الفهرس 
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Abstract
Abstract Multidimensional scaling and cluster analysis are two numerical techniques that assist the researcher in ascertaining the structure of data in some abstract psychological space. Multidimensional scaling allows the researcher to convert large amounts of similarity or proximity data into a geometric picture while Cluster analysis represents an area of statistics that is concerned with sorting the observed data into some groups (clusters) based on the similarity.
It is highly recommended to perform cluster analysis in conjunction with MDS for many reasons:
(i) Cluster analysis may provide the researcher with ways of understanding similarity criteria when interpretations of geometric dimensions are not readily apparent.
(ii) In some clustering problems as in case of lacking metric data attributes. For example, we only have the dissimilarities between data objects. The dissimilarity between two data objects can be metric or nonmetric. To obtain data in the metric space from these dissimilarities, a possible solution is using multidimensional scaling (MDS).
There are several models of MDS and CA available to the researcher; the choice mainly depends upon the type of data believed to be under the study.
In this thesis, several models of MDS and CA were introduced. In addition, we provided a solved mathematical example for each models.
Since the MDS and cluster analysis are mainly based on the proximity data, we introduced the different patterns of proximity measures (similarity and dissimilarity) in addition to solved mathematical example for each measure.
In this study we performed an application of cluster analysis and multidimensional scaling on one data set from different car exhibitions and agencies in Benha city. The data was collected based on the responses we received in all the questionnaires which were distributed among different car exhibitions in Benha city. The sample size was 20 customers. The Twenty customers were asked to rate the 10 cars by showing the cards bearing the name of a pair of cars. All possible pair of cars were shown, and the customers were asked to rate their preferences of one car over the other on a scale of 100 points. If the customer perceived that the two cars were completely dissimilar, a score of 0 was given, and if the two cars were exactly similar a score of 100 was given. The Statistical Package for Social Sciences (SPSS) was used in order to apply the multi-dimensional scaling to convert cars market similarity data into a geometric picture. SPSS was then used to group different cars brands in this geometric map into some clusters. After finalizing the analysis and getting the result, we performed interpretations of the results and provided insights for some companies to know how their brand of products is rated among other similar competing brands of other companies.
To achieve the purpose of this study, the thesis consists of five chapters as follow:
Chapter I: An introduction includes a background on multidimensional scaling and cluster analysis in addition to the aims of the study.
Chapter II: Measures of proximity which discuss the different patterns seen in proximity measures (similarity and dissimilarity).
Chapter III: Multidimensional scaling in terms of concepts and methods.
Chapter IV: Cluster analysis in terms of concepts and methods.
Chapter V: An application of cluster analysis and multidimensional scaling.