A Fuzzy Expert System Approach to Insurance Risk Assessment Using FuzzyCLIPS
`
`Luis A. Carreno
`Dr. Yashvant Jani
`Togai InfraLogic, Inc.
`17000 El Camino Real, Suite 208
`Houston, TX 77058
`Phone: (713) 480 - 8904, Fax: (713) 480 - 8906
`
`Abstract
`
`that
`A knowledge based system (KBS)
`combines fuzzy processing with rule-based
`to provide an
`expert system is developed
`improved decision aid for evaluating risk for life
`insurance. This expert system application
`illustrates the use of FuzzyCLIPS tool to build a
`knowledge based decision support system,
`capable of possessing fuzzy components to
`and KBS
`improve
`user
`interactions
`performance. The design of the fuzzy solution
`consists of a CLIPS rule-based system combined
`with fuzzy logic rules. The results employing
`FuzzyCLIPS are compared with the results
`obtained from the solution of the problem using
`traditional numerical equations. This paper
`briefly describes the problem, proposes a
`solution, describes the test scenarios, presents
`the results and conclusions, and provides a
`sample output of the software product.
`
`Introduction to FuzzyCLIPS
`
`FuzzyCLIPS adds fuzzy processing capability
`to CLIPS (C Language Integrated Production
`System) version 5.1. CLIPS was developed by
`NASNJSC as a rule-based expert system
`development tool. FuzzyCLIPS architecture is a
`separate processing element similar to that used
`to incorporate object-oriented programming into
`CLIPS [1,2]. The basic fuzzy constructs and
`function calls (like definition of a membership
`function and fuzzy rules) can be written
`intermixed with usual CLIPS
`statements
`providing an extension of rule syntax and user
`definitions of membership function
`types.
`Principal fuzzy constructs define rule bases and
`membership functions. There are also functions
`by which a CLIPS [2] program can test the
`degree of membership of a sensor value, execute
`a fuzzy rule base that returns defuzzified control
`values to CLIPS and, optionally, assert facts
`
`giving belief values for the possibilities that
`might be useful in an expert system. In addition,
`C interface functions support embedded fuzzy
`applications that can invoke the fuzzy processor
`for speed
`in embedded control
`directly
`applications. The main features of FuzzyCLIPS
`are: a) fuzzy reasoning capability is combined
`with conventional rule based technology, b) the
`flexibility and portability of CLIPS is retained,
`and c) development of both stand-alone and
`embedded systems is possible.
`
`Problem Statement
`
`An insurance company needs to assess the
`degree of health risk associated with each client
`based on physical characteristics such as height,
`weight, age and additional information such as
`exercise, smoking, drinking, and eating habits.
`The output risk value serves as the basis for the
`determination of insurance premiums billed to
`clients. Generally, insurance premiums have a
`base rate (perfect health, good habits, 35 years
`old) and an increment to adjust the premium
`based on the risk for a particular client. A risk
`value between 0 and 1 suffices to set a net rate.
`The equation is
`Cost = Base Rate +
`(Wsk Base Risk)- l)*Increment
`
`(1)
`
`The relation between decision factors to
`compute the risk and the rate change need be
`neither
`incremental nor
`linear. Complex
`interdependence of
`the factors mean
`that
`computer-based decision aids
`(a
`software
`system) are useful to a human agent and that
`sharp decision boundaries such as
`those
`produced by a normal rule based system are
`sensitive to small uncertainties in the input data.
`Fuzzy logic [8.9,10,11] provides a basis for
`accommodating such uncertainty with finesse. It
`also allows the software system to be defined in
`
`536
`
`Liberty Mutual Exhibit 1025
`Liberty Mutual v. Progressive
`CBM2012-00002
`Page 00001
`
`

`

`human-like terms and aids in the transfer of
`human knowledge and intuition into a KBS.
`The system has two different types of inpuls:
`base and incremental. The base input variables
`are Age (A), Weight (W), and Height (H).
`Incremental input variables deal with particular
`habits and characteristics of prospective clients.
`Such variables are: exercising @), dairy
`products intake (DI), red meat intake (M[),
`vegetable intake (VI),
`fat/sweet intake (FSI),
`smoking (S), and drinking (D) habit. The output
`of the system is the risk used in equation (1).
`The body mass index (BMI) is a measure that
`indicates if a person is overweight [3]. It is
`calculated by dividing the Weight in kilograms
`by the square of the height in meters,
`BMI = Weight/(Height)2.
`Table I shows the scale used to interpret BMI
`and the corresponding BMI-risk .
`
`Table I. Risk contribution due to BMI
`
`BMI
`under 23
`23 -25
`25 - 30
`over 30
`
`Condition
`Underweight
`Ideal
`Overweight
`Obese
`
`BMI-risk
`0.25
`0.0
`0.75
`1 .o
`
`Traditional Numerical Solution
`
`For the traditional method solution, we treat
`all of the variables as a number input or a
`selection from a finite, discrete, closed set of
`possibilities. Each variable is represented as a
`lookup table of intervals where the value of the
`corresponding risk is specified for each interval.
`For example, Table I1 provides the contribution
`to risk due to the Age.
`
`Table 11. Risk contribution due to age
`
`Age
`0 to 30
`31 to60
`61 to 90
`> 90
`
`Ape-risk
`0.25
`0.5
`0.75
`1 .o
`
`This table could be used in a rule-based Kl3S
`in the following form
`
`(age ?age&:( <= ?age 30)
`=> (assert (age-risk .25))
`
`When each factor has been evaluated to
`provide an intermediate risk, the total risk can
`be computed as a weighted combination of these
`risks due to various factors. In a traditional
`system, the first step in the solution is to define
`a mathematical relationship between the inputs
`and outputs of the system. The objective is to
`obtain a numerical value that represents the
`possible risk of a person having medical
`problems due to his physical characteristics and
`eating habits. Risk is defined as having a range
`of [0,1]. The various factors are also assumed to
`have values in the [0,1] range by mappings
`similar to those presented above for age and
`BMI. A risk measure of 1 represents the
`maximum degree of risk, on the contrary, a
`measure of 0 or less represents the minimum
`degree of risk [4].
`In addition to age and BMI, data reflecting a
`person's habits also contribute to the risk
`assessment. Two approaches are used to handle
`such data. The normal approach is to attempt to
`quantify habits in terms of frequency of the
`participation and amount of
`time, or activity
`concemed. The second approach is to estimate
`the frequency and level of activity into literal
`categories (or linguistic values). Qualitative
`values indicating the change in risk due to
`various habits is shown in Table I11 [7].
`
`Table 111. Relationship between habits and
`health risk
`- Risk
`Increases
`High
`Smoking
`High
`Drinking
`Low
`Exercising
`Low
`Veg.Intake
`High
`Meat Intake
`High
`Dairy Intake
`Fat/Sweet Intake High
`
`- Risk
`Decreases
`None
`None
`High
`High
`LOW
`LOW
`LOW
`
`Fuzzy Logic Solution
`
`In a fuzzy logic based system, an expert
`defines the rules to describe the characteristics
`of the risk assessment for each factor [5,6]. The
`input variables are processed by these rules to
`generate an appropriate output. A schematic
`fuzzy decision support system is shown in figure
`1. For fuzzy reasoning max-dot inferencing and
`centroid defuzzification techniques are used.
`
`537
`
`Page 00002
`
`

`

`For this particular example, five different sets
`of fuzzy rules are defined. The first rulebase
`computes a risk-1 based on age and BMI. The
`second rulebase computes a risk-2 based on
`smoking and drinking habits. The third rulebase
`computes a risk-3 based on the amount of
`exercise and intake of vegetables. The last
`rulebase computes a risk-4 based on the intake
`of dairy products, red meat, and fat and sweet
`products. A fifth rulebase relates risks 1-4 to the
`overall risk to complete the risk assessment. The
`importance of breaking down the problem into
`smaller related groups is the fact that the
`number of rules needed to control the system
`decreases dramatically. In our example, the
`number reduced from 42 * 37 (34992) rules to a
`maximum of 686 rules.
`When a client provides age, height, and
`weight, the BMI is computed and an initial
`measure of risk , risk-1, using Rbasel is
`evaluated. This measure serves as the basis for
`subsequent decisions. If the risk obtained is
`considered by the system as very high, no
`further inquiries of the user are necessary. On
`the other hand, if the risk obtained is considered
`low, medium, or high, further inquiries into the
`user's habits are necessary to arrive at a more
`meaningful result.
`
`membership functions associated with each
`variable.
`
`Table IV. Variables and its membership
`functions
`
`Variable
`Risk
`
`BMI
`Age
`Habits
`
`Membership Functions
`Very Low, Low, Medium,
`High, Very High
`Under, Ideal, Over, Obese
`Very Low, Low, Med, High
`Low, Medium, High
`
`The universe of discourse for each of the
`above fuzzy variables is
`[0,1.2] for each risk
`(Fig. 2), [0,60] for BMI (Fig. 3), and [0,100]
`for Age (Fig. 4).
`
`r
`
`8'00
`E
`L
`I
`E
`F nnn
`"vu 000
`
`\
`
`020
`
`040
`
`060
`
`080
`
`100
`
`120
`
`RISK
`
`Fig. 2 Risk Membership Functions
`
`/
`
`Fig.1 A schematic view of the fuzzy logic risk
`assessor
`
`The output of the system consists of a crisp
`value for Risk in the range [0, 11. The system
`also produces a truth value associated with each
`output fuzzy set, i.e., the degree to which each
`fuzzy set defining risk contributes to the output
`value of risk.
`For the fuzzy logic method, as seen in the
`following table, we defined the following sets of
`
`0.0
`
`100
`
`20.0
`
`30.0
`
`40 0
`
`50.0
`
`60.0
`
`BMl
`
`Fig. 3 BMI Membership Functions
`
`J
`
`0
`
`.
`
`10
`
`20
`
`30
`
`40 50 60 70
`
`80
`
`90 100
`
`&e
`
`/
`
`Fig. 4 Age Membership Functions
`
`538
`
`Page 00003
`
`

`

`A sample set of fuzzy logic rules for finall
`value of Risk, based on all the inputs, is showin
`in Table V.
`
`Table V. Sample set of rules for final value of
`risk
`
`RULE A
`IF
`AgeisLow
`& BMI is Ideal
`& E is Medium
`& VI is High
`& DI is Medium
`& MI is Low
`& FSI is Low
`& S is Low
`& D is Low
`THEN Risk is Low
`
`RULE B
`IF
`AgeisHigh
`& BMI is
`Over
`& E is Low
`& VI is Low
`& DI is High
`& MI is
`High
`& FI is Low
`& S is
`Medium
`& D is Med
`THEN Risk is High
`
`As explained earlier, a rulebase with thait
`many inputs is difficult to implement due to the
`large number of possible combinations of the
`input variables. Examples of fuzzy rules, usin,g
`the alternative approach of breaking down the
`input variables into smaller and related groups,
`is shown next.
`
`IF
`
`AgeisHigh&
`BMI is Obese
`THEN Risk-1 is Very High
`
`IF
`
`S isHigh&
`D is Low
`THEN Risk-2 is High
`
`IF
`
`EisHigh&
`VI is Medium
`THEN Risk-3 is Low
`
`IF
`
`MIisLow&
`DI is Medium &
`FSI is Medium
`THEN Risk-4 is Medium
`
`-
`
`In the application, five rulebases are defined.
`As explained earlier, each one produces an
`intermediate risk that is fed into the final
`rulebase to provide a relative assessment of risk;.
`Such risk
`is compared with a base risk
`associated with a base rate, as explained in
`
`section 2. The total risk of a particular person is
`calculated and substituted in Eq. (1) to produce
`a premium amount.
`There are two special cases in the processing
`of the problem: 1) if the initial risk, based on
`age and BMI, is greater than 0.8, the risk is
`considered very high. Therefore, there is no
`need for further processing of the system. 2) if
`the initial assessment of BMI is greater than 30,
`meaning the person is obese, all questions
`related to the habits of consumption of dauy
`products, red meat, and fat/sweet products are
`omitted. Otherwise, the user interface is the
`same for both methods.
`
`Results and Conclusions
`
`To compare both methods, the traditional vs.
`the fuzzy logic based, two experiments were
`designed. For both experiments, a batch
`program was created to process the two methods
`and to produce the individual output for each
`method. In the first experiment, sample data was
`created and processed by the batch program to
`obtain
`the output risk. The sample data
`consisted of a group of persons with constant
`weight/height relationship, and constant eating
`and exercise habits, the only variant was the age
`of the individuals. The constant characteristics
`are: 1) BMI Ideal, 2) S is no, 3) D is Low, 4) VI
`is High, 5) FSI is Low, 6) E is high, 7) DI is
`Low, and 8) MI is Low.
`
`Traditional Method
`
`Fuzzy Logic Memod t
`
`9a91 &e
`
`30 31
`
`60 61
`
`9091 se
`
`Fig. 5 Risk Vs Age for Constant Characteristics
`and Habits
`
`the
`The results were as expected. For
`traditional method, abrupt changes occurred in
`the value of risk associated with ages. As
`observed in figure 5, the risk value jumps at age
`
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`
`Page 00004
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`

`

`30 and then continues to be constant until it
`reaches the age of 60 where it jumps again. The
`process is repeated at age 90.
`For the fuzzy logic solution, as observed in
`Fig.5, no sharp differences or jumps are
`observed at any specific age, i.e., the risk values
`increase smoothly along the whole domain. The
`fuzzy system produces more realistic values for
`different ages, specially for those cases in which
`the age varies from 30 to 31, 60 to 61, or 90 to
`91.
`In the second experiment a sample data set
`was created to produce a population of lo00
`subjects with random physical characteristics
`(age, weight, and height) and random eating
`and exercise habits. The goal of the second
`experiment was to observe the behavior of the
`system in a totally random environment.
`
`0.8
`
`Fig. 6 Risk Oblained From Traditional Method
`
`As observed in figure 6, the behavior of the
`system in
`the
`traditional method
`is very
`unprcdictable and produces a totally random
`spectrum of values for the output risk. The most
`important fact is that there is no correlation
`found between the age of the subjects and the
`risk assigned to that particular subject. This
`result contradicts the common sense reasoning
`about the relationship between the age and risk.
`The results obtained using the fuzzy logic
`method, as shown in figure 7, show a more
`predictable and
`smoother behavior. The
`relationship between
`the age and risk
`is
`maintained, that is, the risk increases with the
`increase in age.
`
`Fig. 7 Risk Obtained From Fuzzy Logic Method
`
`Another important observation in figure 7 is
`the clearly defined grouping of risk values at
`different levels, which are related to eating and
`exercise habits of the population. This result
`allows a better evaluation of the risk at any time
`based on the particular habits of the individual.
`The insurance risk assessor system, using
`fuzzy logic principles, provides
`insurance
`companies and insurance clients with several
`advantages over traditional expert systems: a)
`the expert system behavior can be controlled and
`modified without major consequences to the
`existing expert system, b) the results do not rely
`on mathematical models that could become
`obsolete, c) the premiums and risks are properly
`distributed among the population, d) there is
`appropriate predictability of risk measures and
`premium amounts, and e) the risk measure is
`obtained with high degree of certainty.
`Some of the advantages for the insurance
`clients are: 1) a fair distribution of risk and
`premiums among population,
`eliminating
`current over/under payments, 2) a definite
`predictability of future premiums, eliminating
`uncertainty about future coverage, and 3 )
`identification of weak areas
`that can be
`improved to reduce the risk, therefore reducing
`future premium amounts.
`The insurance risk assessor described in this
`paper represents only a sample of business
`applications using
`fuzzy
`logic principles.
`Business systems with a large number of inputs,
`such as the insurance risk assessor, can be
`prototyped in a relatively short period of time
`using the FuzzyCLIPS tool.
`
`540
`
`Page 00005
`
`

`

`Sample Output
`
`References
`
`The application program described in this
`document provides an interactive session to
`gather information about a client's physical
`characteristics, exercise habits, and eating and
`drinking habits. After receiving all of
`the
`information needed,
`the
`risk values are
`determined, and a final summary report is
`produced. It consists of the four intermediate
`risks , the final risk, the base risk (explained
`earlier), the ratio of the total to base risk, the
`annual insurance premium, and the individual
`contributions of each membership function by
`risk and its predicate truth values.
`......................................
`SUMMARY
`......................................
`Risk based on
`age and bmi ============== > 0.318
`smoking/drinking ==========> 0.600
`cxercise/vegctable intake ====> 0.400
`fat intake ================> 0.842
`......................................
`0.547
`TOTAL RISK =>
`BASE RISK ==>
`0.344
`......................................
`1.59
`RATIO totaVbase risk =>
`......................................
`YOUR ANNUAL PREMIUM => $ 1941.13
`......................................
`INDIVIDUAL MBF CONTRIBUTIONS BY
`RISK
`......................................
`Fat intake Risk ===>
`MBF VH
`Degree of Truth 1.0
`ExerNeggies Risk => MBF H
`Degree of Truth 4.2e-005
`Exerneggies Risk => MBF M
`Degree of Truth 0.99
`Smoke/Drink Risk ==> MBF H
`Degree of Truth 0.99
`SmokeDrink Risk ==> MBF M
`Degree of Truth 4.2e-005
`AgeBMI Risk ====> MJ3F M
`Degree of Truth 0.587
`AgeBMI Risk ====> MBF L
`Degree of Truth 0.412
`......................................
`
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`
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