring to "a set of approaches of computing which parallels the remarkable ability of the human mind to reason and learn in an environment of uncertainty, imprecision and partial truth. " Such a notion is well contrasted with the conventionalbinary logic based hard c- puting and has been effectively utilized with the guiding principle of "exploiting the tolerance for uncertainty,imprecision and partial truth to achieve tractability, - bustness and low solution cost. " The soft computing techniques are often employed as the technical entities in a tool box with tools being FL, ANN, Rough Set, GA etc. Based on one's intuition and experience, an engineer can build and realize hum- like systems by smartly mixing proper technical tools effectivelyand ef?ciently in a wide range of ?elds. For some time, the soft computing techniques are also referred to as intelligent computing tools.