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evaluate the interval functions’ values was proposed also to obviate overestimation, the major drawback in interval computation. In this approach, these interval functions were estimated by solving a series of global optimization problems. An intellective algorithm named as real-code genetic algorithm was used to solve the optimization problems also. Numerical examples were given to illustrate the feasibility and the efficiency. the interval computational model to compute the forward kinematics of robot with uncertain geometric parameters (1) Determinate computational model of robot Fig. 1 D-H convention for robot link coordinate system The robot kinematic model is based on the Denavit-Hartenberg (DH) convention. The relative translation and rotation between link coordinate frame i-1 and i can be described by a homogenous transformation matrix, which is a function of four kinematic parameters , , and as shown in Fig. 1. The homogenous transformation Ai is given in Eq. (1) (1) Using the homogenous transformation matrix the relationship of the end-effector frame with respect to the robot base frame can be represented as in Eq. (2): (2) (2) The robot kinematic model using parameters with interval uncertainty When the kinematic parameters θi, di, αi, ai have no fixed value but having the values falling in the intervals [θi], [di], [αi], [ai] randomly, expanding the Eq. (2) with the intervals, we get, (3) with solution of the interval computational model of robot with uncertain geometric parameters (1) Brief review of some definitions and properties in interval mathematics [7-8] For two interval number and , ( , is the set of real compact intervals), the interval arithmetic was defined as follows. , , and (for ). If , then the interval degenerates to a real number a, i.e. . In this way, interval mathematics can be considered as a generation of real numbers mathematics. However, only some of the algebraic laws, valid for real numbers, remain valid for intervals. The other laws hold only in a weaker form. For example, a non-degenerate interval has no inversion with respect to addition or multiplication. Even the distributive law has to be replaced by the so-called subdistributivity (4) Let be given by a mathematical expression , which is composed by finitely many elementary operations and standard functions . The following inclusion monotone holds. for (5) where,f([x]) is an interval also and which stands for an interval arithmetic evaluation of f over .As x∈[x] , the relation (6) can be obtained. (6) whence (7) Where R(f,[x]) denotes the range of f over . (2) A new approach to evaluate interval functions Overestimation is a major drawback in interval computation. Based on the inclusion monotone relation (7) and the physical/real means expressed by the interval function, a new approach to evaluate interval functions was proposed in this work. Relation (7) is the fundamental property on which nearly all applications of interval arithmetic are based. It shows that it is possible to compute lower and upper bounds for the range over an interval by using only the bounds of the given interval without any further assumption. Obviously, the true value of is existing and unique.