Fuzzy demographic analysis using fuzzy regression models based on fuzzy distance–A case on the impact of fuzzy demographic factors on monetary aggregates in Canada versus Japan
Affiliations: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada
Correspondence:
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Corresponding author. Soheil Sadi-Nezhad, Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada. E-mail: [email protected].
Abstract: The concern for the relationship between demographic changes and asset markets has increased from beginning of 2000. Many researchers analyze the relationship between demographic changes and asset prices through regression models. Most of these studies apply linguistic terms for each different phase of the life cycle (e.g. late working-aged, elderly, adult, and middle-aged) and then define a specific behaviour for each of these cohorts. Although these terms are vague, all the researchers define them as a crisp set with crisp partitions. Additionally, fuzzy regression methods have attracted growing interest from researchers in various scientific, engineering, and humanities area due to the ambiguity in real data. The motivation of this research is that it is rational to consider and apply fuzzy sets to interpret these linguistic terms instead of the crisp partitions. In this study, we propose and apply a new approach in order to calculate the fuzzy frequency for the linguistic term, which can be useful in any other demographic study. Moreover, new fuzzy regression models are developed. These regression models, that are able to consider both fuzzy and crisp regression coefficients are developed based on applying a fuzzy distance concept in which the distance between two triangular fuzzy numbers (TFNs) or between a TFN and a crisp number is a TFN. Multi-objective optimization helps us to find the results without any compromise. The models are solved using the mathematical programming solver LINGO-16 to derive the fuzzy regression coefficients. We apply these models in a numerical example also in a real case study (fuzzy input, crisp output) in which an investigation on the relationship between fuzzy demographic dynamics and monetary aggregates is made.
