As a result of the development in multimedia technology and direct dealing with it in social media, it has led to interest in the techniques of compacting color images because of their importance at present. Since image compression enables the representation of color image data with the fewest number of bits, which reduces transmission time in the network and increases transmission speed. To ensure the compression process is performed without loss of data, the lossless compression methods are used because no data is lost during the compression process. In this research, a new system was presented to compress the color images with efficiency and high quality. Where the swarm intelligent methods were used, as well as hybridizing it with fuzzy using the Gustafson kessel fuzzy method to improve the clustering process and create new clustering methods with fuzzy swarm intelligence to obtain the best results. Swarm algorithms were used to perform the process of clustering the image data to be compressed and then obtaining a clustered data for this image data. In contrast, a lossless compression method was used to perform the encoding of this clustered data where the huffman method was used for encoding. Four methods were applied in this research to different color and lighting images. The PSO swarm intelligent was used, which in turn was hybridized with the Gustafson kessel fuzzy method to produce a new method for fuzzy particle swarm (FPSO), as well as the grey wolf optimization method GWO, which was hybridized with Gustafson kessel and obtained a new method, which is the fuzzy grey wolf optimizer FGWO, and the results were graded efficiently from the first to the fourth method, where the FGWO method with the huffman was the most efficient depending on the standards measurement that were calculated for all methods, the compression ratio was high in this new method, in addition to the standards of MSE, RMSE, PSNR, etc. among the important measurements of the compressing process.