85 references [2] and [11], and later various formulae to construct dependent functions have been successively established in many papers and treatises. This book sorts out theses formulae, proposes several basic formulae, and explicitly defines several basic concepts. Any inconsistency with the previous treatise of the author should be subject to this book. 2.7.3.1 Several Basic Concepts In our real life, the qualifying degree of the measure of an object in universe of discourse U about certain characteristic usually has a desirable interval X0= and an acceptable interval X=, and it’s obvious that X  X0. For example, when buying a piece of clothing, there is a desirable price interval in one’s mind <200 yuan, 250 yuan >, and an acceptable price interval <200 yuan, 280 yuan>. During product inspection, the work piece conforming diameter is <5cm, 5.1cm>, as a desirable interval, but during measurement by vernier calipers, a deviation of ±0.01cm is allowable, in other words, <4.99cm, 5.11cm> is an acceptable interval. When no transformation is implemented, the measure of the object about certain characteristic is within the acceptable interval , which indicates the object has certain property, with degree expressed by a real number between (0,) , and these objects constitute the “positive field” in the static extension set introduced in section 2.6; Contrarily, when the measure of object about certain characteristic is out of the acceptable interval , it’s indicated that the object does not have certain property, with degree expressed by a real number between (,0) , and these objects constitute the “negative field” in the static extension set introduced in section 2.6; when the measure value of object about certain characteristic is a or b, the corresponding object is critical object with corresponding dependent function value of zero, and the whole constitute the “zero boundary” in the static extension set introduced in section 2.6. Here we call the desirable interval X0= standard positive field, and interval X  =∪ transition positive field. Similar to a positive field, a negative field also has a transition negative field and a standard negative field. For example, the motor in a hydropower station frequently operates under the level of dead water, and fails only when the water level drops under a certain threshold. In other words, there is a transitional process for when an object changes from its critical state to losing certain property. Suppose a real number field is  , denote transition negative field by X  =∪, let Xˆ = X ∪ X =, the interval of measures in negative field is X    X , and the interval of measures in standard negative field is X 0    Xˆ . Thus, the Universe of discourse U can be classified into   Standard positive field Positive field  Transition positive field   Universe of discourse U Criticality  Standard negative field  Negative field  Transition negative field 