Aggregation of Fuzzy Preferences as an Efficient

Aggregation of Fuzzy Preferences as an Efficient Approach to the Computational Personality Type Classification Problem Ladislava Jankù, Lenka Lhotská Department of Cybernetics, Faculty of Electrical Engineering Czech Technical University Technická 2, Praha 6, 166 27 CZECH REPUBLIC [email protected], [email protected]

Abstract: - This paper deals with the problem of automatic human operator’s personality type classification by intelligent man-machine interface. Presented approach is based on application of aggregation of the individual

fuzzy preferences into one fuzzy relation with respect to information about relative importance of individual attributes characterizing each of the alternatives. These attributes are obtained from the preference expert systems that are able to provide independent comparative evaluation of all alternatives. Key-Words: - computational personality type classification, expert system, aggregation of fuzzy preferences, intelligent man-machine interface, relation of relative importance,

1 Introduction The tremendous growth in automatic control of large technological processes has generated a necessity to improve communication and collaboration between human operator and control system. Human operator has to have a possibility to interfere to control process, but in the other hand, system failings are mostly caused by human operator’s failure. Intelligent interface, which could be able to monitor and estimate human operator’s psychical state and predict his/her future behavior, could minimize system failings caused by human factor. Investigations on the human’s operator psychical state monitoring and estimation have recently received remarkable attention particularly for the following applications: real-time measurement and processing of physiological data, on-line human operator monitoring, extraction of information from selected measured physiological parameters [13, 14, 18]. Other research in the area of intelligent man-machine interface has been devoted to the design of special multi-agent web based systems, which appear as a suitable solution for large internet and e-commerce systems, but which don’t provide a satisfying solution for the mentioned problem of human operator’s psychological state estimation. Examples of multi-agent oriented applications can be found in [6, 7]. Our previous research in essence involved application on artificial intelligence methods – expert system and machine learning - to the computational personality type classification problem [12, 5]. The major advantage of this approach towards the standard way consisting in psychological investigation was the higher objectivity and independence on the expert presence.

Because of presented approach involves an application of aggregation of fuzzy preferences, we briefly conclude past research in this research area. There are two types of the situations of choice with multiple preference relations in a set of alternatives. The first one is related to the problem of preferences of single decision maker with respect to multiple attributes pertaining to every alternative. The second situation reflects the problem of the decision making in the group of experts. There are many approaches of a mathematical analysis of such situations. One of them is set in the context of multiple person decision making, and is called the theory of social choice and is concerned with the problem of aggregating of given preferences into a one single preference relation [11]. Another approach is concerned with choices of alternatives from a given set based on given on given preference relations [2, 9, 15, 16, 17].

2 Formulation of Personality Classification Problem

Type

The necessity of estimation and prediction of the human’s operator psychical state implies a necessity of utilization of an operator’s internal model. A task of the internal model selection is closely related to the problem of human operator’s personality type classification. Each type of personality is characterized by its own mental model. It appears much more suitable to provide this classification automatically than to follow a standard way consisting in a special kind of psychological investigation. This approach sets a new requirement to intelligent man-machine interface. Interface must be able to classify

human’s operator personality type. To solve this problem, we designed a way and a methodology how to do it. This methodology consists in several physiological parameters measurement while the tested person performs psychical or physical exercises putting a psychical stress to her or him. The problem formulation can be following: How to estimate a human operator’s personality type from the measured physiological data on condition we have some information about relations between the changes of these psychological parameters and human personality type? Unfortunately, this information given by experts is pretty vague and mostly inconsistent. How to avoid this inconsistency? Is admissible to miss any information to exclude inconsistency? Especially, when the expert system is applied to this problem, the knowledge base inconsistency is inadmissible and has to be solved during knowledge base construction. The simplest approach could be missing that information, which is regarded as the least important or incorrect. We followed this way in our previous work [12]. This approach appears as a moot point and was discussed many times from several points of view. The rate of successfulness of the designed expert system depends something on creator’s intuition to exclude the least important or incorrect information. The second great disadvantage of this quite simple approach to information inconsistency is that usually each expert is not able to give an expression to each measured physiological parameter. For instance, he could be able describe very preciously relation between the changes of blood pressure and human personality type, but he could say nothing about the relation between this personality type and skin-galvanic response. This simple approach doesn’t enable to take account of this fact. However, experts differ usually in their relative importance for problem characterizing. On condition the simplest approach is applied, we can’t consider any relative evaluation of opinions of the experts. Hence this personality type classification problem should be treated as a multiple criteria choice problem with respect to relation of relative importance of advisors/experts.

3 Problem Solution Outline As we said above, the situation of choice with multiple preference relation in a set of alternatives can be regarded as a following one: there is a number of experts and each of the preference relations may reflect comparisons between alternatives from the viewpoint of the respective expert. To find an efficient solution, we set a little more different problem formulation towards the standard

approach described in the previous text and presented on Fig. 1. Standard approach involves a construction of one knowledge base consisting of rules concerning with information given by all experts. Output

Expert 1 Expert System Expert 2 Knowledge Base

. . . Expert n

Fig.1: A construction

Standard

way

of

knowledge

base

We decided not to design this well-known kind of knowledge base, but to use a few of preference expert systems [4]. Standard diagnostic expert system gives an answer consisting of one alternative. Preference expert system is a special kind of diagnostic expert system, which gives the evaluation of some relation defined on the set of all possible alternatives. This relation can be fuzzy or non-fuzzy and depends mainly on structure of this preference expert system. For more information on this kind of expert system, see [4].

Expert 1

Preference Expert System 1

Expert 2

Preference Expert System 2

. . . Expert n

. . . Preference Expert System 3

Aggregation Mechanism

Output

Fig.2: The change of the problem formulation: a set of preference expert systems and aggregation mechanism.

In this case, the fuzzy relation ‘Alternative (model, personality type) A is not worse than alternative (model, personality type) B for the given situation’ was used. Knowledge base of each expert system was designed to provide evaluation of this fuzzy relation; it involves knowledge and information obtained by one of the experts. The rules each knowledge base consists of needn’t be consistent with the ones included in the other knowledge bases. Input information of an individual expert system may differ from the input information of the other ones. Generally speaking, the input information depends only on the structure of the particular knowledge base. Only these physiological parameters which the particular knowledge base rules are related to can be regarded as system inputs. As we said above, each preference expert system provides an evaluation of the specific – in this case fuzzy – relation. These evaluations are aggregated with respect to relation characterizing mutual relative importance of used preference expert systems. See Fig. 2.

4 Mathematical Formulation of Multiple Criteria Choice Problem

the

This description follows [10]. Let M be set of alternatives and E a set of experts (attributes)

mI = E x E → [0,1]. (4) For every two attributes p, q the value mI(p, q) of this function is understood as degree determining to which degree the attribute p is not less important than attribute q. Let us denote mRnd(m,e) membership function of the fuzzy set of non-dominant alternatives:

mRnd a e = + −

mR b a e

b∈ X

− mR a b e))} (5)

where the mR(a,b,e) is a membership function describing fuzzy preference relation between pairs of models. Finally, it is necessary to perform extension of relation I characterizing importance of experts to the class of subsets of the set E and to understand resulting fuzzy relation as a fuzzy preference relation in the set X by Q. If we apply the principle of extension in its traditional form, we get for the membership function mQ equation (6). =

nd

nd

p , ∈E

M = {a, b, c, d, e, f, g, h, i},

I

q )}

(6) (1)

E = {es1, es2, es3}. (2) Each alternative is characterized by all attributes from the set E and it is possible to compare mutually all alternatives according to the given criterion by the system. For each attribute e ∈ E, fuzzy preference relation R(e) is given on the set M and is described by the membership function mR mR = M x M x E → [0,1].

This fuzzy preference is aggregation of profiles of individual fuzzy preferences R(e) to one fuzzy relation that includes information on relative importance of individual attributes as well. Thus we get a single fuzzy relation that enables us to perform selection of operator's behavior model with respect to importance of individual expert systems. That seems to be advantageous considering extensibility of the system. Another expert system can be added to the classification mechanism. Application of presented aggregation method to the personality type classification problem is illustrated by the following example.

(3) For every two alternatives a, b and arbitrary attribute e, the value mR(a, b, e) of this function is understood as a degree determining to which degree the variant a is not worse than variant b. Then {R(e), E} is profile of individual fuzzy preferences in the set M. Further relation I characterizing importance (credibility) of individual attributes (experts) is given. This relation is described by the membership function mI,

5 Methodology of Measurements We selected two factors on which the personality type depends - neuroticism and tendency to risk behavior [1, 8]. As we said above, the standard classification process consists in psychological investigation provided by an expert. Our approach is based on monitoring of human operator’s physiological responses (pulse frequency, systolic and diastolic blood pressures, skin resistance,

electromyographical potencial) to the different psychical load. Psychical load has been presented to the operator both in the visual and acoustic forms. As psychical load, standard diagnostic and load tests are used. Short test description follows. The first test consists of a set of the questions investigating verbal, numeric and perceptual logic, space perception and analytic and technical skills. Human operator is invited to answer these questions as quickly as he/she can. Naturally, the correctness is also required. The second test consists in the task of ‘number seven subtracting’. A random number between 900 and 1000 is selected. Operator is invited to subtract seven from this number, then to subtract seven from the obtained result, etc. The necessity to answer in the periodic intervals assures psychical stress genesis. The selected physiological parameters (pulse frequency, systolic and diastolic blood pressures, skin resistance, electromyographical potencial) are measured during the both rest and load test phases. To obtain basic information about tested person life style, we use case history data (coffee and alcohol drinking, medicaments taking, movement activity, etc.). We decided to use a scale consisting of three grades for both neuroticism and tendency to risk behavior classification (three-degree scale for each one). To assure a possibility to compare and evaluate results obtained by application of the described approach, each tested person passed a psychological investigation to diagnose his/her personality type, tendency to psychotic disorder, and tendency to neurotic behavior. This diagnosis was used as an absolute standard during the comparative evaluation. The success rate of each of designed algorithms for human operator’s personality type classification refers to this diagnosis.

6 Experiments & Results Discussion The set of tested persons consisted of 60 persons in age between 18 an 30. This set embodies persons with a tendency to risk behavior, persons with the tendency to neuroticism, and persons without any of the tendencies mentioned above. 600 testing sets, each containing about 30 elements, were selected randomly from the measured data. Then we added manually some special testing sets that describe some more heavily classifiable cases. Firstly, three preference expert systems were applied to all selected testing sets. Table 1 gives an overview of inputs of these systems. In this example, we consider nine possible personality types characterized by the different grade of the neuroticism and by the different grade of tendency to risk behavior.

Our relative evaluations of results provided by the preference expert systems are expressed by means of the matrix of the fuzzy relation of importance (Table 2). Table 1: An overview of the inputs of the applied preference expert systems Input

ES1

ES2

ES3

Systolic blood pressure

YES

-

Diastolic blood pressure

YES

-

-

Pulse frequency

YES

YES

-

Skin-galvanic Response

-

YES

-

Electromyographical potencials

-

-

YES

Table 2: Our relative evaluation of the importance of the applied preference expert systems, the relation “expert system A is not less important than expert system B” ES1

ES2

ES3

ES1

1

0.8

0.9

ES2

0.9

1

0.9

ES3

0.4

0.5

1

Let’s note, the used fuzzy relation is understood as “not less important than”. The average success rate of this system was about 93 percent for neuroticism classification and about 90 percent for tendency to risk behavior classification. The average success rate for the classification of personality type was about 90 percent. The successfulness of the presented approach depends mostly on the qualitative parameters of the preference expert system knowledge bases. If some of the expert systems outputs of which are aggregated may not for any reason provide relation for any pair of alternatives, and other relations are evaluated as the two alternatives are the same, it can “blur” a result. Several alternatives can be evaluated as optimal. Following theoretical example demonstrates this situation. We describe briefly an example concerning with the expert system which is not able to recognize differences for four pairs of the alternatives. In this example, we consider eight possible personality types characterized by the different grade of the neuroticism and by the different grade of tendency to risk behavior. The alternative/model a gives the best description of human operator’s personality, but some

personal qualities are also correlated with the alternative/model b. There are three preference expert systems. Table 3 describes the inputs of these systems. The goal is a correct selection of the appropriate personality type on basis of the measurement of specified physiological parameters. Table 3: An overview of the inputs of the preference expert systems (theoretical example)

b

c

d

e

f

g

h

a

1

1

0.8

1

0.9

1

1

1

b

0.2

1

0.4 0.9 0.6 0.9 0.8

c

0.4 0.8

d

0.1 0.5 0.4

YES

e

0.3 0.2 0.6 0.4

-

YES

f

-

YES

ES1

ES2

ES3

Systolic blood pressure

-

YES

-

Diastolic blood pressure

-

YES

-

Pulse frequency

-

YES

Skin-galvanic Response

-

Electromyographical potencials

YES

g

The evaluation given by the first preference expert system is described by the matrix of fuzzy preference relation “not less suitable than” in the Table 4. Table 4: Matrix of the values of the fuzzy preference relation “Alternative A is not less suitable than alternative B” given by expert system es1 b

a

1

1

b

1

1

Table 5: Matrix of the values of the fuzzy preference relation “Alternative A is not less suitable than alternative B” given by expert system es2 a

Input

a

alternatives are not suitable the grade will be a number close to 1. The evaluations given by other two expert systems with regard to preferences between alternatives of personality types are described in the Tab.3 and Tab.4 by the matrices of the same fuzzy preference relation.

c

d

e

f

h

1

0.9 0.7 0.9 0.7 0.9 1

0.5 0.7 0.5 1

0.2 0.4 0.6 0.3

0

a

b

c

e

a

1

1

0.5 0.2 0.9

0.9

1

b

0.2

1

0.5 0.9 0.6 0.9 0.8

1

c

1

0.5

1

0.7

0.7

1

1

0.5 0.7 0.5

1

e

0

0.3 0.6 0.8

0.8 0.8 0.9 0.9

1

1

f

0

0.1 0.4 0.6 0.3

c

0.5 0.5

1

1

0.7 0.7 0.7 0.7

g

d

0.5 0.5

1

1

0.7 0.7

h

0.9 0.9

f

0.1 0.1 0.4 0.4

1

1

0.9 0.9

g

0

0

0.2 0.2 0.8 0.8

1

1

h

0

0

0.2 0.2 0.8 0.8

1

1

The grade of membership function describes an evaluation of the fuzzy preference relation “not less suitable than” for each pair of alternatives/models. For example, the number 0.4 in the 6th row and 4th column is an evaluation of fuzzy preference relation “alternative f is not less suitable than alternative d”. Because of the preference expert system provides an evaluation of the fuzzy relation “not less suitable than”, on condition both

1

1

1

1

1

h

1

1

1

g

0.8 0.8 0.9 0.9

0.1 0.1 0.4 0.4

0.5 0.9

f

1

d

d

e

1

Table 6: Matrix of the values of the fuzzy preference relation “Alternative A is not less suitable than alternative B” given by expert system es3

h

0.7

0.5 0.9

0.2 0.2 0.7 0.2 0.8 0.4

g

0.7

1

1

0.1 0.2 0.4 0.2 0.6 0.8 0

1

0.1 0.5 0.4

1

1

1

0.8 0.9

1

0.5 0.9

0.1 0.3 0.4 0.6 0.6 0.8 0

1

0.1 0.2 0.2 0.2 0.8 0.4

1 1

Table 7: Our relative evaluation of the importance of the preference expert systems, the relation “expert system A is not less important than expert system B” ES1

ES2

ES3

ES1

1

0.6

0.7

ES2

1

1

1

ES3

1

0.9

1

Evaluations presented in the tables are the input data of the aggregation algorithm described in the previous part.

Firstly, we constructed the membership functions of the fuzzy sets of non-dominated alternatives for each expert system. Table 8: The grades of the membership functions of the fuzzy sets of non-dominated alternatives for each expert system ab

c

mnd (., ES1) = 0 0 0.5 . . 88

d

e

f

g

h

0.5

0.1

0.1

0

0

ab

mnd (., ES2) = 0 0 0.4 . . 82

0.1

0.3

0

0.1

0

mnd (., ES3) = 0 0 0.5 . . 52

0.4

0.1

0

0.1

0

Secondly, we constructed a matrix of the membership function of the aggregated fuzzy relation Q. Table 9: A matrix of the membership function of the aggregated fuzzy relation Q a

b

c

d

e

f

g

h

a

0.8 0.8 0.5 0.5 0.3 0.1 0.1

0

b

0.8 0.8 0.5 0.5 0.3 0.1 0.1

0

c

0.5 0.5 0.5 0.5 0.3 0.1 0.1

0

d

0.5 0.5 0.5 0.5 0.3 0.1 0.1

0

e

0.3 0.3 0.3 0.3 0.3 0.1 0.1

0

f

0.1 0.1 0.1 0.1 0.1 0.1 0.1

0

g

0.1 0.1 0.1 0.1 0.1 0.1 0.1

0

h

0

0

0

0

0

0

0

0

Finally, we constructed the corresponding membership function for the fuzzy set of non-dominated alternatives in the set (M,Q). Table 10: The membership function for the fuzzy set of non-dominated alternatives in the set (M,Q) ms Q(.) =

higher than the evaluation given by ever expert system. For example, see the membership function of fuzzy set of non-dominated alternatives in Table 10. The maximum non-dominance degree of the alternatives e, f, g, h is pretty lower. The overall degree should not exceed maximum non-dominance degree given by the expert systems. Considering this, we obtain a corrected membership function (see Table 11). Table 11: The corrected membership function for the fuzzy set of non-dominated alternatives in the set (M,Q)

a b

c

d

e

f

g

h

0 0. . 4 5

0.5

0.5

0.7

0.9

0.9

1

This function should give the resultant nondominance degrees by which the alternatives are not dominated by the other alternatives. However, these results need a careful analysis. In some special cases, the grade of fuzzy set (M,Q) membership function could be

s

m Q(.) =

c

0 0 0.5 . . 53

d

e

f

g

h

0.5

0.3

0.1

0.1

0

This function can be regarded as a background for the most suitable alternative selection. On condition we take into account only this membership function during the interpretation, the alternatives a, c, and d appears as the alternatives with the similar degree of nondominance.

7 Conclusion & Future Work In conclusion, we give a short overview of this contribution. The approach involving an aggregation of fuzzy preferences to task of computational personality type classification has been studied in this paper. The problem of knowledge inconsistency was formulated as a problem of multiple criteria choice problem. A new type of diagnostic expert system - preference expert system was defined. A structure consisting of preference expert systems and aggregation mechanism was presented and a mathematical formulation based on fuzzy logic was given. Let’s briefly describe main advantages and disadvantages of the presented approach. Extensibility (advantage) - this approach enables not only to perform choice for a set of alternatives but also to include views of several experts into decision making while incorporation of a new expert system into the current system can be done more or less without any problems. Relative importance of expert systems (advantage) this approach enables to include individual preferences of the applied expert systems. Distributed implementation (advantage) – towards the standard expert systems, which are almost pretty large centralized applications, this approach appears as a suitable for parallel implementation, because particular expert systems are mutually independent. This property opens an area for the future work. Particular Expert System Relevance (disadvantage)presented example demonstrates clearly this feature.

Presented approach requires the particular expert system relevance, i.e. each preference expert system has to be able give for each pair of alternatives (a,b) such evaluation, that at least one of the evaluations of the relations between pairs (a,x) and (b,x) differs (considering the letter x substitutes other alternatives). If not, the models are regarded as the similar, and the result is “blurred”. In this case, the evaluation provided by one expert system could be better and more robust than the results obtained by aggregation. This problem has to be solved on the level of the particular expert system knowledge bases. Also the application of other kinds of relations could be useful (a direction for future work). Firstly, in future work, we intend to study preference expert systems based on the other types of preference relations. Aggregation algorithms for mixed structures (mixed structure = a system containing preference expert systems based on different preference relations). Secondly, we would like to focus to the distributed implementation of the presented approach. References: [1] Eysenck, H.J, The Structure of Human Personality, 2nd edition, London 1960 [2] Fodor, J., Ovchinnikov, S.: On aggregation of ttransitive fuzzy binary relations, in Fuzzy Sets and Systems, 72:135-145, 1995 [3] Gath, I., Geva, A.: Unsupervised fuzzy clustering, IEEE Transactions PAMI, 11, 7, 1989, 773-781 [4] Jankù , L.: Fuzzy Graphs and Algorithms as a Mathematical Background for Fuzzy Distributed Systems, research report, BIO 333-10/00. ÈVUT FEL, Praha, 49 pp., 2000 [5] Jankù , L., Šorf, M., Eck, V.: Preliminary Phase of Co-operation between Human Operator and Intelligent Interface - Computational Personality Type Classification, research report, BIO 333-09/00. ÈVUT FEL, Praha, 38 pp., 2000 [6] Moukas A., and Maes, P., "Amalthaea: An Evolving MultiAgent Information Filtering and Discovery System for the WWW." Invited paper, First Issue of Journal of Autonomous Agents and Multi-Agent Systems, 1998 [7] Maes, P. "Agents that Reduce Work and Information Overload." Communications of the ACM, Vol. 37, No.7,pp. 31-40, 146, ACM Press, 1994. [8] Nakoneèny, M., Psychologie osobnosti (Personality psychology), Academia, Praha, 1998 [9] Ovchinnikov, S.: Means and social welfare functions in fuzzy binary relation spaces. In Kacprzyk, J. and Fedrizzi, M.: Multiperson Decision Making Using Fuzzy Sets and Possibility Theory, 143/154, Kluwer [10] Orlovski, S.: Calculus of decomposable properties, fuzzy sets and decisions, Allerton Press, 1994

[11] Slowinski, R. et al.: Fuzzy Sets in Decision Analysis, operations Research and Statistics, Kluwer Academic Publishers, 1998, ISBN 0-7923-8112-2 [12] Šorf, M., Jankù , L., Lhotská , L., Eck, V.: Applications of Expert System and Machine Learning Approach to Intelligent Man-machine Interface. In: Intelligent Techniques and Soft Computing in Nuclear Science and Engineering. Vol. 1. Singapore: World Scientific. p. 191-197. - ISBN 981-02-4356-1, 2000 [13]Takahashi, M. et al.: Development of Real-Time Cognitive State Estimator, Institute of Atomic Energy, Kyoto University, 1995 [14]Takahashi, M. et al.: Mutual Adaptive Interface: Basic Concept, Institute of Atomic Energy, Kyoto University, 1993 [15]Yager, R: Quantifiers in the formulation of multiple objective decision functions,. Information Sciences, 31, 107-139, 1983 [16]Yager, R: Families of OWA operators. Fuzzy Sets and Systems, 55, 255-271, 1993 [17]Yager, R: Connectives and quantifiers in fuzzy sets, Fuzzy Sets & Systems, 40, 39-75, 1991 [18] Yoshikawa, H. et al.: Concept on Mutual Adaptive Interface and Related Experiment Study, Institute of Atomic Energy, Kyoto University, 1994