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This paper puts across the various approaches and methods that have been proposed in the context of Fuzzy Mathematical Morphology. The underlying principles of Dilation & Erosion, the structuring elements used in various techniques, the unique variations put forth by researchers, new applications in spatial relationships, decision making, segmentation of medical images have been discussed.

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Abstract-DataWarehouse is the cornerstone for organizations that base their strategic decisions on the large scale processing of numerical data. The success of the organization depends on these decisions and hence it becomes extremely important to have a quality data warehouse. Conceptual models have been widely recognized as a key determinant of data warehouse quality during the early stages of design. Recently, metrics have been proposed by authors based on hierarchies to quantify the complexity and inturn quality of the conceptual models of data warehouse. They have formally corroborated the measures against Briand's property based framework to ensure their validity. However, Briand's set of properties for software measures are a set of necessary but not sufficient measure axioms. They are advantageous to refute software metrics but not to validate them. Thus, we focus on the theoretical validation of the data warehouse conceptual model metrics using the Distance framework whose sufficiency is ensured by the measurement theory. The results indicate that the metrics are valid measures of the complexity of data warehouse conceptual models. Besides, validation by Distance framework assures that the metrics are in the ratio scale which further aids in data analysis.