Resilient Communities are the Foundations of a Resilient America.

Fuzzy Math: A New Way to Look at Community Resilience

Hi.  I’m John, and I’m a math nerd.  I was good in math at school.  In fact, I earned pin money in college tutoring students in math courses even if I hadn’t taken them. Then, in 1971, when Lotfi Zadeh first published his work on fuzzy math I became seriously addicted.

While we may not recognize it, fuzzy math concepts can provide useful and different ways to look at community resilience.  As I’ve written before, community resilience is a function of a community’s strengths.  Fuzzy math’s membership construct provides a useful way to evaluate a community’s strengths, at least qualitatively (and quantitatively for researchers who are willing to quantify the concept).

We all know that members of a community contribute to the community in varying ways and in varying degrees.  Some full-time residents are involved in the community socially, but make only a small contribution to its economy (e.g., those on welfare).  Others – through their involvement in neighborhood associations – may impact the the security and the livability of their community, and through their employment have an economic impact as well.  We can quantify those contributions through use of a membership function that parses residents’ efforts in terms of how much of a “member” they are in each of a community’s systems.  As an example, we could define an economic membership function as the amount of money a person injects into the community’s economy compared to some average.  The greater the membership in a community system (i.e., the larger the number of members contributing), the more resilient that system is likely to be.

Thus, fuzzy math begins to provide a strong basis to not only justify but to evaluate the progress of ideas such as “inclusive economic competitiveness.”  This concept – normally applied to minority groups in a community – emphasizes that certain groups are not contributing economically in proportion to their numbers (low economic membership) and that they potentially are an area for growth.  While economic “membership” is an obvious application of the fuzzy idea, it can be applied to every community function or system.

An immediate conclusion is that “membership” may be a more useful concept to gauge resilience that population.  But the fuzzy membership function also has another intriguing aspect:  it provides a means of judging the contributions of non-residents to a community’s resilience.  Consider two cities, each with 100,000 residents.  One has a thriving cultural scene, the other does not (think of Charleston, SC, vs Cape Coral, FL).  Non-residents are likely to frequent the first city, and contribute to it economically and socially.  While they are not residents of the community, they are members – they are contributing to the community’s resilience.

We can further divide non-residents into tourists and “semi-residents” – those who live in the region but not in the community.  Both may be members in the community, but the membership of tourists is much more likely to be transient, while semi-residents are likely to have a more lasting attachment.  The type of tourism may also impact the community’s resilience: “educational tourists” will impact both the educational and economic systems of a community, and potentially its workforce as well.

I have been struck by how this fuzzy concept applies in a striking manner to some of our more fragile communities.  The Mayor of Flint, MI, periodically rails against the surrounding communities and their unwillingness to help Flint.  In effect, the semi-residents no longer are members of the Flint community.  In a similar fashion, there is very little semi-resident involvement in Cape Coral, because there is little there to draw others from surrounding communities.  Thus, Cape Coral’s membership is lower than the similarly-populated Charleston, which is a cultural magnet for those in surrounding communities and for tourists – including those who come for medical or educational reasons.  

There is another intriguing (at least to me) way this fuzzy construct can be applied to communities.  In traditional risk management, risks are generally evaluated in terms of some probability function.  We all know, however, that it is almost impossible to quantify the probability of some threats, especially if they have never been experienced by the community (e.g., terrorism).  The fuzzy analog of probability is possibility.  Looking at threats in terms of their possibility  can lend itself to a more balanced and nuanced view of the universe of risk a community faces. An elected leader cannot convert a “10% probability of occurrence” into a “90% chance it won’t happen during my term of office.”  Well, actually, he/she can – it’s hard to make anything foolproof because fools are so ingenious!

Even a math nerd wants to live in a resilient community.  Fuzzy math provides me with a tool for judging how resilient my community is.  More importantly, fuzzy math provides all of us with a new way to look at community resilience.