TY - JOUR AU - Zamirian, M. AU - Kamyad, A. V. PY - 2011 TI - Fuzzy Path Planning in a Plane with Stationary Obstacles JO - Journal of Mathematics and Computer Science SP - 417--424 VL - 2 IS - 3 AB - In this paper a new approach for finding optimal path planning in a plane with stationary obstacles is discussed. At first, we consider a movable rigid object in a plane with stationary obstacles. The goal is to find the shortest path planning which brings rigid object from a given initial point to a given final point such that the length of path be minimized and distance between object and obstacles be maximized. By considering the length of path and the distance between rigid object with obstacles as objective functions, we obtain a multi-objective problem. Because of the imprecise nature of decision maker's judgment, these multiple objectives are viewed as fuzzy variables. Then we determine intervals for the value of objective functions such that these intervals for the distance between rigid object and obstacles are given by decision maker, and for the length of path is achieved by solving two optimal nonlinear problems (ONP). Now, we define a decreasing or increasing membership function for any objective functions on achieved intervals. Then the optimal policy is to find an optimal path which maximize all of membership functions, simultaneously. After a little calculation, we obtain an ONP. By solving this ONP, a (local) Pareto optimal solution for original goal is attained. Numerical example is also given. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.02.03.03 DO - 10.22436/jmcs.02.03.03 ID - Zamirian2011 ER - TY - BOOK TI - Robot motion planning AU - J. C. Latombe PB - Kluwer Academic Publishers PY - 1991 DA - 1991// CY - Boston ID - Latombe1991 ER - TY - JOUR TI - Two novel approaches for unmannd under water vehicle path planning: constrained optimization and semi-infinite constrained optimization AU - Y. Wang AU - D. M. Lane AU - G. J. Falconer JO - Robotia PY - 2000 DA - 2000// VL - 18 ID - Wang2000 ER - TY - JOUR TI - Solving some optimal path planning problems using an approach based on measure theory AU - A. H. Borzabadi AU - A. V. Kamyad AU - M. H. Farahi AU - H. H. Mehne JO - Applied Mathematics and Computation PY - 2005 DA - 2005// VL - 170 ID - Borzabadi2005 ER - TY - BOOK TI - Nonlinear multi-objective optimization AU - K. Mittinen PB - Kluwer Academic PY - 1993 DA - 1993// CY - New York ID - Mittinen1993 ER - TY - BOOK TI - Multiobjective programming and planning AU - J. L. Kohon PB - Academic Press PY - 1985 DA - 1985// CY - New York ID - Kohon 1985 ER - TY - BOOK TI - Fuzzy set and interactive multi-objective optimization AU - M. Sakawa PB - Plenum Press PY - 1993 DA - 1993// CY - New York ID - Sakawa1993 ER - TY - BOOK TI - A possibility approach for multi-objective programming problems AU - M. Delgado AU - J. L. Verdegay AU - M. A. Vila PB - Kluwer Academic PY - 1991 DA - 1991// CY - New York ID - Delgado1991 ER - TY - BOOK TI - Control and optimization: the linear treatment of nonlinear problems AU - J. E. Rubio PB - Manchester University Press PY - 1986 DA - 1986// CY - Manchester ID - Rubio 1986 ER -