**Measuring in Weighted Environments: Moving from Metric to Order Topology (Knowing When Close Really Means Close)**

Claudio Garuti

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/63670

#### **Abstract**

This chapter addresses the problem of measuring closeness in weighted environ‐ ments (decision-making environments). This chapter show the importance of having a trustworthy cardinal measure of proximity in weighted environments. A weighted environment is a nonisotropic structure where different directions (axes) may have different importance (weight), thus there exist privilege directions. In this kind of structure, it would be very important to have a cardinal reliable index that can say the closeness or compatibility of a set of measures of one individual with respect to the group or to anyone other. Common examples of this structure are the interaction between factors in a decision-making process (system-values interaction), matching profiles, pattern recognition, and any situation where a process of measurement with qualitative variables is involved.

**Keywords:** weighted environments, measurement, compatibility, compatibility index G, order topology
