MILORD: The architecture and the management of linguistically expressed uncertainty

The objective of this article is to describe the MILORD Shell and particularly its architecture and its management of uncertainty. MILORD is an expert systems building tool consisting of two inference engines and an explanation module. the system allows one to perform different calculi of uncertainty on an expert defined set of linguistic terms expressing uncertainty. Each calculus corresponds to specific conjunction, disjunction, and implication operators. the internal representation of each linguistic uncertainty value is a fuzzy subset of the interval [0,1]. the different calculi of uncertainty applied to the set of linguistic terms give, as a result, a fuzzy subset that is approximated, by means of a linguistic approximation process, to a linguistic certainty value belonging to the set of linguistic terms. This linguistic approximation keeps the calculus of uncertainty closed. This has the advantage that, once the linguistic certainty values have been defined, the system computes, off-line, the conjunction, disjunction, and implication operations for all the pairs of linguistic uncertainty values in the term set and stores the results in matrices. Therefore, when MILORD is run, the propagation and combination of uncertainty is performed by simply accessing these precomputed matrices. MILORD also deals with nonmonotonic reasoning in the same framework of uncertainty management. Finally, an application to the diagnosis and treatment of pneumoniae is presented.     

Building a financial diagnosis system based on fuzzy logic production system

The purpose of this study is to build a financial expert system based on fuzzy theory and Fuzzy LOgic Production System (FLOPS), which is an expert tool for processing the ambiguity. The study consists if four parts. For the first part, the basic features of expert systems are presented. For the second part, fizzy concepts and the evaluation of classical expert systems to fuzzy expert systems will be presented. For the third part, the expert system shell (FLOPS) used in this study will be described. For the last part, it will be presented the financial diagnosis system, developed by using the Wall's seven ratios, traditional seven ratios and also 34 ratios selected by a financial expert. After analyzing and investigating these three kinds of methods, financial diagnosis system will be developed as a fuzzy expen system which used a membership function based on averages and standard deviation. At the last step, the new approach will be tried by increasing the fuzzy sets for five membership functions. Some practical examples will be given. Throughout the paper, the way of building a financial diagnosis system based on fuzzy expert system is stressed.     

A fuzzy expert system shell using both exact and inexact reasoning

This paper presents a comprehensive expert system shell which can deal with both exact and inexact reasoning. A prototype of this proposed shell, code named as SYSTEM Z-IIe, has been implemented successfully. It is a rule-based system which employs fuzzy logic and numbers for its reasoning. Two basic inexact concepts, fuzziness and uncertainty, are both used and distinct from each other clearly in the system. Moreover, these two concepts have been built into two levels for inexact reasoning, i.e. the level of the rules and facts, and the level of the values of the objects of these rules and facts. Other features of Z-IIe include multiple fuzzy propositions in rules and dual fact input mechanisms. It also allows any combinations of fuzzy and normal terms and uncertainties. Fuzzy numeric comparison logic control is also available for the rules and facts. Its natural language interface which uses English with restricted syntax improves the efficiency of knowledge engineering. Z-IIe is also coupled to a Database Management System for supplying facts from existing databases if appropriate. All these features can be combined to build very powerful expert systems and are illustrated by an example.     

Fuzzy concepts in expert systems

The authors present a comprehensive expert-system building tool, called System Z-II, that can deal with exact, fuzzy (or inexact), and combined reasoning, allowing fuzzy and normal terms to be freely mixed in the rules and facts of an expert system. This fully implemented tool has been used to build several expert systems in the fields of student curriculum advisement, medical diagnosis, psychoanalysis, and risk analysis. System Z-II is a rule-based system that uses fuzzy logic and fuzzy numbers for its inexact reasoning. It uses two basic inexact concepts, fuzziness and uncertainty, which are distinct from each other in the system     

USING META-PROGRAMMING,CONSTRAINT LOGIC PROGRAMMING AND APPROXIMATE REASONING FOR EXPERT SYSTEMS DESIGN

Abstract

This paper presents an enhancement of the CARESS system—A Constraint Approximative Reasoning System Support—introduced in (Popescu and Roventa, 1994). CARESS is an experimental system with primarily two objectives:

(1)knowledge representation and manipulation techniques and to implement them in PROLOG III, and

(2) to develop a knowledge programming environment for building expert systems. We discuss here the use of meta-programming, constraint logic programming and approximate reasoning for the design of expert systems

It has already been proven that meta-programming and logic programming are powerful techniques for expert system design. Fuzzy logic can be used to model one kind of uncertainty. Constraint logic programming is useful for dealing with the constraints given by operations using fuzzy sets.     

SoHyFIS-Yager: A self-organizing Yager based Hybrid neural Fuzzy Inference System

The Hybrid neural Fuzzy Inference System (HyFIS) is a multilayer adaptive neural fuzzy system for building and optimizing fuzzy models using neural networks. In this paper, the fuzzy Yager inference scheme, which is able to emulate the human deductive reasoning logic, is integrated into the HyFIS model to provide it with a firm and intuitive logical reasoning and decision-making framework. In addition, a self-organizing gaussian Discrete Incremental Clustering (gDIC) technique is implemented in the network to automatically form fuzzy sets in the fuzzification phase. This clustering technique is no longer limited by the need to have prior knowledge about the number of clusters present in each input and output dimensions. The proposed self-organizing Yager based Hybrid neural Fuzzy Inference System (SoHyFIS-Yager) introduces the learning power of neural networks to fuzzy logic systems, while providing linguistic explanations of the fuzzy logic systems to the connectionist networks. Extensive simulations were conducted using the proposed model and its performance demonstrates its superiority as an effective neuro-fuzzy modeling technique.     

Application of simulated annealing fuzzy model tuning to umbilicalcord acid-base interpretation

Fuzzy logic and fuzzy set theory provide an important framework for representing and managing imprecision and uncertainty in medical expert systems, but the need remains to optimize such systems to enhance performance. The paper presents a general technique for optimizing fuzzy models in fuzzy expert systems (FESs) by simulated annealing (SA) and N-dimensional hill climbing simplex method. The application of the technique to a FES for the interpretation of the acid-base balance of blood in the umbilical cord of newborn infants is presented. The Spearman rank order correlation statistic was used to assess and to compare the performance of a commercially available crisp expert system, an initial FES, and a tuned FES with experienced clinicians. Results showed that without tuning, the performance of the crisp system was significantly better (correlation of 0.80) than the FES (correlation of 0.67). The performance of the tuned FES was better than the crisp system and effectively indistinguishable from the clinicians (correlation of 0.93) on training data and was the best of the expert systems on validation data. Unlike most applications of fuzzy logic where all fuzzy sets have normalized heights of unity, in this application it was found that a reduction in the height of some fuzzy sets was effective in enhancing performance. This suggests that the height of fuzzy sets may be a generally useful parameter in tuning FESs     

Discrete Interval Type 2 Fuzzy System Models Using Uncertainty in Learning Parameters

Fuzzy system modeling (FSM) is one of the most prominent tools that can be used to identify the behavior of highly nonlinear systems with uncertainty. Conventional FSM techniques utilize type 1 fuzzy sets in order to capture the uncertainty in the system. However, since type 1 fuzzy sets express the belongingness of a crisp value x' of a base variable x in a fuzzy set A by a crisp membership value mu_A(x'), they cannot fully capture the uncertainties due to imprecision in identifying membership functions. Higher types of fuzzy sets can be a remedy to address this issue. Since, the computational complexity of operations on fuzzy sets are increasing with the increasing type of the fuzzy set, the use of type 2 fuzzy sets and linguistic logical connectives drew a considerable amount of attention in the realm of fuzzy system modeling in the last two decades. In this paper, we propose a black-box methodology that can identify robust type 2 Takagi-Sugeno, Mizumoto and Linguistic fuzzy system models with high predictive power. One of the essential problems of type 2 fuzzy system models is computational complexity. In order to remedy this problem, discrete interval valued type 2 fuzzy system models are proposed with type reduction. In the proposed fuzzy system modeling methods, fuzzy C-means (FCM) clustering algorithm is used in order to identify the system structure. The proposed discrete interval valued type 2 fuzzy system models are generated by a learning parameter of FCM, known as the level of membership, and its variation over a specific set of values which generate the uncertainty associated with the system structure     

Effect of rule weights in fuzzy rule-based classification systems

This paper examines the effect of rule weights in fuzzy rule-based classification systems. Each fuzzy IF-THEN rule in our classification system has antecedent linguistic values and a single consequent class. We use a fuzzy reasoning method based on a single winner rule in the classification phase. The winner rule for a new pattern is the fuzzy IF-THEN rule that has the maximum compatibility grade with the new pattern. When we use fuzzy IF-THEN rules with certainty grades, the winner is determined as the rule with the maximum product of the compatibility grade and the certainty grade. In this paper, the effect of rule weights is illustrated by drawing classification boundaries using fuzzy IF-THEN rules with/without certainty grades. It is also shown that certainty grades play an important role when a fuzzy rule-based classification system is a mixture of general rules and specific rules. Through computer simulations, we show that comprehensible fuzzy rule-based systems with high classification performance can be designed without modifying the membership functions of antecedent linguistic values when we use fuzzy IF-THEN rules with certainty grades     

Fuzzy Logic for Biological and Agricultural Systems

Fuzzy logic is a powerful concept for handling non-linear, time-varying, adaptive systems. It permits the use of linguistic values of variables and imprecise relationships for modeling system behavior. The paper presents an overview of fuzzy logic modeling techniques, its applications to biological and agricultural systems and an example showing the steps of constructing a fuzzy logic model.     

A fuzzy neural network with fuzzy impact grades

Fuzzy rule derivation is often difficult and time-consuming, and requires expert knowledge. This creates a common bottleneck in fuzzy system design. In order to solve this problem, many fuzzy systems that automatically generate fuzzy rules from numerical data have been proposed. In this paper, we propose a fuzzy neural network based on mutual subsethood (MSBFNN) and its fuzzy rule identification algorithms. In our approach, fuzzy rules are described by different fuzzy sets. For each fuzzy set representing a fuzzy rule, the universe of discourse is defined as the summation of weighted membership grades of input linguistic terms that associate with the given fuzzy rule. In this manner, MSBFNN fully considers the contribution of input variables to the joint firing strength of fuzzy rules. Afterwards, the proposed fuzzy neural network quantifies the impacts of fuzzy rules on the consequent parts by fuzzy connections based on mutual subsethood. Furthermore, to enhance the knowledge representation and interpretation of the rules, a linear transformation from consequent parts to output is incorporated into MSBFNN so that higher accuracy can be achieved. In the parameter identification phase, the backpropagation algorithm is employed, and proper linear transformation is also determined dynamically. To demonstrate the capability of the MSBFNN, simulations in different areas including classification, regression and time series prediction are conducted. The proposed MSBFNN shows encouraging performance when benchmarked against other models.     

A fuzzy ID3 induction for linguistic data sets

In real life, humans communicate by means of words. Computing with words enables flexibility via fuzzy logic to reach more informative results for the classification and decision‐making. Fuzzy logic handles the imprecise information. In our paper, we propose a novel fuzzy ID3 algorithm for the classification on linguistic data set, where data can be given as linguistic variables. Linguistic variables are defined by using triangular fuzzy numbers given as LR (left‐right) fuzzy numbers. And weighted averaging based on levels (WABL) method is used as the defuzzification method for each data. Then, fuzzy c‐means algorithm is performed to handle the membership degrees for each variable given in each data set used in an experimental study. At last, the fuzzy ID3 algorithm is applied. The rules are generated, and the reasoning is done by different T‐operators. Our study is encouraged by (using) statistical analysis. In conclusion, it is seen that our algorithm proposed for linguistic data is as good as the proposed approach for numeric data. Also, it is shown that the proposed linguistic approach by using different T‐operators on linguistic data gives better results than numerical approach on some data sets.     

Complexity reduction and interpretability improvement for fuzzy rule systems based on simple interpretability measures and indices by bi-objective evolutionary rule selection

The aim of this paper is to develop a general post-processing methodology to reduce the complexity of data-driven linguistic fuzzy models, in order to reach simpler fuzzy models preserving enough accuracy and better fuzzy linguistic performance with respect to their initial values. This post-processing approach is based on rule selection via the formulation of a bi-objective problem with one objective focusing on accuracy and the other on interpretability. The latter is defined via the aggregation of several interpretability measures, based on the concepts of similarity and complexity of fuzzy systems and rules. In this way, a measure of the fuzzy model interpretability is given. Two neuro-fuzzy systems for providing initial fuzzy models, Fuzzy Adaptive System ART based and Neuro-Fuzzy Function Approximation and several case studies, data sets from KEEL Project Repository, are used to check this approach. Both fuzzy and neuro-fuzzy systems generate Mamdani-type fuzzy rule-based systems, each with its own particularities and complexities from the point of view of the fuzzy sets and the rule generation. Based on these systems and data sets, several fuzzy models are generated to check the performance of the proposal under different restrictions of complexity and fuzziness.     

Water allocation improvement in river basin using Adaptive Neural Fuzzy Reinforcement Learning approach

An accurate simulation model is a necessary tool for optimizing allocation of scarce water resources in large-scale river basins. Adaptive Neural Fuzzy Inference System (ANFIS) method is used to simulate seven interconnected sub-basins in a regional river system located in Iran. Simulated predictions of the method are compared with historical data measurements. ANFIS is a powerful tool for simulating water resources systems of all sub-basins. In this study, a new methodology, Adaptive Neural Fuzzy Reinforcement Learning (ANFRL) is presented for obtaining optimal values of the decision variables. By combining ANFIS with Fuzzy Reinforcement Learning within the content of historical data over a consecutive monthly management period, ANFRL method was derived. Based upon the results of this research, this methodology can be used to develop fuzzy rule systems that accurately simulate the behavior of complex river basin systems within the context of uncertainty. As previous researches have shown that, when simulation model accurately reproduces observed river basin behavior, the optimization model yields better results. Application of this approach in the present case study shows that the effects of uncertainty, imprecise and random factors are 21, 11 and 15% over water resources system, water demand estimated and hydrological regime, respectively. Finally, the results of this method showed that about 16% improvement in water allocation was attained when compared to the primary water resources management in this case study.     

Application of genetic algorithm for fuzzy rules optimization on semi expert judgment automation using Pittsburg approach

Genetic algorithm is well-known of its best heuristic search method. Fuzzy logic unveils the advantage of interpretability. Genetic fuzzy system exploits potential of optimization with ease of understanding that facilitates rules optimization. This paper presents the optimization of fourteen fuzzy rules for semi expert judgment automation of early activity based duration estimation in software project management. The goal of the optimization is to reduce linguistic terms complexity and improve estimation accuracy of the fuzzy rule set while at the same time maintaining a similar degree of interpretability. The optimized numbers of linguistic terms in fuzzy rules by 27.76% using simplistic binary encoding mechanism managed to improve accuracy by 14.29% and reduce optimization execution time by 6.95% without compromising on interpretability in addition to promote improvement of knowledge base in fuzzy rule based systems.     

Parallel Interval Type-2 Subsethood Neural Fuzzy Inference System

Neuro-fuzzy models are being increasingly employed in the domains like weather forecasting, stock market prediction, computational finance, control, planning, physics, economics and management, to name a few. These models enable one to predict system behavior in a more human-like manner than their crisp counterparts. In the present work, an interval type-2 neuro-fuzzy evolutionary subsethood based model has been proposed for its use in finding solutions to some well-known problems reported in the literature such as regression analysis, data mining and research problems relevant to expert and intelligent systems. A novel subsethood based interval type-2 fuzzy inference system, named as Interval Type-2 Subsethood Neural Fuzzy Inference System (IT2SuNFIS) is proposed in the present work. Mathematical modeling and empirical studies clearly bring out the efficacy of this model in a wide variety of practical problems such as Truck backer-upper control, Mackey–Glass time-series prediction, Narazaki–Ralescu and bell function approximation. The simulation results demonstrate intelligent decision making capability of the proposed system based on the available data. The major contribution of this work lies in identifying subsethood as an efficient measure for finding correlation in interval type-2 fuzzy sets and applying this concept to a wide variety of problems pertaining to expert and intelligent systems. Subsethood between two type-2 fuzzy sets is different from the commonly used sup-star methods. In the proposed model, this measure assists in providing better contrast between dissimilar objects. This method, coupled with the uncertainty handling capacity of type-2 fuzzy logic system, results in better trainability and improved performance of the system. The integration of subsethood with type-2 fuzzy logic system is a novel idea with several advantages, which is reported for the first time in this paper.     

语言变量模糊本体的表示与构建

语言变量模糊本体是语言变量在语义Web中的明确的规范化说明,有利于模糊系统与语义Web的结合,使得语义web更加方便地处理模糊信息。通过引入语言变量模糊本体的概念,研究使用RDF表示模糊本体的方法,将本体与模糊概念表示为“资源”。进而以工业洗衣机的模糊控制为例,提出从模糊系统构造语言变量模糊本体的过程。     

Bearing condition prediction considering uncertainty: An interval type-2 fuzzy neural network approach

Rolling-element bearings are critical components of rotating machinery. It is important to accurately predict in real-time the health condition of bearings so that maintenance practices can be scheduled to avoid malfunctions or even catastrophic failures. In this paper, an Interval Type-2 Fuzzy Neural Network (IT2FNN) is proposed to perform multi-step-ahead condition prediction of faulty bearings. Since the IT2FNN defines an interval type-2 fuzzy logic system in the form of a multi-layer neural network, it can integrate the merits of each, such as fuzzy reasoning to handle uncertainties and neural networks to learn from data. The interval type-2 fuzzy linguistic process in the IT2FNN enables the system to handle prediction uncertainties, since the type-2 fuzzy sets are such sets whose membership grades are type-1 fuzzy sets that can be used in failure prediction due to the difficult determination of an exact membership function for a fuzzy set. Noisy data of faulty bearings are used to validate the proposed predictor, whose performance is compared with that of a prevalent type-1 condition predictor called Adaptive Neuro-Fuzzy Inference System (ANFIS). The results show that better prediction accuracy can be achieved via the IT2FNN.     

Adaptive fuzzy PI controller with shifted control singletons

It is well known the fact that the design of a fuzzy control system is based on the human expert experience and control engineer knowledge regarding the controlled plant behavior. As a direct consequence, a fuzzy control system can be considered as belonging to the class of intelligent expert systems. The tuning procedure of a fuzzy controller represents a quite difficult and meticulous task, being based on prior data regarding good knowledge of the controlled plant. The complexity of the tuning procedure increases with the number of the fuzzy linguistic variables and, consequently, of the fuzzy inference rules and thus, the tuning process becomes more difficult. The paper presents a new design strategy for such expert fuzzy system, which improves their performance without increasing the number of fuzzy linguistic variables. The novelty consists in extending the classic structure of the fuzzy inference core with an intelligent module, which tunes one of the control singletons, providing a significant simplification of the design and implementation procedure. The proposed strategy implements a logical, not physical, supplementation of the linguistic terms associated to the controller output. Therefore, a fuzzy rules set with a reduced number of linguistic terms is used to implement the expert control system. This logical supplementation is based on an intelligent algorithm which performs a shifting of only one of the control singletons (the singleton associated to the SMALL_ linguistic variable), its value becoming variable, a fact that allows an accurate control and a better performance for the expert control system. The logic of this intelligent algorithm is to initially provide a high controller output, followed by a slowdown of the control signal near to the operating set point. The main advantage of the proposed expert control strategy is its simplicity: a reduced number of linguistic terms, combined with an intelligent tuning of a single parameter, can provide results as accurate as other more complex available solutions involving tuning of several parameters (well described by the technical literature). Also, a simplification of the preliminary off-line tuning procedure is performed by using a reduced set of fuzzy rules. The generality of the proposed expert control strategy allows its use for any other controlled process.     

On the use of interval mathematics in fuzzy expert systems

Fuzzy expert systems attempt to model the cognitive processes of human experts. They currently accomplish this by capturing knowledge in the form of linguistic propositions. Real-world problems dictate the need to include mathematical knowledge as well. Pattern matching is a critical part of the inference procedure in expert systems. Matches are made between data clauses, premise clauses, and conclusion clauses, forming an inference chain. Preprocessing the clauses may generate intervals of real numbers which are compared in the fuzzy matching algorithm. These same intervals may be used in arithmetic expressions. the purpose of this article is to devise a method for incorporating arithmetic expressions into inference process of Fuzzy Expert Systems. Interval arithmetic is used to evaluate these expressions. Logical relations between intervals are analyzed using probability theory. © 1994 John Wiley & Sons, Inc.