PII: 0888-613X(93)90008-2


Foreword: Special Issue 
on Fuzzy Expert Systems 

In this special issue on "Fuzzy Expert Systems," six papers cover a wide 
range of c o n c e r n s - - f r o m  theory to applications including: (1) a rule base 
reorganization, (2) a linear interpolation, (3) a neuro-fuzzy approach to 
pairwise comparison, (4) properties of reduction, in transitive matrices, (5) 
a consistency checking procedure, and (6) a context dependency model. 
We present a brief review of these papers next. 

In "Rule Base Reorganization and Search with a Fuzzy Cluster Analysis," 
Tiirksen and Jiang proposes a fuzzy cluster analysis for the purpose of 
restructuring a knowledge base where rules are either S- or R-implication 
types. The proposed algorithm can be implemented either with a composi- 
tional or an analogical tolerance relation. It is shown that analogical 
tolerance relation is more efficient in a rule base restructuring and a rule 
firing schema, under the proposed search scheme. 

In "Approximate Reasoning by Linear Rule Interpolation and General 
Approximation," K6czy and Hirota investigate the problem of sparse fuzzy 
rule bases. They review various methods of analogical reasoning available 
in current literature. They discuss concepts of graduality, measurability, 
distance, and similarity in the fuzzy sense. The fundamental equation of 
rule interpolation is introduced with a-cuts and resolution principle. The 
method is extended to multi-dimensional spaces. 

In "Neuro-Fuzzy Approach to Data Analysis of Pairwise Comparisons," 
Ichihashi and Tiirksen propose an artificial neural network model with an 
iterative on-line learning scheme. Two quantification methods of pairwise 
comparisons are presented in order to derive the associated weights. The 
proposed approach can also be implemented even when we have access to 
incomplete pairwise comparisons. The proposed approach is compared 
with Guttman's method and Saaty's AHP. 

In " O n  Reduction of Transitive Fuzzy Matrices and Its Applications," 
Di Nola, Kolodziejczjk, and Sessa show that the class of s-trarisitive 
(w-transitive) fuzzy matrices properly contain the class of m a x - m i n  transi- 
tive fuzzy matrices. It is also shown that the basic properties of the 
reduction models remain valid also for s-transitive fuzzy matrices. 

Address correspondence to L B. Tiirksen, Department o f  Industrial Engineering, University of 
Toronto, Toronto, Ontario M5S 1A4 Canada. 
Received March 12, 1992; accepted March 12, 1993. 

International Journal of Approximate Reasoning 1993; 9:165 166 
© 1993 Elsevier Science Publishing Co., Inc. 
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166 I.B. Tfirksen et al. 

In "Consistency Checking for Fuzzy Expert Systems," Leung and So 
introduce an affinity measure based on a similarity measure and apply this 
measure for consistency checking in mixed fuzzy and non-fuzzy expert 
system environments. 

In "The Context Model: A n  Integrating View of Vagueness and Uncer- 
tainty," Gebhardt and Kruse address two different types of partial igno- 
rance, i.e., vagueness and uncertainty. In this paper they restrict their 
presentation to Bayes Theory and D e m p s t e r - S h a f e r  Theory. "Context 
Model" applications are illustrated for the spoiled sandwich effect, the 
three prisoners problem, and the unreliable alarm paradigm. 

We hope that our readers will find these topics of some interest to their 
ongoing theoretical and applied investigations. 

I. Burhan Tfirksen, Hideo Tanaka, and Junzo Watada