A rank-expert deviation function to classify complex objects

This paper proposes a novel function for classifying environmental, social, and socio-environmental objects. It is based on the sum of rank deviations between a given object and a reference object considering the significance of the object's characteristics (factors). Characteristics are estimated using weight coefficients, which are provided by expertise or another method. A verbal numerical scale is developed to assess the proximity of objects by the numerical value of the deviation function. As is demonstrated below, this function is not a metric in the geometric sense but a proximity function defined in multidimensional scaling theory. As illustrative examples, the values of the deviation function are calculated for two applications: an environmental problem of comparing the vulnerability of territories to accidental oil spills and an economic problem of choosing real estate objects to purchase. A recommended sequence with a set of procedures based on the deviation function is presented to solve these problems.