



This paper features the decisionmaking model to measure the ideality of products, based on the Theory of Inventive Problem Solving (TRIZ). These products are designed using innovative activities from the point of view of evolution toward increased ideality as one of the patterns of technical evolution in the TRIZ methodology.
In order to give customers (especially highend customers) highlyvalued products, companies have to chase the ideal final result (IFR). The decisionmaking model, therefore, uses idealized conceptual designs to realize highlyvalued products rationally from the standpoint of chasing the IFR.
The basis of the decisionmaking model is the analytic hierarchy process (AHP).^{4} It is devised to evaluate ideality from various aspects corresponding to useful functions (such as product design parameters) and harmful effects (such as side effects with useful functions).
Both the hierarchy diagrams (the AHP) and the series of useful functions and harmful effects in an object product use the decisionmaking model to measure the ideality index.
The purpose of this study is to propose the decisionmaking model for evaluating the highlyvalued product for customers in product development activities from the standpoint of evolution toward increased ideality.
According to the evolution toward increased ideality, the useful functions performance of main parameters will be improved and harmful effects such as weight, space, noise and cost will be decreased in technical systems. Over time the technical systems advance toward increased ideality. By using the AHP from the improvement of ideality in a TRIZ field a technique for design proposals can be used.^{2}^{,}^{7} In particular, TRIZ expert Vladimir Petrov referred to the idealization level behavior through nine cells of the contradiction matrix and explained the levels of idealization with examples.^{7}
In order to measure the ideality index for design proposal alternatives from the viewpoint of evolution toward increased ideality, the author suggests drawing two types of hierarchy structure diagrams. This is due to the proposed decisionmaking model based on the AHP: one is for useful functions and another is for harmful effects. Based on these two types of diagrams, the coefficient can be expected to be measured by showing the degree of ideality rationally for design proposals to be considered through TRIZ activities.
First the decisionmaker unit has to estimate the weight (level of importance) for each design proposal by using the AHP and the desiring level. Next, calculate the weight (degree of incident) for each design proposal based on an acceptable level. Lastly, calculate for the ideality index for each design proposal by dividing the total sum of weight by each useful function and harmful effect to reach a design proposal.
The acceptable level is the minimum level that is adequate for customers. It is the opposite direction of the desiring level. The ideality index for each design proposal is bigger (more than 1) and it is valuable for customers (especially highend customers).
The flowchart regarding implementation procedures of the proposed decisionmaking model is shown in Figure 1.

Step 1: Making two types of hierarchy structure diagrams from the point of view of evolution toward increased ideality
Two types of hierarchy structure diagrams are drawn to improve required useful functions and to avoid reducing harmful effects.
Step 2: Estimation of weight (level of importance) of each useful function and harmful effect
Estimate the relative weight of each useful function and harmful effect by using the AHP (it is a type of relative measurement approach).
UWi: Weight of UFi (useful function) (level of importance for customers)
HWj: Weight of HEj (harmful effect) (degree of incidence against customers)


Step 3: Setting up a desiring level for each useful function at an acceptable level for each harmful effect
Define the desiring level for each useful function at an acceptable level for each harmful effect of a technical system (for example, a new product in the pipeline).
Step 4: Estimation of weight (degree of relative merit) of each design proposal for each useful function and harmful effect
Measure the outcome of each design proposal by estimating the achievement (weight) for the desiring level of each useful function .
Step 5: Estimation of total score of each design proposal for a series of useful functions and harmful effects.
Calculate the total score of each design proposal by method of weighted mean between the weight of each design proposal and each useful function. The weight of each useful function is estimated in Step 2. Then calculate the total score of each design proposal as it relates to each harmful effect by the same method.

UminR: TS (total score) of DL (desiring level)

Hk: TS (total score) of DP (design proposal) k for a series of harmful effects

HmaxUR: TS (total score) of AL (acceptable level),

Step 6: Estimation of the ideality index of each design proposal
Calculate the ideality index of each design proposal based on the total score of each design proposal to be estimated from Step 5.
IkII (ideality index) of DPk (design proposal)

Min I: DL (desiring level) of II (ideality index)
Two types of hierarchy structure diagrams were drawn that focus on a paper cup for drinking coffee while walking – a mobile paper cup. One hierarchy structure diagram is for useful functions (shown in Figure 9) and another hierarchy structure diagram is for HFs (shown in Figure 10).


The hierarchy structure diagram for useful functions is the diagram showing the required useful functions of a mobile paper cup. On the other hand, the hierarchy structure diagram for harmful effects is the one showing the predictable side effects.
The objective of making these hierarchy structure diagrams is to evaluate each design proposal (or alternative of a mobile paper cup) rationally at the next step or later (Steps 2 through 6).
Figures 11, 12 and 13 illustrate the three design proposals (alternatives of a mobile paper cup) for evaluating the ideality index:



When estimating the weight of each useful function and harmful effect use the AHP (relative measurement approach).^{5} In order to use the analytic hierarchy process (AHP) correctly, keep in mind the meaning of weight for useful functions and harmful effects. The weight of each useful function is the level of importance for users (customers). It is the estimated weight of each useful function from a useful function improvement standpoint. The weight of each harmful effect is the reduction of harmful effects; it is the degree of incidence against the users.
A paired comparison of judgments from the AHP is applied by homogeneous elements. For example, a series of useful functions and harmful effects are homogeneous elements of the hierarchy structure diagram for useful functions and harmful effects (shown in Figures 9 and 10). The fundamental scale of absolute values for representing the intensities of judgments is shown in Table 1.
Table 1: The Fundamental Scale^{6}  
Intensity of Importance  Definition 
1  Equal importance 
2  Weak 
3  Moderate importance 
4  Moderate plus 
5  Strong importance 
6  Strong plus 
7  Very strong or demonstrated importance 
8  Very, very strong 
9  Extreme importance 
Reciprocals of above  If i has one of the above numbers assigned to it when compared with activity j then j has the reciprocal value when compared with i 
The scale shown in Table 1 has been validated for effectiveness through applications and theoretical comparisons with other scales such as the scales focusing on useful functions and harmful effects in TRIZ.
According to basic theory of the AHP the numbers are used to represent how many times the larger of the two elements dominates the smaller one with respect to a common property or criterion. The smaller element is the reciprocal with respect to the larger one.^{6}
Based on the fundamental scale, the weight of each useful function is shown in Table 2:
Table 2: Weight of Each Useful Function (UF) of a Mobile Paper Cup  
Three Useful Functions (three items)  Consistency Index  If CI < 0.1, it is OK In this case, CI = 0.02  
UF1 Easiness to Drink  UF2 Heatretaining Property (coffee stays hot)  UF3 Insulating the Heat of Hot Coffee  Geometric Average  UWi (i = 13)  
UF1 Easiness to Drink  1.000  1.500  1.000  1.145  0.380 
UF2 Heatretaining Property (coffee stays hot)  0.667  1.000  1.200  0.928  0.308 
UF3 Insulating the Heat of Hot Coffee  1.000  0.833  1.000  0.941  0.312 
Total  3.014  1.000 
The estimated weight of each harmful effect on the basis of the same scale is shown in Table 3:
Table 3: Weight of Each Harmful Effect (HE) of a Mobile Paper Cup  
Five Harmful Effects (five items)  Consistency Index  If CI < 0.1, it is OK In this case, CI = 0.07  
HE1 Waterproof Property  HE2 Mobility of Coffee  HE3 Economical Efficiency  HE4 Environmental Policy  HE5 Safety  Geometric Average  HWj (j = 15)  
HE1 Waterproof Property  1.000  0.333  2.000  1.000  2.000  1.059  0.196 
HE2 Mobility of Coffee  3.000  1.000  3.000  2.000  1.500  1.933  0.357 
HE3 Economical Efficiency  0.500  0.333  1.000  1.200  0.333  0.582  0.107 
HE4 Environmental Policy  1.000  0.500  0.833  1.000  1.000  0.839  0.155 
HE5 Safety  0.500  0.667  3.000  1.000  1.000  1.000  0.185 
Total  5.414  1.000 
The definitions for a desiring level for each useful function and an acceptable level for each harmful effect from the perspective of new product activities in the pipeline are shown in Tables 4 and 5.
Table 4: Each Desiring Level for Each Useful Function (UF) for the Mobile Paper Cup  
Useful Functions  Desiring Level (way to advance "＋") Concrete Performance Measures 
UF_{1}: Drink coffee while walking (easiness to drink)  Makes it easy to bring coffee to the mouth with one hand while walking slowly (about 50 m/min). It is expected to be possible to bring coffee (in one hand) while walking, even more quickly (speed is about 90m100m/min on foot). 
UF_{2}: Prevent decreasing temperature (heatretaining property)  It is possible to keep at 80 degrees Celsius for five minutes. It is expected to be possible to keep it hot for a longer time (more than five minutes). 
UF_{3}: Holding the cup's body with hot coffee inside for a while (insulating the heat of hot coffee)  It is expected to insulate the heat of hot coffee It is possible to hold the cup's body even at a high temperature (coffee is more than 90 degrees Celsius) for a while (approximately ten minutes). 
Table 5: Each Acceptable Level for Each Harmful Effect (HE) for the Mobile Paper Cup  
Harmful Effect  Acceptable Level (way to advance to zero) 
HE_{1}: Prevent leaking coffee between glued connections of the cup's body (waterproof property)  Leaking some coffee between glued connections of the cup's body should be realized at less or equal to hundredth part of probability. (quality of paper cup) 
HE_{2}: Prevent spilling coffee from mouth while drinking (mobility of coffee)  An individual can move coffee (fluid) from the cup to the mouth without spilling coffee from the mouth while drinking. (zero per occurrence ) 
HE_{3}: Inexpensive coffee cup (economical efficiency)  Cost of each cup is less than five yen. (usual coffee cup) 
HE_{4}: Environmentallyfriendly design (environmental policy)  The ratio of waste material is less than ten percent. (the ratio of reuse is more than 90 percent ) 
HE_{5}: Prevent dominant hand from burning while drinking (safety)  Prevent dominant hand from burning while drinking. (percentage of risk: less than one percent) 
In order to estimate the effectiveness of the three design proposals (shown in Figures, 11, 12 and 13) and before producing them as possible to a customer, use the modified AHP (including desiring level and acceptable level shown in Tables 4 and 5). The results of the paired comparison table of each design proposal by the AHP including the desiring level include:
Table 6: Paired Comparison Table Including a Desiring Level of Useful Function 1 of Design Proposals (DPs)  
Easiness to Drink  Consistency Index  If CI < 0.1, it is OK In this case, CI = 0.011  
DP1  DP2  DP3  minR_{1}  Geometric Average  Weight  UW (1, k) K = 13  
DP1  1.000  9.000  9.000  2.000  3.568  0.549  1.604 
DP2  0.111  1.000  1.000  0.143  0.355  0.055  0.160 
DP3  0.111  1.000  1.000  0.143  0.355  0.055  0.160 
minR_{1}  0.500  7.000  7.000  1.000  2.225  0.342  *minR_{1 }= 1.000 
Total  6.502  1.000 
Function 1 of Design Proposals (DPs)
Table 7: Paired Comparison Table Including a Desiring Level of Useful Function 2 of Design Proposals (DPs)  
Heatretaining Property  Consistency Index  If CI < 0.1, it is OK In this case, CI = 0.017  
DP1  DP2  DP3  minR_{2}  Geometric Average  Weight  UW (2, k) K = 13  
DP1  1.000  0.500  0.500  2.000  0.841  0.197  1.414 
DP2  2.000  1.000  1.000  2.000  1.414  0.332  2.378 
DP3  2.000  1.000  1.000  2.000  1.414  0.332  2.378 
minR_{2}  0.500  0.500  0.500  1.000  0.595  0.139  *minR_{2 }= 1.000 
Total  4.264  1.000 
The following tables by the AHP include harmful effects:
Table 8: Paired Comparison Table Including a Desiring Level of Useful Function 3 of Design Proposals (DPs)  
Insulating the Heat of Hot Coffee  Consistency Index  If CI < 0.1, it is OK In this case, CI = 0.081  
DP1  DP2  DP3  minR_{3}  Geometric Average  Weight  UW (3, k) K = 13  
DP1  1.000  0.500  5.000  2.000  1.495  0.300  1.093 
DP2  2.000  1.000  6.000  1.000  1.861  0.373  1.361 
DP3  0.200  0.167  1.000  0.143  0.263  0.053  0.192 
minR_{3}  0.500  1.000  7.000  1.000  1.368  0.274  *minR_{3 }= 1.000 
Total  4.987  1.000 
Table 9: Paired Comparison Table Including an Acceptable Level of the Harmful Effect 1 of Design Proposals (DPs)  
Waterproof Property  Consistency Index  If CI < 0.1, it is OK In this case, CI = 0.003  
DP1  DP2  DP3  maxUR_{1}  Geometric Average  Weight  EW (1, k) K = 13  
DP1  1.000  0.333  0.333  0.500  0.485  0.109  0.577 
DP2  3.000  1.000  1.000  2.000  1.565  0.351  1.861 
DP3  3.000  1.000  1.000  2.000  1.565  0.351  1.861 
maxUR_{1}  2.000  0.500  0.500  1.000  0.841  0.189  *maxUR_{1 }= 1.000 
Total  4.457  1.000 
Table 10: Paired Comparison Table Including an Acceptable Level of the Harmful Effect 2 of Design Proposals (DPs)  
Mobility of Coffee  Consistency Index  If CI < 0.1, it is OK In this case, CI = 0.088  
DP1  DP2  DP3  maxUR_{2}  Geometric Average  Weight  EW (2, k) K = 13  
DP1  1.000  0.125  0.167  1.000  0.380  0.059  0.874 
DP2  8.000  1.000  5.000  7.000  4.091  0.641  9.410 
DP3  6.000  0.200  1.000  4.000  1.480  0.232  3.405 
maxUR_{2}  1.000  0.143  0.250  1.000  0.435  0.068  *maxUR_{2 }= 1.000 
Total  6.385  1.000 
Table 11: Paired Comparison Table Including an Acceptable Level of the Harmful Effect 3 of Design Proposals (DPs)  
Economical Efficiency  Consistency Index  If CI < 0.1, it is OK In this case, CI = 0.013  
DP1  DP2  DP3  maxUR_{3}  Geometric Average  Weight  EW (3, k) K = 13  
DP1  1.000  2.000  3.000  1.000  1.565  0.359  1.107 
DP2  0.500  1.000  2.000  0.500  0.841  0.193  0.595 
DP3  0.333  0.500  1.000  0.500  0.537  0.123  0.380 
maxUR_{3}  1.000  2.000  2.000  1.000  1.414  0.325  *maxUR_{3 }= 1.000 
Total  4.357  1.000 
Table 12: Paired Comparison Table Including an Acceptable Level of the Harmful Effect 4 of Design Proposals (DPs)  
Environmental Policy  Consistency Index  If CI < 0.1, it is OK In this case, CI = 0.020  
DP1  DP2  DP3  maxUR_{4}  Geometric Average  Weight  EW (4, k) K = 13  
DP1  1.000  1.000  2.000  1.000  1.189  0.286  0.841 
DP2  1.000  1.000  1.000  0.500  0.841  0.203  0.595 
DP3  0.500  1.000  1.000  0.500  0.707  0.170  0.500 
maxUR_{4}  1.000  2.000  2.000  1.000  1.414  0.341  *maxUR_{4 }= 1.000 
Total  4.151  1.000 
Table 13: Paired Comparison Table Including an Acceptable Level of the Harmful Effect 5 of Design Proposals (DPs)  
Safety  Consistency Index  If CI < 0.1, it is OK In this case, CI = 0.038  
DP1  DP2  DP3  maxUR_{5}  Geometric Average  Weight  EW (5, k) K = 13  
DP1  1.000  0.167  0.200  1.000  0.427  0.081  0.855 
DP2  6.000  1.000  0.500  4.000  1.861  0.351  3.722 
DP3  5.000  2.000  1.000  4.000  2.515  0.474  5.030 
maxUR_{5}  1.000  0.250  0.250  1.000  0.500  0.094  *maxUR_{5 }= 1.000 
Total  5.303  1.000 
Keep in mind the five tables are based on a series of harmful effects. When using the AHP including the acceptable level an individual will have to consider that the more the design proposal weighs, the more harmful effects decrease and the value of each design proposal increases. This is because the direction of an acceptable level advances to zero (shown in Table 5). The weight of each harmful effect, therefore, is reciprocal in value compared to the one of each useful function.
Table 14 shows the total score of each design proposal for a series of useful functions:
Table 14: Total Score of Each Design Proposal for a Series of Useful Functions  
UF1 Easiness to Drink  UF2 Heatretaining Property (coffee stays hot)  UF3 Insulating the Heat of Hot Coffee  Total Score (TS)  
Weight of UFi  0.380  0.308  0.312  1.000 
*minRi  1.000  1.000  1.000  1.000 
DP1: U1  1.604  1.414  1.093  1.386 
DP2: U2  0.160  2.378  1.361  1.218 
DP3: U3  0.160  2.378  0.192  0.853 
After that, calculate the total score of each design proposal for a series of harmful effects by the same method shown in Table 15.
Table 15: Total Score of Each Design Proposal for a Series of Harmful Effects  
HE1 Waterproof Property  HE2 Mobility of Coffee  HE3 Economical Efficiency  HE4 Environmental Policy  HE5 Safety  Total Score (TS)  
Weight of HEj  0.196  0.357  0.107  0.155  0.185  1.000 
*maxURj  1.000  1.000  1.000  1.000  1.000  1.000 
DP1: H1  0.577  0.874  1.107  0.841  0.855  0.832 
DP2: H2  1.861  9.410  0.595  0.595  3.722  4.568 
DP3: H3  1.861  3.405  0.380  0.500  5.030  2.627 
Based on the total score of each design proposal for a series of useful functions and harmful effects, calculate the ideality index:
Table 16: The Ideality Index of Each Design Proposal (DP)  
ΣUF (useful function) Total Score (TS)  ΣHE (harmful effect) Total Score (TS)  Ideality Index  
Min I  1.000  1.000  1.000 
DP1: I1  1.386  0.832  1.665 
DP2: I2  1.218  4.568  0.267 
DP3: I3  0.853  2.627  0.325 
The result of Table 15 shows that design proposal 1 is expected to be the most attractive mobile paper cup for users. Consumers (or users) using consumable goods like paper cups decide what paper they like. An engineer decides on new product activities such as improving ideality since they have to chase the IFR.
The importance of the ideality index calculated through the proposed decisionmaking model is for engineers (with new product activities) and TRIZ practitioners to use this model. It is possible to predict the most valuable design proposal (alternative) before proceeding to the production stage. The most valuable design proposal (based on TRIZoriented thinking as it corresponds to the highest ideality index is more than one (it means desiring level of ideality index). It could possibly solve the serious contradictions before they appear. The solo lid and insulating sleeve shown in Figure 11 is a highlyvalued idea for solving contradictions for a usual paper cup under the condition of walking while drinking coffee.^{3} Practitioners of TRIZ should use the proposed decisionmaking model when predicting the most valuable design proposals in TRIZ activities.
Note: This paper was originally presented at The Altshuller Institute's TRIZCON2009.
Sawaguchi Manabu is a researcher and consultant for the SANNO Institute for Management, Japan. Contact Manabu Sawaguchi at SAWAGUCHI_Manabu (at) hj.sanno.ac.jp.