A Fuzzy Expert System Approach to Insurance Risk Assessment Using FuzzyCLIPS
`
`Luis A. Carreno
`Dr. Yashvant Jani
`Togai InftaLogic, Inc.
`17000 El Camino Real, Suite 208
`Houston, TX 77058
`Phone: (713) 480 - 8904, Fax: (713) 480 - 8906
`
`Abstract
`
`that
`system (KBS)
`A knowledge based
`combines
`fuzzy processing with rule-based
`expert
`system is developed to provide an
`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
`improve
`user
`interactions
`and
`KBS
`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
`NASA/JSC 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
`directly
`for
`speed
`in
`embedded
`control
`applications. The main features of FuzzyCLlPS
`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 +
`((Risk /Base Risk)—l)*Increment
`
`(1)
`
`to
`The relation between decision factors
`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,l0,l1] provides a basis for
`accommodating such uncertainty with finesse. It
`also allows the software system to be defined in
`
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`human-like terms and aids in the transfer of
`
`When each factor has been evaluated to
`
`human knowledge and intuition into a KBS.
`The system has two different types of inputs:
`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
`(E),
`dairy
`products intake (DI), red meat
`intake (Ml),
`vegetable intake (VI),
`fat/sweet intake (FSI),
`smoking (8), 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 1. Risk contribution due to BMI
`
`BMI
`
`under 23
`23 -25
`
`25 - 30
`over 30
`
`ondition
`
`BMI-risk
`
`Underweight
`Ideal
`
`Overweight
`Obese
`
`0.25
`0.0
`
`0.75
`1.0
`
`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 II provides the contribution
`to risk due to the Age.
`
`Table 11. Risk contribution due to age
`
`Age
`0 to 30
`31 to 60
`61 to 90
`> 90
`
`Age-risk
`0.25
`0.5
`0.75
`1.0
`
`This table could be used in a rule-based KBS
`
`in the following form
`
`(age ?age&:( <= ‘?age 30)
`=> (assert (age-risk 25))
`
`provide an intennediatc 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
`concerned. 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 III [7].
`
`Table HI. Relationship between habits and
`health risk
`
`E
`Increases
`High
`Smoking
`High
`Drinking
`Low
`Exercising
`Low
`Veg. Intake
`High
`Meat Intake
`High
`Dairy Intake
`Fat/Sweet Intake High
`
`Risk
` §
`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 defuzzifieation techniques are used.
`
`537
`
`Page 00002
`
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`
`

`
`membership functions associated with each
`variable.
`
`Table IV. Variables and its membership
`functions
`
`Vmable
`Risk
`
`BlVlI
`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
`
`[O,1.2] for each risk
`above fuzzy variables is
`(Fig. 2),
`[(),6O] for BMI (Fig. 3), and [0,l00]
`for Age (Fig.4).
`
`W:
`
`55
`I4
`3:;
`it!
`It‘
`ltd.
`
`'\1‘
`ttllé .
`g
`7'." V §
`I
`
`'
`
`§“ .05.»
`
`V
`
`A
`4
`
`"‘
`
`Fig. 4 Age Membership Functions
`
`538
`
`Page 00003
`
`For this particular example, five different sets
`of fuzzy rules are defined. The first rulebase
`computes a risk_l 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_l, 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.
`
`
`
`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, 1]. 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
`
`For the fuzzy logic method, as seen in the
`following table, we defined the following sets of
`
`Page 00003
`
`

`
`A sample set of fuzzy logic rules for final
`value of Risk, based on all the inputs, is shown
`in Table V.
`
`Table V. Sample set of rules for final value of
`risk
`
`RLJLEB
`IF
`
`R[][,EA
`IF
`
`Age is Low
`& BMI is Ideal
`& E is Medium
`
`&VlisHigh
`& D1 is Medium
`
`& MI is Low
`& FSI is Low
`& S is Low
`&DisLow
`THEN Risk is Low
`
`Age is High
`& BM] is
`Over
`
`&EisLow
`& V1 is Low
`
`& D1 is High
`& MI is
`High
`&FIisLow
`& S is
`Medium
`& D is Med
`
`THEN Risk is High.
`
`As explained earlier, a rulebase with that
`many inputs is difficult to implement due to the
`large number of possible combinations of the
`input variables. Examples of fuzzy rules, using
`the alternative approach of breaking down the
`input variables into smaller and related groups,
`is shown next.
`
`IF
`
`Age is High &
`BMI is Obese
`THEN Risk_l is Very High
`
`IF
`
`5 is High &
`D is Low
`
`THEN Risk__2 is High
`
`IF
`
`E is High &
`V1 is Medium
`THEN Risk_3 is Low
`
`IF
`
`MI is Low &
`DI is Medium &
`FSI is Medium
`THEN Risk_4 is Medium
`
`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 dairy
`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) V1
`is High, 5) FSI is Low, 6) E is high, 7) D1 is
`Low, and 8) MI is Low.
`
`Tmllllonal Method
`
`Fuzzy Lnglc Me-innit
`
`sags:
`
`saga:
`
`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
`
`Fig. 5 Risk Vs Age for Constant Characteristics
`and Habits
`
`the
`expected. For
`as
`results were
`The
`traditional method, abrupt changes occurred in
`the value of risk associated with ages. As
`observed in figure 5, the risk value jumps at age
`
`539
`
`Page 00004
`
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`
`

`
`it
`30 and then continues to be constant until
`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 1000
`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.
`
`
`
`Fig. 6 Risk Obtained From Traditional Method
`
`As observed in figure 6, the behavior of the
`system in
`the
`traditional method is
`very
`unpredictable 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 ligure 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.
`
`e
`P.g,..lw'-ua-passe: xeuieseanoets
`9*
`5
`3.
`9
`0
`0
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`0
`,.+
`1.
`
`4:
`hi
`an
`
`.
`
`.'
`.9!
`
`n
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`
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`
`>
`
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`
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`‘V
`“
`.-ua-e
`9 9:5: u¢aeon
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`
`5
`
`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
`fuuy 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:
`l) 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
`
`represents only a sample of business
`paper
`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 FuzzyCL[PS tool.
`
`540
`
`Page00005
`
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`
`

`
`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 :22:
`:> 0.600
`exercise/vegetable intake ====>
`0.400
`fat intake =:==:=:==:::=:=:>
`**************************************
`
`0.547
`TOTAL RISK =>
`0.344
`BASE RISK :=>
`**************************************
`
`1.59
`RATIO total/base risk =>
`**************************************
`
`YOUR ANNUAL PREMIUM :> $ 1941.13
`**************************************
`
`INDIVIDUAL MBF CONTRIBUTIONS BY
`RISK
`**************************************
`
`Fat intake Risk ===>
`
`MBF VH
`
`Degree of Truth 1.0
`Exer/Veggies Risk =>
`MBF H
`Degree of Truth 4.2e-005
`Exer/Veggies Risk :>
`MBF M
`Degree of Truth 0.99
`Smoke/Drink Risk :=> MBF H
`Degree of Truth 0.99
`Smoke/Drink Risk => MBF M
`Degree of Truth 4.2e-005
`==:=>
`M
`Degree of Truth 0.587
`Age/BMI Risk ==::>
`MBF L
`Degree of Truth 0.412
`**************************************
`
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`Programming Guide, Alpha Release, Oct. 19,
`1992.
`1. Basic
`2. CLIPS Reference Manual, Vol
`Programming Guide JSC-25012, NASA/JSC
`Sept. 10, 1991.
`
`3. The New Good Ilousekeeping Family Health
`and Medical Guide, section three, pp. 608-615,
`(Hearst Corporation, New York, 1989).
`
`(1992), Life
`4. Carreno, L. A., Steel, R.,
`Insurance Risk Assessment Using a Fuzzy Logic
`Expert System, Proceedings of
`the North
`American Fuzzy Logic Society (NAFIPS 92) pp.
`627-635.
`
`(1992), Applications of Fuzzy
`5. Cox, E.,
`Systems Models. AI Expert, 7(l0), pp. 34-39.
`
`6. Cox, E. (1993), How a Machine Reasons:
`Part 8. AI Expert, 8(3), pp. 13-16.
`
`7. Hermann, M. (1993) A Diet You Can Live
`With. Special Report - Home Library, 2(1), pp.
`3-14.
`
`8. Oswszewski, K. (1993), An Investigation into
`Possible Applications of Fuzzy Set Methods in
`Actuarial Science, published by the Society of
`Actuaries, Schaumburg, pp. 23-67.
`
`(1993) Three Faces of
`J.
`9. Schmuller,
`Fuzziness: Theory, Practice, and Applications.
`PC AI, 7(2), pp. 14-15.
`
`10. Sugeno, M., Asai, K., and Tcrano, T.,
`(1992)
`Fuzzy
`Systems
`Theory
`and
`Its
`Applications, Academic Press, New York.
`
`11. Zadeh, L. A., (1988), Fuzzy Logic. IEEE
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`
`54]
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