دانلود کتاب هوش محاسباتی و ریاضیات برای مقابله با مسائل پیچیده 4

The toolkit offered by classical mathematics has undeniable and proven successes in a wide range of applications. Nevertheless, there are more and more problems in real life that require at least approximate solutions. In many cases, the classical mathematical discussion is absolutely hopeless, due to high complexity, uncertain and often confusing (partially contradictory) information. Moreover, in many situations, finding the exact model needs tremendous effort and usually, there is no hope for proper model identification and validation in the classical sense. Although in some cases the mainstream (classic, symbolic) artificial intelligence may provide feasible solutions, it usually works only with a sufficiently large collection of representing data, which can be a great barrier in real life, especially in human-influenced problems. On the other hand, we all experience that Mother Nature may provide various effective solutions for very complex problems. Thus, mimicking the structure or the behaviour of animals or a group of animals, or other living creatures, or modelling human thinking can be a way to a possible solution. Computational Intelligence involves such methods and offers highly competitive solutions to very complex, real-life problems. Besides these successes, the main language of CI remains Mathematics, and interactions of mathematical thinking with CI often unveil interesting, deep connections and enlighten the theoretical background of practical CI methods.