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Shakespeare and Fuzzy Logic[1]

There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy. - Hamlet (1.5.167-8), Hamlet to Horatio[2]

Shakespeare teaches us in this Hamlet quote that reality is much more complex than our mental projections and understanding. Reality is fuzzier than we would care to think. Although introducing subjectivities to modeling seems to harm the ‘objectivity’ for the purists, this objectivity is more of a deliberate ignorance of real life issues than a sound strategy for modeling. There is a myriad of ambiguities and uncertainties in the information we receive decode and signal which tends to limit the functionality of traditional methods that are based on crisp logic. For instance, while USD 500 premium means you will have to give USD 500 to purchase the policy, the opinion whether this premium is adequate for the insurer or not, and reasonable or too expensive for the consumer is quite subjective. Fuzzy theory is developed to overcome this insufficiency by taking account of ambiguity in information. A number can be crisp as well as fuzzy, which recognises the ‘degree of truth’. In doing so, set theory, which is the groundwork of probability theories, is transformed into fuzzy set theory and all following applications are updated to be able to integrate fuzziness.

When using fuzzy logic, people’s qualitative description as well as quantitative estimation can be elaborated to maximise its utility. Fuzzy logic offers a more natural language, a way to deal with imprecise or incomplete data, and a way to group items together so that complexity is reduced, rule sets can be smaller, and speed of solution can be increased. This is extremely crucial for data science and actuarial modeling because they can occasionally face lack of data, face time sensitive data and need sound qualitative inputs to profile the complexity of the emerging situation.

Fuzzy Logic can be a useful way to improve many data science and actuarial models:

  • It can be a closer match to the way humans think.
  • Linguistic variables introduce both clarity and flexibil­ity.
  • Fuzzification can handle incomplete and inconsistent data.
  • Rules sets can be cleaner and fewer in number.
  • Defuzzification produces quantifiable results.

This is not to say that fuzzy logic systems are not without their shortcomings. In the application of fuzzy logic systems to risk assessment and risk decision-making, many practical issues and challenges can be encountered. Even with a solid theoretical foundation, the success of a system depends on many factors such as the quality of the experts’ opinions, the system’s own credibility and its linkage to management decisions. It can aid deep and sound thinking but cannot replace it.

Fuzzy logic models can also be used with other models such as decision trees, hidden Markov and Bayesian and artificial neural networks to model complicated risk issues like policyholder behaviors. A risk assessment and decision-making platform for ratemaking built on a fuzzy logic system can provide consistency when analyzing risks with limited data and knowledge. It allows people to focus on the foundation of risk assessment, which involves the cause-and-effect relationship between key factors as well as the exposure for each individual risk. Rather than a direct input for the likelihood and severity of a risk event, it supports human reasoning from the facts and knowledge to the conclusion in a comprehensive and reliable manner.

[1] Shang K, Hossen Z, (2013); CAS/CIA/SOA Joint Risk Management Section; Applying Fuzzy Logic to Risk Assessment and Decision-Making

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Comment by Sione Palu on July 12, 2016 at 6:30pm

Mamdani inference fuzzy system would be appropriate for actuarial modelling otherwise use ANFIS (adaptive neuro-fuzzy inference system) which is sugeno type inference system for automatic rule discovery.  ANFIS is a hybrid of fuzzy logic system & neural network or neuro-fuzzy system in the literature.  ANFIS is the state of the art.

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