Identifying potential synthesis cases in distributed expert systems: a fuzzy logic approach
Introduction
When different expert systems (ESs) or intelligent agents cooperate together for solving the same problem, each of them may obtain a solution based on its domain knowledge, reasoning method, and evidences which are used to derive the solution. How to synthesize these multiple solutions from different ESs or agents to produce the final solution for the problem solving is one of several critical issues in a cooperative team in the field of distributed expert systems (DESs) [2].
Many synthesis strategies have been developed for solving different synthesis cases in the past 15 years [1], [4], [6], [7].
Generally speaking, synthesis situations can be classified into conflict cases and non-conflict cases based on the relationship of original evidence sets from ESs [8]. Most of the strategies used in previous research have dealt with conflict resolutions [4], [5], [7]. In recent years, we have proposed some mathematical models and neural network strategies for solving non-conflict cases [6].
Non-conflict cases are very complicated cases. Broadly speaking, they may include overlap cases, disjoint cases, and inclusion cases, based on relationship of original evidence sets which are used to derive the solution from different ESs. An absolutely disjoint case and an absolutely included case are extreme cases. Between these two extreme cases, there are many situations for the relationships of original evidence sets which can vary from a little bit of overlap, medium overlap, significant overlap, to full inclusion. Different overlap degrees among evidence sets represent how much extra evidence is used by ESs to get solutions. In order to get correct results for solution synthesis, the designers of synthesis strategies not only need to consider using different strategies in different synthesis cases, but also need to take the overlap degree into account. For example, if a synthesis case is in an overlap case with a small overlap degree, a strategy used to solve the problem should be very different from the strategy which works in an overlap case with a very big overlap degree. The first case is much closer to a disjoint case and the second case is closer to an inclusion case or a conflict case depending on the sizes of original evidence sets [8].
In this paper, we propose a fuzzy logic approach to identify different synthesis cases and overlap degrees among original evidence sets. The purpose of this research is to offer a guideline for designing and selecting correct strategies for solution synthesis in DESs. The remainder of this paper is organized as follows. In Section 2, the solution synthesis is described and potential synthesis cases are analyzed. In Section 3, the principle of this fuzzy logic approach is introduced and a basic framework of the approach is proposed. In 4 Fuzzification, 5 Approximate reasoning, 6 Defuzzification, the methods of fuzzification, approximate reasoning, and defuzzification are introduced in detail, respectively. Finally, in Section 7, this paper is concluded and further work is outlined.
Section snippets
Solution synthesis
We now formally describe the problems. Suppose there are n ESs in a DES used to evaluate the values of an attribute of an object (e.g. in a medical DES, the identity of an organism infecting a specific patient). The solution for an ESi can be represented as
The basic framework of a fuzzy logic approach
The framework of fuzzy logic approach for identifying potential synthesis cases is graphically illustrated in Fig. 4.
There are five units in this approach, which are: (1) a library of fuzzy functions, (2) a fuzzy rule base, (3) a fuzzification module, (4) an approximate reasoning module, and (5) a defuzzification module.
The inputs of the framework are SizeRatio and IntersectionRatio which are defined in Section 4.1. The outputs of this framework are identified synthesis cases with application
Input and output parameters
There are two input parameters, SizeRatio and IntersectionRatio, to be identified. These two parameters offer the fundamental information, which is used to determine the relationship of two original evidence sets. Definition 5 If S denotes the size of the smaller set of the two original evidence sets, and L denotes the size of the larger set of the two original evidence sets, SizeRatio is defined as (S/L)×100, where SizeRatio∈[0%,100%]. Definition 6 If I represents the size of the intersection area of the two original
Approximate reasoning
The approximate reasoning is fired to calculate output membership values, which further can be used to compute corresponding output values. The approximate reasoning is based on the using of rules in the rule base.
Defuzzification
There are many defuzzification approaches. The centroid defuzzification method [3] is one approach to defuzzify the output membership values.Where μ(vi) is the ith output membership value, vi is its corresponding output value, and k is the number of fuzzy rules which are activated.
DV is the final output value of Non-conflictDegree in a particular case. DV can be used to evaluate the type of synthesis case, and can also be used as an important factor for selecting or
Conclusion
In this paper, we have identified eight potential cases of synthesis in DESs by a fuzzy logic approach. A framework of this approach has been proposed which consists of a fuzzification module, a fuzzy rule base, an approximate reasoning module, a defuzzification module, and a library of fuzzy membership functions. All of the fuzzy membership functions for corresponding fuzzy sets have been carefully defined and rules of fuzzy logic operations during the procedure of approximate reasoning have
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