Fuzzy numbers capture the linguistic measures that people use to calculate their way through life.
“Is the truck coming at me “too fast”, or can I cross the street?”
“Should I make this investment, or is it “too risky”?”
“Am I going to be “late” for the appointment?”
The extension of the number system to include fuzzy numbers is the most recent development in the evolution of our number system. The reasons for this are practical. The real world measures itself on a “grayscale”, and expresses these measures in everyday language.
Existing numbers – natural numbers, integers, fractions, infinite decimals, complex numbers – do not adequately capture the imprecise, vague, and ambiguous values encoded in natural languages – values like “fast”, “risky”, or “late”.
These linguistic measures are used pervasively. The person driving to the appointment calls from the car, “Sorry I’m late, but I will get there as fast as I can”. This tells the story without any quantitative reference. The measures are linguistic – “late”, “fast”.
The cell call also tells a story that is interpreted differently by different people. The person at the other end of the call has her own version of “late” and “fast”. She puts her own spin on the information. She does this easily, almost without thinking, and certainly without the benefit of calculus, Boolean algebra, or a statistical analysis.
If information in stories is to be interpreted mathematically using the processes that people use cognitively, fuzzy numbers are needed to bridge the gap between existing numbers and natural language.
Once fuzzy numbers are used, it is possible to turn spins on different scenarios into mathematical equations. You can find three examples with graphs to illustrate the connection in the” About Fuzzy Logic” dropdown.
Lorna Strobel Stewart Ph.D.