In this paper, a novel method to solve Fully Fuzzy Mixed Integer Linear Programming (FFMILP) problems is presented. Our method is based on the definition of membership function and a fuzzy interactive technique for solving the classical multiobjective programming. It is worthwhile to note that this is the first time that the fully fuzzy mixed integer linear programming problem is discussed and a solving method is presented. To illustrate the steps of the proposed method, some numerical examples are solved and the results are compared with other methods in the literature. Computational results present the application of the method.

Slotless double-sided outer armature permanent-magnet (PM) linear motors (SDOPMLs) have high efficiency and low detent force. Despite their simple control strategy and easy manufacturing process, finding an accurate model of these motors to calculate the machine quantities is challenging. It is particularly critical for obtaining the optimum design of these machines which may include too many iterations in a short time. To overcome this challenge, a 2-D analytical model based on the subdomain method is presented to determine the magnetic flux density components for the motor under the study. According to this analytical procedure, the motor cross-section is divided to 11 sub-regions, then the superposition theorem is utilized to analyze the flux density distribution in all sub-regions due to various magnetization patterns, (i.e., parallel, two-segment Halbach, ideal Halbach, and bar magnet in shifting directions) as well as armature reaction current, respectively. According to the calculated magnetic flux density components, machine quantities like flux linkage, induced voltage, inductances, and electromagnetic force components are explained. Also, the obtained analytical results are compared with those of the finite-element method (FEM) to confirm the accuracy of the proposed model. The proposed model can be used in the design and optimization stage of the linear slotless motor against the numerical model to save time. Finally, a comparative study between the performance of the single-sided and double-sided slotless PM linear motors in the same volume is implemented. This comparison shows the advantage of the double-sided motor in terms of the unbalanced magnetic force (UMF).