Approximate Reasoning Scheme Research Articles

Z-number based fuzzy neural network for system identification

In this paper, a novel Z-number based Fuzzy Neural Network (Z-FNN) based on the integration of Z-valued fuzzy logic and neural networks is proposed. Z-valued fuzzy rule base is presented and its inference process is described using interpolative approximate reasoning. Accordingly, the structure of the Z-FNN is proposed using a distance measure and interpolative approximate reasoning scheme. Based on presented architecture the learning algorithm of Z-FNN is designed. The updating of the unknown parameters of the network is carried out using Genetic Algorithms (GA). The proposed Z-FNN system is utilized for dynamic plant identification. The effectiveness of Z-FNN has been tested by comparing its performance with the performances of other fuzzy systems available in the literature. The proposed approach has been proven to be a suitable alternative for the identification of nonlinear systems characterized by uncertain and imprecise information.

Closeness in similarity-based reasoning with an interpolation condition

This study considers an approximate reasoning scheme where the knowledge base is a set of fuzzy IF–THEN rules and the inference mechanism is characterized in terms of closeness. We propose the interpretation of this scheme, which uses Ruspini's theory of conditional consistency and implication measures, and its adaptation to fuzzy sets. In the proposed interpretation, we find the necessary and sufficient conditions to ensure that the computation of the conclusion fulfills the interpolation condition. We show that the inference mechanism is equivalent to the compositional rule of inference in the form of inf⁡→ composition. Finally, we construct a particular interpretation where all of the considered requirements are satisfied and the inference operator reduces to a piecewise linear interpolation function.

An axiomatizable logical foundation for lattice-ordered qualitative linguistic approach for reasoning with words

It is commonsense that people do express, think, reason, and make decision directly using linguistic terms in natural language rather than using numerical quantification. How to establish the formalized approach imitating the common way of human being’s to manipulate directly linguistic terms without numerical approximation to provide the rational decision is still an open research area. Investigations on the algebraic structure of linguistic term set for varied decision making applications (especially in social science) still lack a formalism for development of strict linguistic valued logic system as a theoretical foundation and its approximate reasoning scheme in practice. To attain this goal we characterize and construct a typical structure of commonly used linguistic term sets in natural language by a lattice-ordered algebra structure – lattice implication algebra (LIA), where Łukasiewicz implication algebra, as a special case of LIA, plays a substantial role. By using Łukasiewicz logic’s axiomatizability in terms of Pavelka type fuzzy logic, we propose a new axiomatizable lattice ordered qualitative linguistic truth-valued logic system based on LIA to place an important foundation for further establishing formal linguistic truth-valued logic based approximate reasoning and decision making with applications. This proposed logic system has a distinct feature of handling comparable or incomparable linguistic terms directly without numerical quantification, will be especially beneficial for perception-based decision making processes. It attempts to enhance the quantitative theory of decision science with qualitative, algebraic and logic-oriented approaches to achieve reasoning with words.

Speaker Verification System Based on the Cerebellum Architecture

The Cerebellar Model Articulation Controller (CMAC) and fuzzy systems have been active areas of research since its initial introduction. Fuzzy CMAC is basically a CMAC that is coupled with a fuzzy system. This paper presents the incorporation of fuzzy systems into CMAC with Approximate Analogical Reasoning Scheme (AARS) as its inference rules and Discrete Incremental Clustering (DIC) as its technique to classify the input space, which is used for the speaker verification system. Features extracted from a known speaker using either Mel Frequency Cepstrum Coefficients (MFCC) or Delta Mel Frequency Cepstrum Coefficients (DMFCC) methods are used as the inputs for the system. The variables used for the performance analysis are False Acceptance Rate (FAR), False Rejection Rate (FRR), and Equal Error Rate (EER), training and testing time.

On the Suitability of the Bandler–Kohout Subproduct as an Inference Mechanism

Fuzzy relational inference (FRI) systems form an important part of approximate reasoning schemes using fuzzy sets. The compositional rule of inference (CRI), which was introduced by Zadeh, has attracted the most attention so far. In this paper, we show that the FRI scheme that is based on the Bandler-Kohout (BK) subproduct, along with a suitable realization of the fuzzy rules, possesses all the important properties that are cited in favor of using CRI, viz., equivalent and reasonable conditions for their solvability, their interpolative properties, and the preservation of the indistinguishability that may be inherent in the input fuzzy sets. Moreover, we show that under certain conditions, the equivalence of first-infer-then-aggregate (FITA) and first-aggregate-then-infer (FATI) inference strategies can be shown for the BK subproduct, much like in the case of CRI. Finally, by addressing the computational complexity that may exist in the BK subproduct, we suggest a hierarchical inferencing scheme. Thus, this paper shows that the BK-subproduct-based FRI is as effective and efficient as the CRI itself.

Fuzzy modifiers based on fuzzy relations

In this paper we introduce a new type of fuzzy modifiers (i.e. mappings that transform a fuzzy set into a modified fuzzy set) based on fuzzy relations. We show how they can be applied for the representation of weakening adverbs ( more or less, roughly) and intensifying adverbs ( very, extremely) in the inclusive and the non-inclusive interpretation. We illustrate their use in an approximate reasoning scheme.

Diagnostic reasoning under conflicting data: the application of the transferable belief model

One of the issues in diagnostic reasoning is inferring about the location of a fault in cases where process data carry inconsistent or even conflicting evidence. This problem is treated in a systematic way by making use of the transferable belief model (TBM), which represents an approximate reasoning scheme derived from the Dempster–Shafer theory of evidence. The key novelty of TBM concerns the paradigm of the open world, which turns out to lead to a new means of assigning beliefs to anticipated fault candidates. Thus, instead of being ignored, inconsistency of data is displayed in a portion of belief that cannot be allocated to any of the suspected faults but rather to an unknown origin. This item of belief is referred to as the strength of conflict (SC). It is shown in this paper that SC can be interpreted as a degree of confidence in the diagnostic results, which seems to bring a new feature to diagnostic practice. The basics of TBM are reviewed in the paper and the implementation of the underlying ideas in the diagnostic reasoning context is presented. An important contribution concerns the extension of basic TBM reasoning from single observations to a batch of observations by employing the idea of discounting of evidence. The application of TBM to fault isolation in a gas–liquid separation process clearly shows that extended TBM significantly improves the performance of the diagnostic system compared to ordinary TBM as well as classical Boolean framework, especially as regards diagnostic stability and reliability.

CAD for fault tree-based diagnosis of industrial processes

Despite extensive research in the area of model-based fault diagnosis, the number of applied solutions is still rather limited. The reason for this is to be partly sought in the relatively high costs related to the development of a diagnostic system. Hopefully, the efficiency of the development cycle can be substantially improved with the use of computer-aided design (CAD) tools. This fact served as a major motivation for the realisation of a CAD prototype which performs automatic synthesis of rule-based diagnostic systems for industrial processes. The tool relies on fault propagation models and an object-oriented modelling paradigm. A model of the whole process derives from the component models and information about the way the components are interconnected. As the library of component models is inherent to the tool, the major input expected from the user is a process flowsheet. This can be simply provided through a graphic user-interface. The synthesis of propagation models, and synthesis of the rules thereof, is performed using an automatic synthesis procedure. An algorithm that transforms fault trees into event trees and diagnostic rules is presented. Handling complex structures, such as feedback loops, is also addressed. For on-line execution of the resulting diagnostic rules, the approximate reasoning scheme referred to as the transferable belief model (TBM) is suggested. The underlying CAD tool is suitable for performing several routine tasks that occur in the process of the development of a diagnostic system. This is illustrated on an example of a laboratory test rig.

An expert system for reliability centered maintenance in the chemical industry

A new framework for the implementation of reliability centered maintenance (RCM) in the initial design phases of industrial chemical processes was developed and implemented. Fuzzy reasoning algorithms were designed to evaluate and assess the likelihood of equipment failure mode precipitation and aggravation. Furthermore, an approximate reasoning scheme which considers local, product, and adjacent machinery effects was constructed to prioritize the equipment failure modes likely to precipitate in the process. The new RCM approach was implemented through an expert system. The computer system reads the process flowsheet generated by ASPEN Plus and, based on relevant machine operating data, it provides the user with the final process RCM availability structure diagram. This availability diagram consists of a listing of all critical machine failure modes likely to precipitate, prioritized according to their overall negative impact on the process, as well as important information on their corresponding local and system effects, and suggested controls for their detection.

Type I and Type II fuzzy system modeling

Two system modeling approaches are proposed with a unification of fuzzy methodologies. Type I and Type II knowledge representation are reviewed together with their proposed approximate reasoning schemes. Type I representation and inference are based on Boolean normal forms. Type I models are myopic because, in these models, either the disjunctive or the conjunctive Boolean normal forms are selected rather arbitrarily for knowledge representation and inference and then they are fuzzified. Whereas in Type II models, representation and inference are based on fuzzy disjunctive and conjunctive normal forms which are derived from the fuzzy truth tables.

Bidirectional approximate reasoning based on interval-valued fuzzy sets

This paper proposes a bidirectional approximate reasoning method based on interval-valued fuzzy sets, where fuzzy production rules are used for knowledge representation, and the fuzzy terms appearing in the fuzzy production rules of a rule-based system are represented by interval-valued fuzzy sets. The proposed method is more flexible than the one presented in the paper by Bien and Chun [IEEE Trans. Fuzzy Systems 2 (1994) 177] due to the fact that it allows the fuzzy terms appearing in the fuzzy production rules of a rule-based system to be represented by interval-valued fuzzy sets rather than general fuzzy sets. Furthermore, because the proposed method requires only simple arithmetic operations, and because it allows bidirectional approximate reasoning, it can be executed much faster and more flexible than the single-input-single-output approximate reasoning scheme presented in the paper by Gorzalczany [Fuzzy Sets and Systems 21 (1981) 10].

Compatibility relations for the representation of associations between variables in knowledge-based systems, and their use in approximate reasoning

Compatibility relations are proposed as formal representations of the production (if-then) rules capturing associations between a primary, A, and a secondary B, variable. The most general form of the if-then rule considered is: if A takes on its value in a set, then B takes on its value in a set [or in different possible sets, each with its associated degree of belief (conviction)]. Moreover, with each rule is associated a degree of belief as to its validity. We consider an approximate reasoning scheme stated as: we know a possibility distribution representing the value of A (premise) and an association between A and B represented by an if-then rule, and we seek the induced possibility distribution representing the value of B (consequence). The approach to approximate reasoning proposed is based on possibility theory and possibility measures induced by multivalued mappings.

An expert system oriented to complex pattern recognition problems

The general framework bimbo, designed for acquiring knowledge on expert systems oriented to pattern analysis, is presented. bimbo, which is itself an expert system, works in a largely automated mode and makes use of a large body of general knowledge and of powerful heuristics. The learning methodology explicitly addresses the problem of the presence of errors and noise in the data and utilizes an approximate reasoning scheme based on fuzzy sets. bimbo has been applied in a test case taken from the field of continuous speech recognition, with very good results in increasing the system accuracy and decreasing the demands upon human time.