Fuzzy multidimensional scaling

FALSCAL: A fuzzy multidimensional scaling algorithm

The conventionally adopted Alternating Least squares SCALing (ALSCAL) procedure of multidimensional scaling (MDS) is a valuable mathematical scheme for analyzing data in areas where organized concepts and underlying dimensions are inadequately defined or developed. Fuzzy set theory (FST) attempts to formulate human reasoning and perceptions, therefore targeting problems in areas where human fac...

Multidimensional scaling of fuzzy dissimilarity data

Multidimensional scaling is a well-known technique for representing measurements of dissimilarity among objects as distances between points in a pdimensional space. In this paper, this method is extended to the case where dissimilarities are expressed as intervals or fuzzy numbers. Each object is then no longer represented by a point but by a crisp or a fuzzy region. To determine these regions,...

Fuzzy Dissimilarity based Multidimensional Scaling and its Application to Collaborative Learning Data

Using Multidimensional Scaling for Assessment Economic Development of Regions

Addressing socio-economic development issues are strategic and most important for any country. Multidimensional statistical analysis methods, including comprehensive index assessment, have been successfully used to address this challenge, but they donchr('39')t cover all aspects of development, leaving some gap in the development of multidimensional metrics. The purpose of the study is to const...

Fuzzy Sets and Vague Environments

In this paper we propose a natural approach to handle imprecise numbers as they arise for example from measurements. Fuzzy sets turn out to be a canonical representation for such imprecise numbers that are induced by taking diierent tolerance or error bounds into account. Fuzzy sets are induced by scaling factors that describe the magnitude of the imprecision. On the other, the scaling factors ...

Combining fuzzy AHP with MDS in identifying the preference similarity of alternatives

Multidimensional scaling (MDS) analysis is a dimension-reduction technique that is used to estimate the coordinates of a set of objects. However, not every criterion used in multidimensional scaling is equally and precisely weighted in the real world. To address this issue, we use fuzzy analytic hierarchy process (FAHP) to determine the weighting of subjective/perceptive judgments for each crit...