MODELLING HUMAN REASONING

IN INTELLIGENT DECISION SUPPORT SYSTEMS

V. N. Vagin and A. P. Yeremeyev

Moscow Power Engineering Institute

Krasnokazarmennaya 14, 111250, Moscow, Russia

Keywords: Reasoning by analogy, intelligent decision support system, structural analogy, generalization, rough set.

Abstract: Methods of analogy-based solution searches in intelligent decision support systems are considered. The

special attention is drawn to methods based on a structural analogy that use the analogy of properties and

relations and take the context into account. Besides the problem of concept generalization is viewed. Several

algorithms based on the rough set theory are compared and the possibility to use them for generalization of

data stored in real-world databases is tested.

1 INTRODUCTION

Investigation of mechanisms that are involved in the

analogous reasoning process is an important

problem both for psychologists and specialists in

artificial intelligence (AI). The analogy can be used

in various applications of AI and for solving various

problems, e.g., for generation of hypotheses about an

unknown problem domain or for generalizing

experience in the form of an abstract scheme. The

great interest in this problem is caused by the

necessity of modelling human reasoning (common

sense reasoning) in AI systems and, in particular, in

intelligent decision support systems (IDSS).

In the encyclopaedia the word analogy (analogia,

Greek: correspondence, similarity, likeness,

closeness) is defined as the similarity of objects

(phenomena, processes) with respect to some

properties. Reasoning by analogy is the transfer of

knowledge obtained from an object to a less studied

one which is similar to the latter with respect to

some essential properties or attributes. Reasoning of

this kind is a source of scientific hypotheses.

Thus, analogy-based reasoning can be defined

as a method that allows to understand a situation

when compared with another one. In other words, an

analogy is an inference method that allows to detect

likeness between several given objects due to

transfer of facts and knowledge valid for both

objects, to other objects and to determine means of

problem solution or to forecast unknown properties.

It is this type of inference that is used by a human in

the first stages of solving a new problem. At the

present time, there are a great number of various

models, schemes, and methods that describe

mechanisms of reasoning by analogy. Another

important problem is a problem of concept

generalization especially in case it is necessary to

treat incomplete and inconsistent information.

However the real data bases (DB) contain, as a rule,

“raw” data and without analysis and generalization

these flows of “raw” data are of no use.

The common point of these data is that they

contain a large number of hidden regularities. At

present, to reveal these regularities and construct

inductive models, generalization methods and

computer systems that implement these methods are

being developed. Using generalization methods in

decision-making systems, the features that

characterize the group to which one or another

object belongs are selected. This is achieved by

analyzing already classified objects and forming a

certain set of rules (generalized model). Then, this

generalized model can be used for recognizing

objects not known to the system in advance. The

problem of classifying objects under excessive,

incomplete, or inconsistent information is very

important. We consider the opportunities of using

the rough set theory for solving problems of

inductive concept generation, as well as to propose

methods for improving known algorithms. A new

algorithm for discretization of continuous attributes

which considerably improves the efficiency of

generalization procedures is proposed. The

generalized structure of a real-time IDSS is given in

Fig. 1. The search for an analogous solution may be

applied in units of analysis of the problem situation,

learning, adaptation and modification, modelling,

and forecasting (Vagin, Eremeev, 2001).

277

N. Vagin V. and P. Yeremeyev A. (2007).

MODELLING HUMAN REASONING IN INTELLIGENT DECISION SUPPORT SYSTEMS.

In Proceedings of the Ninth International Conference on Enterprise Information Systems - AIDSS, pages 277-282

DOI: 10.5220/0002355502770282

 SciTePress

2 REASONING BY ANALOGY

Questions about the nature of analogies, a formal

definition, justification of reasoning by analogy, etc.,

arose in the time of epicureans and stoics. The

attempts to answer these questions, starting from the

first attempts of Leibniz to formalize this notion up

to our time, have not received a final answer

(Pospelov, 1989; Varshavskii, Eremeev, 2005).

At the present time, there are a great number of

various models, schemes, and methods that describe

mechanisms of reasoning by analogy (Varshavskii,

Eremeev, 2005; Long, Garigliano, 1994; Eremeev,

Varshavsky, 2005; Haraguchi, Arikawa, 1986).

In (Haraguchi, Arikawa, 1986), the authors have

proposed two types of analogies: an analogy for

solving problems and an analogy for forecasting.

The analogy for solving problems assumes

applying reasoning by analogy for increasing the

efficiency of the problem solution which, generally

speaking, can be solved without analogy as well, as,

e.g., in programming and proving theorems.

Analogy for prediction (forecasting) uses

reasoning by analogy for obtaining new facts. Due to

the transformation of knowledge based on the

likeness of objects, one can make the conclusion that

new facts probably hold. For example, if an analogy

is applied to a system of axioms, the result may be

certain theorems valid with respect to the system.

Here, using the similarity between axiom systems,

one can transform a theorem in a system to a logical

formula in another system and make a conclusion

that the latter is a theorem.

Depending on the nature of information

transferred from an object of analogy to the other

one, the analogy of properties and the analogy of

relations can be distinguished.

The analogy of properties considers two single

objects or a pair of sets (classes) of homogeneous

objects, and the transferred attributes are properties

of these objects, for example, analogy between

illness symptoms of two persons or analogy in the

structure of the surfaces of Earth and Mars, etc.

The analogy of relations considers pairs of

objects where the objects can be absolutely different

and the transferred attributes are properties of these

relations. For example, using the analogy of

relations, bionics studies processes in nature in order

to use the obtained knowledge in a modern

technology.

According to plausibility degrees one can

distinguish three types of analogies: strict scientific

analogies, nonstrict scientific analogies, and

nonscientific analogies.

A strict scientific analogy is applied to scientific

studies and mathematical proofs. For example, the

formulation of the attributes of the similarity of

triangles is based on a strict analogy which results in

a deductive inference, i.e., which deduces a valid

conclusion.

Unlike the strict analogy, a nonstrict scientific

analogy results only in plausible (probable)

reasoning. If the probability of a false statement is

taken equal to 0 and that of the true statement is

taken equal to 1, then the probability of inference by

a nonstrict analogy lies in the interval from 0 to 1.

To increase this probability, one needs to satisfy a

number of requirements to the method of reasoning

by analogy, otherwise, a nonstrict analogy may

become nonscientific.

A nonscientific analogy is often used

deliberately to perplex the opponent. Sometimes, a

BLOCK OF TRAINING,

ADAPTATION AND

MODIFICATION

DATA

BASE

MODEL

BASE

KNOWLEDGE

BASE

SIMULATION

BLOCK

PREDICTION

BLOCK

KNOWLEGE

ASQUISITION AND

ACCUMULATION BLOCK

USER INTERFACE (DECISION-MAKER)

OUTDOOR ENVIROMENT INTERFACE (OBJECT, DBMS etc.)

PROBLEM

SITUATION

ANALYZER

DECISION

MAKING

BLOCK

Figure 1: The generalized structure of a real-time IDSS.

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278

nonscientific analogy is used unintentionally, by

someone not knowing the rules of analogies or

having no factual knowledge concerning the objects

and their properties that underlie the inference.

We consider the methods of solution search on

the basis of structural analogy which allows to take

into account a context and based on the theory of

structural mapping. We use semantic networks

(SNs) as a model of knowledge representation.

3 REASONING BY STRUCTURAL

ANALOGY TAKING INTO

ACCOUNT A CONTEXT

In (Long, Garigliano, 1994), the authors have

proposed to consider an analogy as a quadruple

A = <O, C, R, P> where O and R are the source

object and the receiver one and C is the intersection

object, i.e., the object that structurally intersects

them and has larger cardinality of a set of properties

as compared with these objects. In other words, the

analogy between the source object and the receiver

object is considered in the context of the

intersection, and P is a property for definition of the

original context. The structure of this analogy is

represented in Fig. 2.

Using the described structure of the analogy, the

authors of (Long, Garigliano, 1994) have proposed

the algorithm for the problem solution that is based

on analogy of the properties. A SN with information

about the problem domain, a receiver R, and a

property for defining the original context P provide

input data for this algorithm.

The algorithm for the problem solution on the

basis of analogy taking into account the context

consists of the following steps.

Step 1. Determine all objects of the SN, except

for receiver R, that have property P. If there are no

objects of this kind, then the search for a solution

fails, otherwise, go to step 2.

Step 2. For the objects found in step 1,

determine all possible intersections of C with R

taking into account P. If there are no intersections of

C, then the search for a solution fails, otherwise, go

to step 3.

Step 3. From the objects extracted in step 1,

determine all possible sources O for analogies with

the receiver R and the intersection C taking into

account P. In the case of success (possible analogies

for R are defined), go to step 4, otherwise, the search

for a solution fails.

Step 4. From the analogies extracted in step 3,

choose the most appropriate (taking into account the

requirements of the decision making person (DMP)).

In the case of success, go to step 5; otherwise, the

search for a solution fails.

Step 5. The analogies obtained in step 4 are

given to the DMP which means successful

termination of the algorithm.

Having obtained analogies, the DMP may then

make the final choice of the best ones. On the basis

of these facts, the facts (properties) that hold for the

source O are transferred to the receiver R.

Consider the modified algorithm for a problem

solution that uses the structural analogy based on the

modified structure of analogy and the algorithm for

the search of minimal intersections (Varshavskii,

Eremeev, 2005). The modification consists in the

fact that P is considered not as a unique property,

but as a set of properties that determine the original

context of the analogy. As compared with the base

variant, one of the main advantages of this modified

algorithm is the possibility of implementing the

search for a solution on the basis of analogy without

refining the original context, since in the result of

the search for the minimal intersection, one can

easily distinguish all possible contexts for the

analogy. Another important advantage of the

modified algorithm is the possibility of a more

detailed refinement of the original context for the

determination of analogies. Moreover, in the

modified algorithm there is a possibility to construct

analogy taking into account the context between

well-known objects, the source and the receiver.

4 GENERALIZATION PROBLEM

For the description of an object we will use features

, a

, …, a

, which are further called attributes.

Each object x is characterized by a set of given

values of these attributes: x = {v

, v

, …, v

} where v

is a value of the i-th attribute. Such description of an

object is called feature description. For example, the

attributes may be a colour, a weight, a form, etc.

Let we have a learning set U of objects. It

contains both the positive examples (which are

concerning to interesting concept) and the negative

examples. The concept generalization problem is the

construction of the concept allowing the correct

classifying with the help of some recognizing rule

(decision rule) of all positive and negative objects of

Figure 2: The structure of the analogy.

MODELLING HUMAN REASONING IN INTELLIGENT DECISION SUPPORT SYSTEMS

279

a learning set U. Here the construction of the

concept is made on the basis of analysis of a

learning set.

Let’s introduce the following notions related

with the set U. Let U = {x

, x

, …, x

} is a non-

empty finite set of objects. A = {a

, a

, …, a

} is a

non-empty finite set of attributes. For each attribute

the set V

is defined which refers to the value set of

an attribute a. We will denote the given value of an

attribute a for an object x ∈ U by a(x). At the

decision of the generalization problem, it is often

necessary to receive the description of the concept

which is specified by a value of one of the attributes.

We will denote such attribute d and call it decision

or a decision attribute. The attributes which are

included in A are called conditional attributes. The

decision attribute can have some values though quite

often it is binary. The number of possible values of a

decision attribute d is called the rank of the decision

and is designated at r(d). We will denote the value

set of the decision by

} ..., , ,{

)(21

vvvV =

. The

decision attribute d is defined by the partition of U

into classes C

= {x ∈ U: d(x) =

v }, 1 ≤ i ≤ r(d).

Generally, the concept generated on the basis of

the learning set U is an approximation to a concept

of the set X where the closeness degree of these

concepts depends on the representativeness of a

learning set, i.e. how complete the features of set X

are expressed in it.

5 CONCEPT GENERALIZATION

METHODS BASED ON THE

THEORY OF ROUGH SETS

The rough set theory has been proposed in the

beginning of 80

years of the last century by the

Polish mathematician Z. Pawlak. We will consider

how the rough set theory can be used to solve

concept generalization problem – see also (Pawlak,

2002; Bazan, 1998; Vagin, Golovina, ec.,2004;

Nguyen, Nguyen, 1996). In Pawlak’s works the

concept of an information system has been

introduced. An information system is understood as

the pair S = (U,A) where U = {x

, x

, …, x

} is a

non-empty finite set of objects named the learning

set or universe, and A = {a

, a

, …, a

} is a non-

empty finite set of attributes. A decision table is an

information system of the form S = (U, A ∪ {d}),

where d ∉ A is a distinguished attribute called

decision or a decision attribute. A is a set of

conditional attributes.

Now let us consider the methods of concept

generalization using the theory of rough sets.

Generally, work of the algorithm based on the rough

set theory consists of the following steps: search of

equivalence classes of the indiscernibility relation,

search of upper and lower approximations, search of

a reduction of the decision system and constructing a

set of decision rules. Moreover, discretization is

applied to processing attributes with a continuous

domain. In the case of the incomplete or inconsistent

input information, the algorithm builds two systems

of decision rules, one of them gives the certain

classification, the second gives the possible one.

Further, we will consider the most labour-consuming

steps: search of reduction and discretization making.

5.1 The Problem of Search of

Reduction

Let’s consider the process of search of reduction

that is very important part of any method used the

rough set approach. Quite often an information

system has more than one reduction. Each of these

reductions can be used in the procedure of decision-

making instead of a full set of attributes of an

original system without a change of dependence of

the decision on conditions that is characteristic for

an original system. Therefore, the problem of a

choice of the best reduction is reasonable. The

answer depends on an optimality criterion related to

attributes. If it is possible to associate with attributes

the cost function which expresses complexity of

receiving attribute values, then the choice will be

based on the criterion of the minimal total cost. The

problem of searching for a reduction with minimal

length is NP-hard (Skowron, Rauszer, 1992).

Thus, the problem of a choice of relevant

attributes is one of the important problems of

machine learning. There are several approaches

based on the rough set theory. One of the first ideas

was to consider as the relevant attributes those

attributes which are contained in intersection of all

reductions of an information system.

Other approach is related to dynamic reductions

(Bazan, 1998), i.e. conditional attribute sets

appearing “sufficiently often” as reductions of sub-

samples of an original decision system. The

attributes belonging to the “most” of dynamic

reductions are considered as relevant. The value

thresholds for “sufficiently often” and “most” should

be chosen for given data.

The third approach is based on introduction of

the notion of significance of attributes that allows by

real values from the closed interval [0, 1] to express

how important an attribute in a decision table.

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5.2 The Modification of the

Discretization Algorithm

The stage of discretization is necessary for the most

of modern algorithms for generalization. The

discretization is called a transformation of a

continuous domain of attributes in a discrete one.

For example, the body temperature of the human

being which is usually measured by real numbers

can be divided into some intervals, corresponding to

a low, normal, high and very high temperature. The

choice of suitable intervals and partition of

continuous domains of attributes is a problem whose

complexity grows in exponential dependence on the

number of attributes to which discretization should

be applied. The general approach of the most

discretization algorithms is based on that any

irreducible set of cuts of a decision table S is a

reduction of other decision table constructed on the

basis of S.

Our algorithm is directed towards decreasing

time and memory consumption. It is based on the

Jonson’s strategy and extension of idea of iterative

calculation of the number of pair of objects,

discerned by a cut. This idea has been offered in

(Nguyen, Nguyen, 1996), however, originally, it is

applicable only when some restrictions on the

decision table are imposed. This idea is based on

assumption that there is a close relation between two

consecutive cuts. So, for example, it is possible to

notice, that in each row of the table all the cells with

value 1 are placed successively within one attribute.

Therefore some pairs of objects are discerned by

both consecutive cuts, and changes in the number of

discernible pairs of objects can be only due to

objects which attribute values lay between two these

cuts. In (Nguyen, Nguyen, 1996), the situation,

when no more than one object lies in this interval, is

considered. We generalize this idea on a case of the

arbitrary number of such objects. Thus, our

algorithm extends idea of iterative calculating

number of pairs of objects discerned by a cut to an

arbitrary decision table. In the majority of the

algorithms which are based on the rough set theory

and carrying out splitting of continuous attribute

domains into finite number of intervals, the stage of

discretization is considered as preparatory before

search of significant attributes. And consequently at

a stage of discretization, there is a splitting the

domains of all continuous attributes including

insignificant. In this work, the combined

implementation of discretization with search of a

reduction is offered to make discretization only for

those quantitative attributes which appear to be

significant during search of reduction.

Thus, the developed algorithm for search of

significant attributes is based on two ideas:

1) combination of discretization of quantitative

attributes with search of significant attributes,

2) search for an approximation of reduction, but no

for reduction itself. Let’s name it as Generalized

Iterative algorithm based on the Rough Set

approach, GIRS.

5.3 Results of the Experiments

The implemented experiments have shown that the

developed algorithm allows to reduce time for

search of significant attributes essentially, due to

combination with the discretization stage and use of

the proposed algorithm.

The results of the experiments executed on 11

data sets from a well known collection UCI Machine

Learning Repository (Merz, Murphy, 1998) of the

University of California are given in Table 1.

For all data sets taken into the comparison, the

Classification accuracy Data set

ID3 C4.5 MD Holte-II

GIRS

Monk-1 81.25 75.70 100 100

100

Monk-2 65.00 69.91 99.70 81.9

83.10

Monk-3 90.28 97.20 93.51 97.2

95.40

Heart 77.78 77.04 77.04 77.2

78.72

Hepatitis n/a 80.80 n/a 82.7

84.51

Diabetes 66.23 70.84 71.09 n/a

81.00

Australian 78.26 85.36 83.69 82.5

88.71

Glass 62.79 65.89 66.41 37.5

70.10

Iris 94.67 96.67 95.33 94.0

96.24

Mushroom 100 100 100 100

100

Soybean 100 95.56 100 100

100

Average 81.63 83.18 88.67 85.3

88.89

Table 1: Comparison of classification accuracy of the developed algorithm with other generalization algorithms.

MODELLING HUMAN REASONING IN INTELLIGENT DECISION SUPPORT SYSTEMS

281

developed algorithm has shown classification

accuracy that not concedes to other generalization

algorithms, and in some cases surpasses them.

Average accuracy of classification is approximately

88.9%. It is necessary to note that the classification

accuracy received by our algorithm is much above

that the classification accuracy achieved by methods

of an induction of deciding trees (ID3, ID4, ID5R,

C4.5) at the solving the majority of the problems. It

is explained by the impossibility of representation of

the description of some target concepts as a tree.

Moreover, it is possible to note that combining of

search of significant attributes and the discretization

procedure is very useful. Most clearly, it is visible

from the results received at the decision of the

Australian credit task. It is possible to explain by the

presence in these data the attributes both with

continuous and with discrete domains. The

modification of the search procedure of significant

attributes is directed namely to processing of such

combination.

6 CONCLUSIONS

The method of reasoning by analogy on the basis of

structural analogy was considered from the aspect of

its application in modern IDSS, in particular, for a

solution of problems of real-time diagnostics and

forecasting. The example of the algorithm for

solution search on the basis of analogy of properties

that takes into account the context was proposed.

This algorithm uses a modified structure of analogy

that is capable of taking into account not one

property (as in the base algorithm), but a set of

properties. These properties determine the original

context of analogy and transfer from the source to

the receiver only those facts that are relevant in the

context of the constructed analogy.

The presented method was applied at

implementation of a prototype of IDSS on the basis

of non-classical logics for monitoring and control of

complex objects like power units.

We have also considered the concept

generalization problem and the approach to its

decision based on the rough set theory. The heuristic

discretization algorithm directed towards the

decreasing of time and memory consumption has

been proposed. It is based on Jonson’s strategy and

extension of idea of iterative calculation number of

pairs of objects discerned by a cut. Also the search

algorithm of the significant attributes combined with

the stage of discretization is developed. It allows to

avoid splitting into intervals of continuous domains

of insignificant attributes.

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