A fuzzy inference system for fault detection and isolation: Application to a fluid system

This work focuses on the design and implementation of a fuzzy inference system for fault detection and isolation (FDI) which can learn from example fault data, and the determination of a suitable optimisation strategy for the membership functions. A FDI system was developed which is based on adaptive fuzzy rules. A number of optimisation strategies were then applied; it was found that an evolutionary algorithm not only produced the best results but did so with relatively little processing effort and with excellent consistency.The adaptive fuzzy system, thus optimised, was tested against a neural network, which was trained to produce analogue outputs as an indication of fault magnitude. The fuzzy solution produced the best accuracy.We can conclude that an adaptive fuzzy inference system for FDI, using an evolutionary algorithm to learn from examples, can provide an accurate and readily comprehensible solution to diagnosing and evaluating fluid process plant faults.     

Generalized intuitionistic fuzzy geometric interaction operators and their application to decision making

Considering that there may exist some interactions between membership function and non-membership function of different intuitionistic fuzzy sets, we present some new operational laws from the probability point of view and give a geometric interpretation of the new operations. Based on which, a new class of generalized intuitionistic fuzzy aggregation operators are developed, including the generalized intuitionistic fuzzy weighted geometric interaction averaging (GIFWGIA) operator, the generalized intuitionistic fuzzy ordered weighted geometric interaction averaging (GIFOWGIA) operator and the generalized intuitionistic fuzzy hybrid geometric interaction averaging (GIFHGIA) operator. The properties of these new generalized aggregation operators are investigated. Moreover, approaches to multiple attributes decision making are given based on the generalized aggregation operators under intuitionistic fuzzy environment, and an example is illustrated to show the validity and feasibility of new approach. Finally, we give a systematic comparison between the work of this paper and that of other papers.     

A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread

One of the most important aspects of the (statistical) analysis of imprecise data is the usage of a suitable distance on the family of all compact, convex fuzzy sets, which is not too hard to calculate and which reflects the intuitive meaning of fuzzy sets. On the basis of expressing the metric of Bertoluzza et al. [C. Bertoluzza, N. Corral, A. Salas, On a new class of distances between fuzzy numbers, Mathware Soft Comput. 2 (1995) 71-84] in terms of the mid points and spreads of the corresponding intervals we construct new families of metrics on the family of all d-dimensional compact convex sets as well as on the family of all d-dimensional compact convex fuzzy sets. It is shown that these metrics not only fulfill many good properties, but also that they are easy to calculate and easy to manage for statistical purposes, and therefore, useful from the practical point of view.     

Using memory and fuzzy rules in a co-operative multi-thread strategy for optimization

In this article, we analyze a co-operative multi-thread search-based optimization strategy, where each solver thread represents a different optimization algorithm (or the same one with different settings), and they are all controlled by a centralized co-ordinator. We also propose the use of memory to keep track of both the state of the individual threads and the obtained solutions. Based on this memory, a very simple fuzzy rule base is used to control the system behavior.We also present the results of three computational experiments. The first of these checks the strategy by comparing it with an independent search strategy and a sequential algorithm, and the superiority of the co-operative scheme is confirmed. The second analyzes how definition of the threads affects the quality of the results, and the importance of there being a balanced set between intensification and diversification is corroborated. The third explores the use of memory with two different fuzzy rules, and the results indicate that the best combination is to use memory together with two rules (solver dependent and solver independent ones) (although this combination should not be activated at the beginning of the search in order to avoid premature convergence).     

Lattice-valued approach to closed sets under fuzzy relations: Theory and applications

Motivated by fuzzy control problems and by some investigations of eigen fuzzy sets, we deal with a closedness of fuzzy sets under fuzzy relations in two ways: in one sense by directly analyzing fuzzy concepts and in the other by investigating the corresponding crisp problems in the cutworthy framework. Our main task is to investigate particular fuzzy functional equations and inequations appearing in this context, which turn out to be essentially connected with fuzzy control problems. We analyze procedures and find solutions of these equations and inequations, pointing to important applications.     

Ellipsoids and ellipsoid-shaped fuzzy sets as natural multi-variate generalization of intervals and fuzzy numbers: How to elicit them from users, and how to use them in data processing

In this paper, we show that ellipsoids are natural multi-variate generalization of intervals and ellipsoid-shaped fuzzy sets are a natural generalization of fuzzy numbers. We explain how to elicit them from users, and how to use them in data processing.     

Directional relative position between objects in image processing: a comparison between fuzzy approaches

The importance of describing relationships between objects has been highlighted in works in very different areas, including image understanding. Among these relationships, directional relative position relations are important since they provide an important information about the spatial arrangement of objects in the scene. Such concepts are rather ambiguous, they defy precise definitions, but human beings have a rather intuitive and common way of understanding and interpreting them. Therefore in this context, fuzzy methods are appropriate to provide consistent definitions that integrate both quantitative and qualitative knowledge, thus providing a computational representation and interpretation of imprecise spatial relations, expressed in a linguistic way, and including quantitative knowledge. Several fuzzy approaches have been developed in the literature, and the aim of this paper is to review and compare them according to their properties and according to the types of questions they seek to answer.     

The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets

This paper provides a continuation of ideas presented by Davvaz and Mahdavipour [B. Davvaz, M. Mahdavipour, Roughness in modules, Inform. Sci. 176 (2006) 3658-3674]. The notion of hypermodule is a generalization of the notion of module. In this paper, we consider the quotient hypermodule M/A and interpret the lower and upper approximations as subsets of the quotient hypermodule M/A. Then, we introduce the concept of quotient rough sub-hypermodule. Also, using the concept of fuzzy sets, we introduce and discuss the concept of fuzzy rough hypermodules and then we obtain the relation between fuzzy rough sub-hypermodules and level rough sets. This relation is characterized as a necessary and sufficient condition.     

Credal networks

This paper presents a complete theory of credal networks, structures that associate convex sets of probability measures with directed acyclic graphs. Credal networks are graphical models for precise/imprecise beliefs. The main contribution of this work is a theory of credal networks that displays as much flexibility and representational power as the theory of standard Bayesian networks. Results in this paper show how to express judgements of irrelevance and independence, and how to compute inferences in credal networks. A credal network admits several extensions—several sets of probability measures comply with the constraints represented by a network. Two types of extensions are investigated. The properties of strong extensions are clarified through a new generalization of d-separation, and exact and approximate inference methods are described for strong extensions. Novel results are presented for natural extensions, and linear fractional programming methods are described for natural extensions. The paper also investigates credal networks that are defined globally through perturbations of a single network.     

From on-line sketching to 2D and 3D geometry: a system based on fuzzy knowledge

The paper describes the development of a fuzzy knowledge-based prototype system for conceptual design. This real time system is designed to infer user's sketching intentions, to segment sketched input and generate corresponding geometric primitives: straight lines, circles; arcs, ellipses, elliptical arcs, and B-spline curves. Topology information (connectivity, unitary constraints and pairwise constraints) is received dynamically from 2D sketched input and primitives. From the 2D topology information, a more accurate 2D geometry can be built up by applying a 2D geometric constraint solver. Subsequently, 3D geometry can be received feature by feature incrementally. Each feature can be recognised by inference knowledge in terms of matching its 2D primitive configurations and connection relationships. The system accepts not only sketched input, working as an automatic design tool, but also accepts user interactive input of both 2D primitives and special positional 3D primitives. This makes it easy and friendly to use. The system has been tested with a number of sketched inputs of 2D and 3D geometry.     

A fuzzy inference system for pump failure diagnosis to improve maintenance process: The case of a petrochemical industry

Pump operating problems may be either hydraulic or mechanical and there is interdependence between the failure diagnoses of these two categories. Consequently, a correct diagnosis of a pump failure needs to consider many symptoms and hydraulic or mechanical causes. But, due to nonlinear, time-varying behavior and imprecise measurement information of the systems it is difficult to deal with pumps failures with precise mathematical equations, while human operators with the aid of their practical experience can handle these complex situations, with only a set of imprecise linguistic if-then rules and imprecise system state, but this procedure is time consuming and needs the knowledge of human experts and experienced maintenance personnel. The purpose of this study is to provide a correct and timely diagnosis mechanism of pump failures by knowledge acquisition through a fuzzy rule-based inference system which could approximate human reasoning. The proposed fuzzy inference system by: (1) reduction of human error, (2) reduction of repair time (3) creation of expert knowledge which could be used for training (4) reduction of unnecessary expenditures for upgrades and finally, (5) reduction of maintenance costs, will improve the maintenance process. The novelty of this work is the knowledge acquisition (the extraction of linguistic rules) through the interactive impact of the critical failure modes on the both hydraulic and mechanical operating parameters including flow rate, discharge pressure, NPSHR (Net Positive Suction Head Required), BHP (Brake Horse Power), efficiency, vibration and temperature. The proposed approach is tested and applied to a petrochemical industry.     

From laser-scanned data to feature human model: a system based on fuzzy logic concept

This paper describes the development of a prototype system using fuzzy logic concept for constructing a feature human model, which is to be stored in a 3D digital human model database. In our approach, the feature human model is constructed by unorganized cloud points obtained from 3D laser scanners. Firstly, noisy points are removed, and the orientation of the human model is adjusted; secondly, a feature based mesh generation algorithm is applied on the cloud points to construct the mesh surface of a human model; lastly, semantic features of the human model are extracted from the mesh surface. Compared with earlier approach, our method strongly preserves the topology of a human model; more details can be constructed; and both the robustness and the efficiency of the algorithm are improved. At the end of the paper, in order to demonstrate the functionality of feature human models, potential applications are given.     

A unified fuzzy logic approach to trajectory planning and inverse kinematics for a fire fighting robot operating in tunnels

In this paper a fuzzy logic approach to automatic trajectory planning and closed-loop inverse kinematics for a robotic system purposely designed to extinguish fires in road and railway tunnels is presented. The robot is composed of a self-cooling monorail vehicle carrying a fire fighting monitor. A fuzzy inference system is adopted for the automatic generation of the task-space trajectory for the robot and to distribute the motion among the available joints in the presence of redundant degrees of mobility. Redundancy also allows assigning additional tasks besides the primary task. Simulation case studies are presented to test the performance of the whole system in a typical intervention scenario.     

An application of fuzzy set theory to the external performance evaluation of distribution centers in logistics

 The purpose of this paper is to propose an algorithm for external performance evaluation in the area of logistics from retailers' viewpoint under fuzzy environment. The fundamental concepts we have adopted include the factor analysis, eigenvector method, fuzzy Delphi method, fuzzy set theory and multi-criteria decision-making method. We use factor analysis to condense twenty external performance sub-criteria into six criteria to construct the hierarchical structure of external performance evaluation of distribution centers. The fuzzy Delphi method is integrated with the eigenvector method to form a set of pooled weights of the extracted criteria. The concepts of triangular fuzzy number and linguistic variables are used to assess the preference ratings of linguistic variable, ‘importance’ and ‘appropriateness’. Through the hierarchy integration, we obtain the final scores of distribution centers' performance. Then we use a revised Chang and Chen's ranking method to rank the final scores of distribution centers for choosing the best distribution center in the area of logistic management.     

Hierarchical clustering of subpopulations with a dissimilarity based on the likelihood ratio statistic: application to clustering massive data sets

The problem of clustering subpopulations on the basis of samples is considered within a statistical framework: a distribution for the variables is assumed for each subpopulation and the dissimilarity between any two populations is defined as the likelihood ratio statistic which compares the hypothesis that the two subpopulations differ in the parameter of their distributions to the hypothesis that they do not. A general algorithm for the construction of a hierarchical classification is described which has the important property of not having inversions in the dendrogram. The essential elements of the algorithm are specified for the case of well-known distributions (normal, multinomial and Poisson) and an outline of the general parametric case is also discussed. Several applications are discussed, the main one being a novel approach to dealing with massive data in the context of a two-step approach. After clustering the data in a reasonable number of ‘bins’ by a fast algorithm such as k-Means, we apply a version of our algorithm to the resulting bins. Multivariate normality for the means calculated on each bin is assumed: this is justified by the central limit theorem and the assumption that each bin contains a large number of units, an assumption generally justified when dealing with truly massive data such as currently found in modern data analysis. However, no assumption is made about the data generating distribution.

Bayesian inference in disputed authorship: A case study of cognitive errors and a new system for decision support

Bayesian inference provides a formal framework for assessing the odds of hypotheses in light of evidence. This makes Bayesian inference applicable to a wide range of diagnostic challenges in the field of chance discovery, including the problem of disputed authorship that arises in electronic commerce, counter-terrorism and other forensic applications. For example, when two documents are so similar that one is likely to be a hoax written from the other, the question is: Which document is most likely the source and which document is most likely the hoax? Here I review a Bayesian study of disputed authorship performed by a biblical scholar, and I show that the scholar makes critical errors with respect to several issues, namely: Causal Basis, Likelihood Judgment and Conditional Dependency. The scholar’s errors are important because they have a large effect on his conclusions and because similar errors often occur when people, both experts and novices, are faced with the challenges of Bayesian inference. As a practical solution, I introduce a graphical system designed to help prevent the observed errors. I discuss how this decision support system applies more generally to any problem of Bayesian inference, and how it differs from the graphical models of Bayesian Networks.     

Learning science in a virtual reality application: The impacts of animated-virtual actors’ visual complexity

As the technology in computer graphics advances, Animated-Virtual Actors (AVAs) in Virtual Reality (VR) applications become increasingly rich and complex. Cognitive Theory of Multimedia Learning (CTML) suggests that complex visual materials could hinder novice learners from attending to the lesson properly. On the other hand, previous studies have shown that visual complexity correlates with presence and may increase the perceived affective quality of the virtual world, towards an optimal experience or flow. Increasing these in VR applications may promote enjoyment and higher cognitive engagement for better learning outcomes. While visually complex materials could be motivating and pleasing to attend to, would they affect learning adversely? We developed a series of VR presentations to teach second-year psychology students about the navigational behaviour of Cataglyphis ants with flat, cartoon, or lifelike AVAs. To assess learning outcomes, we used Program Ratings, which measured perception of learning and perceived difficulty, and retention and transfer tests. The results from 200 students did not reveal any significant differences in presence, perceived affective quality, or learning outcomes as a function of the AVA’s visual complexity. While the results showed positive correlations between presence, perceived affective quality and perception of learning, none of these correlates with perceived difficulty, retention, or transfer scores. Nevertheless, our simulation produced significant improvements on retention and transfer scores in all conditions. We discuss possible explanations and future research directions.     

How to fully represent expert information about imprecise properties in a computer system: random sets,fuzzy sets,and beyond: an overview

To help computers make better decisions, it is desirable to describe all our knowledge in computer-understandable terms. This is easy for knowledge described in terms on numerical values: we simply store the corresponding numbers in the computer. This is also easy for knowledge about precise (well-defined) properties which are either true or false for each object: we simply store the corresponding “true” and “false” values in the computer. The challenge is how to store information about imprecise properties. In this paper, we overview different ways to fully store the expert information about imprecise properties. We show that in the simplest case, when the only source of imprecision is disagreement between different experts, a natural way to store all the expert information is to use random sets; we also show how fuzzy sets naturally appear in such random set representation. We then show how the random set representation can be extended to the general (“fuzzy”) case when, in addition to disagreements, experts are also unsure whether some objects satisfy certain properties or not.