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Software effort estimation at early stages of project development holds great significance for the industry to meet the competitive demands of today's world. Accuracy, reliability and precision in the estimates of effort are quite desirable. The inherent imprecision present in the inputs of the algorithmic models like Constructive Cost Model (COCOMO) yields imprecision in the output, resulting in erroneous effort estimation. Fuzzy logic based cost estimation models are inherently suitable to address the vagueness and imprecision in the inputs, to make reliable and accurate estimates of effort. In this paper, we present an optimized fuzzy logic based framework for software development effort prediction. The said framework tolerates imprecision, incorporates experts knowledge, explains prediction rationale through rules, offers transparency in the prediction system, and could adapt to changing environments with the availability of new data. The traditional cost estimation model COCOMO is extended in the proposed study by incorporating the concept of fuzziness into the measurements of size, mode of development for projects and the cost drivers contributing to the overall development effort.