Relying on the universality of quantum mechanics and on recent results known as the “threshold theorems,” quantum information scientists deem the question of the feasibility of large‐scale, fault‐tolerant, and computationally superior quantum computers as purely technological. Reconstructing this question in statistical mechanical terms, this article suggests otherwise by questioning the physical significance of the threshold theorems. The skepticism it advances is neither too strong (hence is consistent with the universality of quantum mechanics) nor too weak (hence is independent (...) of technological contingencies). *Received June 2009; revised August 2009. †To contact the author, please write to: Department of History and Philosophy of Science, College of Arts and Sciences, Indiana University, Bloomington, IN 47405; e‐mail: [email protected]. (shrink)

In computer networks, vertices represent hosts or servers, and edges represent as the connecting medium between them. In localization, some special vertices are selected to locate the position of all vertices in a computer network. If an arbitrary vertex stopped working and selected vertices still remain the resolving set, then the chosen set is called as the fault-tolerant resolving set. The least number of vertices in such resolving sets is called the fault-tolerant metric dimension of the (...) network. Because of the variety of applications of the metric dimension in different areas of sciences, many generalizations were proposed, and fault tolerant is one of them. In this paper, we computed the fault-tolerant metric dimension of triangular snake, ladder, Mobius ladder, and hexagonal ladder networks. It is important to observe that, in all these classes of networks, the fault-tolerant metric dimension and metric dimension differ by 1. (shrink)

The debate around the notions of a priori knowledge and a posteriori knowledge has proven crucial for the development of many fields in philosophy, such as metaphysics, epistemology, metametaphysics etc. We advocate that the recent debate on the two notions is also fruitful for man-made distributed computing systems and for the epistemic analysis thereof. Following a recently proposed modal and fallibilistic account of a priori knowledge, we elaborate the corresponding concept of a priori belief: We propose a rich taxonomy (...) of types of a priori beliefs and their role for the different agents that participate in the system engineering process, which match the existing view exceedingly well and are particularly promising for explaining and dealing with unexpected behaviors in fault-tolerant distributed systems. Developing such a philosophical foundation will provide a sound basis for eventually implementing our ideas in a suitable epistemic reasoning and analysis framework and, hence, constitutes a mandatory first step for developing methods and tools to cope with the various challenges that emerge in such systems. (shrink)

Computational intelligence techniques are being investigated as an extension of the traditional fault diagnosis methods. This article presents, for the first time, a scheme for fault detection and isolation via artificial neural networks and fuzzy logic. It deals with the sensor fault of a three-link selective compliance assembly robot arm robot. A second scheme is proposed for fault detection and accommodation via analytical redundancy, and it deals with the sensor fault of a three-link SCARA robot. (...) These proposed FDI approaches are implemented on Matlab/simulink software and tested under several types of faults. The results show the importance of this process. Then, the sensor faults are detected and isolated successfully. Also, the actuator faults are detected and a fault tolerance strategy is used for reconfigurable control using a sliding-mode observer. (shrink)

The potential for scalable quantum computing depends on the viability of fault tolerance and quantum error correction, by which the entropy of environmental noise is removed during a quantum computation to maintain the physical reversibility of the computer’s logical qubits. However, the theory underlying quantum error correction applies a linguistic double standard to the words “noise” and “measurement” by treating environmental interactions during a quantum computation as inherently reversible, and environmental interactions at the end of a quantum computation (...) as irreversible measurements. Specifically, quantum error correction theory models noise as interactions that are uncorrelated or that result in correlations that decay in space and/or time, thus embedding no permanent information to the environment. I challenge this assumption both on logical grounds and by discussing a hypothetical quantum computer based on “position qubits.” The technological difficulties of producing a useful scalable position-qubit quantum computer parallel the overwhelming difficulties in performing a double-slit interference experiment on an object comprising a million to a billion fermions. (shrink)

A useful logic in which to specify normative system behaviour, deontic logic has a broad spectrum of possible applications within the field: from legal expert systems to natural language processing, database integrity to electronic contracting and the specification of fault-tolerant software.

Computers today are not only the calculation tools - they are directly (inter)acting in the physical world which itself may be conceived of as the universal computer (Zuse, Fredkin, Wolfram, Chaitin, Lloyd). In expanding its domains from abstract logical symbol manipulation to physical embedded and networked devices, computing goes beyond Church-Turing limit (Copeland, Siegelman, Burgin, Schachter). Computational processes are distributed, reactive, interactive, agent-based and concurrent. The main criterion of success of computation is not its termination, but the adequacy of (...) its response, its speed, generality and flexibility; adaptability, and tolerance to noise, error,faults, and damage. Interactive computing is a generalization of Turing computing, and it calls for new conceptualizations (Goldin, Wegner). In the info-computationalist framework, with computation seen as information processing, natural computation appears as the most suitable paradigm of computation and information semantics requires logical pluralism. (shrink)

This thesis analyzes from a philosophical perspective different models for nonmonotonic inference, belief revision and the handling of inconsistencies. ;The first chapter serves as an introduction to the subject, giving examples and analyzing the main concepts. As a result of these discussions, this thesis tries to: produce a refined map of the main notions related to this subject, maintain that there can be a fault tolerant logic that stands in support of fault tolerant reasoning, and defend (...) the use of deductive databases as models for changes of belief. ;The second chapter explores monotonic proposals to deal with uncertain reasoning. These include logics based on a classical notion of consequence, interpretations of defeasible reasoning as containing implicit premises, and systems in which temporal change is an integral part of the representation of states of affairs, via temporal indices or more elaborate devices. ;The third chapter explores quantitative approaches to nonmonotonic reasoning like dispositional logic, and theories of probabilistic reasoning including Bayesian, certainty factors, and Dempster-Shafer. ;The fourth chapter explores qualitative approaches. Here we mention conditional, default, and nonmonotonic logics, and the circumscription and autoepistemic formalisms. ;The fifth chapter studies different proposals to deal with contradictions. It starts with a review of the types of belief inconsistencies, and then it presents mechanisms to prevent, control or correct them. I explore paraconsistent logics, specially relevance logics, to "bracket" the area of conflict and allow inferences about non-related topics to continue unaffected. Then I examine different methods to get rid of the inconsistencies, including the use of dependency-directed backtracking and of relevance logic. ;Finally, I present my conclusions, and mention some of the open problems. (shrink)

The problem of adaptive finite-time fault-tolerant control and output constraints for a class of uncertain nonlinear half-vehicle active suspension systems are investigated in this work. Markovian variables are used to denote in terms of different random actuators failures. In adaptive backstepping design procedure, barrier Lyapunov functions are adopted to constrain vertical motion and pitch motion to suppress the vibrations. Unknown functions and coefficients are approximated by the neural network. Assisted by the stochastic practical finite-time theory and FTC theory, (...) the proposed controller can ensure systems achieve stability in a finite time. Meanwhile, displacement and pitch angle in systems would not violate their maximum values, which imply both ride comfort and safety have been enhanced. In addition, all the signals in the closed-loop systems can be guaranteed to be semiglobal finite-time stable in probability. The simulation results illustrate the validity of the established scheme. (shrink)

This paper presents the architecture and initial feasibility results of a proto-type communication network that utilizes genetic programming to evolve services and protocols as part of network operation. The network evolves responses to environmental conditions in a manner that could not be preprogrammed within legacy network nodes a priori. A priori in this case means before network operation has begun. Genetic material is exchanged, loaded, and run dynamically within an active network. The transfer and execution of code in support of (...) the evolution of network protocols and services would not be possible without the active network environment. Rapid generation of network service code occurs via a genetic programming paradigm. Complexity and Algorithmic Information Theory play a key role in understanding and guiding code evolution within the network. (shrink)

This paper focuses on the problem of load frequency control and sensor fault-tolerant control in the multiarea power grid. To solve these problems, a sliding mode control strategy based on an interval observer is designed. First, an interval observer is designed to obtain the boundary estimation information of the system state online, which is used to reconstruct the load disturbance online. Based on the reconstructed values, an integral sliding mode controller is designed to keep the system frequency stable (...) when the load is disturbed. Then, sensor fault is diagnosed by interval residual. An augmented observer is designed to estimate sensor fault online by equivalent transformation, and the sensor fault is compensated by the fault estimation to reduce the influence of fault on system performance and ensure the reliable and stable operation of the power system. The simulation results show the superiority of the proposed control strategy. (shrink)

This paper presents an active fault-tolerant control strategy for quadrotor helicopters to simultaneously accommodate sensor faults and external disturbances. Unlike most of the existing fault diagnosis and fault-tolerant control schemes for quadrotor helicopters, the proposed fault diagnosis scheme is able to estimate sensor faults while eliminating the effect of external disturbances. Moreover, the proposed fault-tolerant control scheme is capable to eliminate the adverse effect of external disturbances as well by designing a disturbance (...) observer to effectively estimate the unknown external disturbances and integrating with the designed integral sliding-mode controller. In this case, the continuous operation of the quadrotor helicopter is ensured while avoiding the unexpected control chattering. In addition, the stability of the closed-loop system is theoretically proved. Finally, the effectiveness and advantages of the proposed scheme are validated and demonstrated through comparative numerical simulations of the quadrotor helicopter under different faulty and uncertain scenarios. (shrink)

In this study, an adaptive output feedback fault tolerant control scheme is proposed for a class of multi-input and multioutput nonlinear systems with multiple constraints. The neural network is adopted to handle the unknown nonlinearity by means of its superior approximation capability. Based on it, the state observer is designed to estimate the unmeasured states, and the nonlinear disturbance observer is constructed to tackle the external disturbances. In addition, the Nussbaum function is utilized to cope with the actuator (...) faults, which are coupled with the unknown control directions. Combining with the Lyapunov theory, a NN-based output feedback FTC law is developed for the MIMO nonlinear systems, and the boundedness of all closed-loop system error signals is proved. Simulation results on the unmanned helicopter are performed to demonstrate the effectiveness of the proposed controller. (shrink)

Computer Science and Artificial Intelligence will be the twenty-first century logic development of the main power source, and in the twenty-first century will largely determine the face of logic. At least in the early twenty-first century, logic will focus on the following topics: how to deal with common sense reasoning in the logic of Eph coordination, non-monotonic and fault tolerance factors? how to make robots with human intelligence and creativity, as established from the empirical evidence used to guide future (...) action in the induction of judgments can be wrong? how the knowledge representation and knowledge reasoning, in particular, is based on the existing knowledge base and between the cognitive subject knowledge and the reasoning? how contextual factors, combined with a variety of natural language understanding and reasoning, so that intelligent robots to employing natural language for successful communication with people? . . . . And so on. (shrink)

The task of computing a function F with the help of an oracle X can be viewed as a search problem where the cost measure is the number of queries to X. We ask for the minimal number that can be achieved by a suitable choice of X and call this quantity the query complexity of F. This concept is suggested by earlier work of Beigel, Gasarch, Gill, and Owings on “Bounded query classes”. We introduce a fault (...) class='Hi'>tolerant version and relate it with Ulam's game. For many natural classes of functions F we obtain tight upper and lower bounds on the query complexity of F. Previous results like the Nonspeedup Theorem and the Cardinality Theorem appear in a wider perspective. (shrink)

This groundbreaking proceedings volume explores the integration of Artificial Intelligence (AI) across key domains—healthcare, finance, education, robotics, industrial and other engineering applications —unveiling its transformative potential and practical implications. With a multidisciplinary lens, it transcends technical aspects, fostering a comprehensive understanding while bridging theory and practice. Approaching the subject matter with depth, the book combines theoretical foundations with real-world case studies, empowering researchers, professionals, and enthusiasts with the knowledge and tools to effectively harness AI. Encompassing diverse AI topics—machine learning, natural (...) language processing, computer vision, data analytics and supervisory control — the volume showcases state-of-the-art techniques propelling AI advancements. Structured into four parts: Part 1: Artificial Intelligence (AI), explores evolving deep neural networks, reinforcement learning, and explainable AI, providing a deep dive into the technical foundations of AI advancements. Part 2: Robotics and Control Systems, delves into the integration of AI in robotics and automatic control, addressing supervisory control, automated robotic movement coordination, anomaly detection, dynamic programming, and fault tolerance, offering insights into the evolving landscape of intelligent automation. Part 3: AI and Society, examines the societal impact of AI through chapters on ethical considerations, economic growth, environmental engagements, and hazard management, providing a holistic perspective on AI's role in shaping society. Part 4: PhD Symposium, presents the future of AI through cutting-edge research, covering legal and ethical dimensions, privacy considerations, and computationally efficient solutions, offering a glimpse into the next generation of AI advancements. Catering to a diverse audience—from industry leaders to students—the volume consolidates the expertise of renowned professionals, serving as a comprehensive resource for navigating the ever-evolving AI landscape. An essential reference for those staying at the forefront of AI developments. (shrink)

Cloud computing deals with voluminous heterogeneous data, and there is a need to effectively distribute the load across clusters of nodes to achieve optimal performance in terms of resource usage, throughput, response time, reliability, fault tolerance, and so on. The swarm intelligence methodologies use artificial intelligence to solve computationally challenging problems like load balancing, scheduling, and resource allocation at finite time intervals. In literature, sufficient works are being carried out to address load balancing problem in the cloud using (...) traditional swarm intelligence techniques like ant colony optimization, particle swarm optimization, cuckoo search, bat optimization, and so on. But the traditional swarm intelligence techniques have issues with respect to convergence rate, arriving at the global optimum solution, complexity in implementation and scalability, which limits the applicability of such techniques in cloud domain. In this paper, we look into performance modeling aspects of some of the recent competitive swarm artificial intelligence based techniques like the whale, spider, dragonfly, and raven which are used for load balancing in the cloud. The results and analysis are presented over performance metrics such as total execution time, response time, resource utilization rate, and throughput achieved, and it is found that the performance of the raven roosting algorithm is high compared to other techniques. (shrink)

Data Transfer Service (DTS) is an open-source project that is developing a document-centric message model for describing a bulk data transfer activity, with an accompanying set of loosely coupled and platform-independent components for brokering the transfer of data between a wide range of (potentially incompatible) storage resources as scheduled, fault-tolerant batch jobs. The architecture scales from small embedded deployments on a single computer to large distributed deployments through an expandable ‘worker-node pool’ controlled through message-orientated middleware. Data access and (...) transfer efficiency are maximized through the strategic placement of worker nodes at or between particular data sources/sinks. The design is inherently asynchronous, and, when third-party transfer is not available, it side-steps the bandwidth, concurrency and scalability limitations associated with buffering bytes directly through intermediary client applications. It aims to address geographical–topological deployment concerns by allowing service hosting to be either centralized (as part of a shared service) or confined to a single institution or domain. Established design patterns and open-source components are coupled with a proposal for a document-centric and open-standards-based messaging protocol. As part of the development of the message protocol, a bulk data copy activity document is proposed for the first time. (shrink)

Quantum computers are hypothetical quantum information processing (QIP) devices that allow one to store, manipulate, and extract information while harnessing quantum physics to solve various computational problems and do so putatively more efficiently than any known classical counterpart. Despite many ‘proofs of concept’ (Aharonov and Ben–Or 1996; Knill and Laflamme 1996; Knill et al. 1996; Knill et al. 1998) the key obstacle in realizing these powerful machines remains their scalability and susceptibility to noise: almost three decades after their conceptions, experimentalists (...) still struggle to maintain useful quantum coherence in QIP devices with more than a pair of qubits (e.g., Blatt and Wineland 2008). This slow progress has prompted debates on the feasibility of quantum computers, yet the quantum information community has dismissed the skepticism as “ideology” (Aaronson 2004), claiming that the obstacles are merely technological (Kaye et al. 2007, 240). In a recent paper (Hagar 2009) I’ve argued that such a skepticism with respect to the feasibility of quantum computers need not be deemed ideological at all, and that the aforementioned ‘proofs of concept’ are physically suspect. Using analogies from the foundations of classical statistical mechanics (SM), I’ve also argued that instead of active error correction, the appropriate framework for debating the feasibility of large–scale, fault–tolerant and computationally superior quantum computers should be the project of error avoidance: rather than trying to constantly ‘cool down’ the QIP device and prevent its thermalization, one should try to locate those regions in the device’s state space which are thermodynamically ‘abnormal’, i.e., those regions in the device’s state space which resist thermalization regardless of external noise. This paper is intended as a further contribution to the debate on the feasibility of large–scale, fault–tolerant and computationally superior quantum computers. Relying again on analogies from the foundations of classical SM, it suggests a skeptical conjecture and frames it in the ‘passive’, error avoidance, context.. (shrink)

Darwin’s insight that species are mutable, and descent, and origin by means of natural selection is one of the most widely acknowledged strategies for the origin of species and their survival in nature. In his famous contribution, however, Darwin also writes that he is convinced that “... Natural Selection has been the main but not exclusive means of modification ” (Darwin in The origin of species. Oxford Univeristy Press, Oxford, p. 7, 1996 ). This research suggests robustness as another fundamental (...) strategy for survival in nature. The paper does not contradict the popular view, which usually sees robustness as a feature making systems fault-tolerant, thereby focusing on the identification of strategies and techniques for making systems robust (i.e., how to achieve robustness). The paper rather extends this view with an interpretation resting on the question—WHY is robustness omnipresent in the world around us? From this point of view, robustness is interpreted as a fundamental mechanism that is in place because of another fundamental feature in nature—the design and use of sub-optimal systems. The paper argues that, in a sense, nature under-specifies systems but compensates for this by providing systems with various degrees of robustness. We believe that this interpretation may lead to fundamentally new design approaches and insights in several fields. (shrink)

Nijhawan argues that neural compensation is necessary to account for couplings of perception and action. Although perhaps true in some cases, computational tolerance for asynchronously arriving continuous information is of more importance. Moreover, some of the everyday venues Nijhawan uses to argue for the relevance of prediction and compensation can be better ascribed to skill.

The fault prediction and abductive fault diagnosis of three-phase induction motors are of great importance for improving their working safety, reliability, and economy; however, it is difficult to succeed in solving these issues. This paper proposes a fault analysis method of motors based on modified fuzzy reasoning spiking neural P systems with real numbers for fault prediction and abductive fault diagnosis. To achieve this goal, fault fuzzy production rules of three-phase induction motors are first (...) proposed. Then, the rMFRSNPS is presented to model the rules, which provides an intuitive way for modelling the motors. Moreover, to realize the parallel data computing and information reasoning in the fault prediction and diagnosis process, three reasoning algorithms for the rMFRSNPS are proposed: the pulse value reasoning algorithm, the forward fault prediction reasoning algorithm, and the backward abductive fault diagnosis reasoning algorithm. Finally, some case studies are given, in order to verify the feasibility and effectiveness of the proposed method. (shrink)

Generally we think it good to tolerate and to accord recognition. Yet both are complex phenomena and our teaching must acknowledge and cope with that complexity. We tolerate only what we object to, so our message to students cannot be simply, ‘promote the good and prevent the bad’. Much advocacy of toleration is not what it pretends to be. Nor is it entirely clear what sort of conduct should count as intolerant. Sometimes people are at fault for tolerating what (...) they should not, or for tolerating what they should find unexceptionable. So virtue does not always lie with toleration. Tolerance can also seem condescending; should we therefore replace it with recognition? But recognition may not be able to coexist with the disapproval that makes toleration necessary. However, not everything about toleration and recognition is controversial; there are fixed points from which students can grapple with the issues presented by both. (shrink)

This chapter contains sections titled: Introduction The Fault Lines of Toleration in the Context of Education Toleration and Mutual Respect Toleration and an Autonomy Facilitating Education Appreciation Instead of Non‐Bigoted Acceptance Restrained Manifestation Limited Associational Liberty Implications Conclusion Notes References.

According to the naive theory of vagueness, the vagueness of an expression consists in the existence of both positive and negative cases of application of the expression and in the non- existence of a sharp cut-off point between them. The sorites paradox shows the naive theory to be inconsistent in most logics proposed for a vague language. The paper explores the prospects of saving the naive theory by revising the logic in a novel way, placing principled restrictions on the transitivity (...) of the consequence relation. A lattice-theoretical framework for a whole family of “tolerant logics” is proposed and developed. Particular care is devoted to the relation between the salient features of the formal apparatus and the informal logical and semantic notions they are supposed to model. A suitable non-transitive counterpart to classical logic is defined. Some of its properties are studied, and it is eventually shown how an appropriate regimentation of the naive theory of vagueness is consistent in such a logic. (shrink)

THE ELEMENTARY MORAL DISTINCTION. The ultimate objects of moral assessment are people and their lives. I will call this the "elementary moral distinction." Many today seem to have lost sight of it. How often are we told that we should show respect for other people, only to discover that what we are actually being asked to show respect for is how those other people live? The equation of the two should be resisted. We do not always respect a person by (...) respecting how he lives. Sometimes quite the reverse. If someone is wasting his life but still deserves to be respected, the default way to show him the respect that he deserves is to do something that improves the way he is living- shake him out of it, block his path, change his incentives, shield him from further exploitation, and so forth. Sometimes, of course, there is no action open to us that will yield any improvement in how he lives, while on other occasions the only things we can do are disproportionate. In such cases we have to tolerate his continuing to live as badly he does. But toleration is one thing, and respect is quite another. Toleration is the moral virtue of those who appropriately curb their wish to eliminate what they do not respect. One cannot respect the way someone is living and tolerate it at the same time. (shrink)

ABSTRACT Michael Rescorla has argued that it makes sense to compute directly with numbers, and he faulted Turing for not giving an analysis of number-theoretic computability. However, in line with a later paper of his, it only makes sense to compute directly with syntactic entities, such as strings on a given alphabet. Computing with numbers goes via notation. This raises broader issues involving de re propositional attitudes towards numbers and other non-syntactic abstract entities.

In recent years, there has been a proliferation of studies of international justice. This book is a valuable contribution to that trend. Tan presents his theory as a rival to Rawls’s “law of peoples”. He argues that his critique of Rawls’s work on international justice points to deep flaws in Rawls’s general account of justice and not merely to a mistaken application in a particular area. Specifically, Tan claims that the core fault of the law of peoples is its (...) neglect of individual liberty and that this neglect “stems ultimately from political liberalism’s mistaken stress on toleration as the fundamental liberal principle”. Tan argues that comprehensive liberalism is superior to political liberalism because it takes “individual autonomy to be fundamental”. (shrink)

In the 1720s Francis Hutcheson developed a systematic account of the origins of ethical judgments that would have a profound influence on later writers. Ethical judgments, he argues, arise from the perceptions of internal senses that are, themselves, rooted in ‘Passions and Affections’. This paper describes his account and draws attention to an important tension at its heart. When judging particular cases, Hutcheson praises kindly, generous, and merciful affections as exemplary. But when he proposes a mathematical formula for ‘computing (...) the Goodness’ of a person’s character, this formula yields results that are at odds with many of his judgments about the kindly, generous, and merciful. I trace the sources of this tension and identify ways in which Hutcheson might have avoided it. (shrink)

We have developed a process model that learns in multiple ways while finding faults in a simple control panel device. The model predicts human participants' learning through its own learning. The model's performance was systematically compared to human learning data, including the time course and specific sequence of learned behaviors. These comparisons show that the model accounts very well for measures such as problem‐solving strategy, the relative difficulty of faults, and average fault‐finding time. More important, because the model learns (...) and transfers its learning across problems, it also accounts for the faster problem‐solving times due to learning when examined across participants, across faults, and across the series of 20 trials on an individual participant basis. The model shows how learning while problem solving can lead to more recognition‐based performance, and helps explain how the shape of the learning curve can arise through learning and be modified by differential transfer. Overall, the quality of the correspondence appears to have arisen from procedural, declarative, and episodic learning all taking place within individual problem‐solving episodes. (shrink)

In coal mining industry, the running state of mine ventilators plays an extremely significant role for the safe and reliable operation of various industrial productions. To guarantee the better reliability, safety, and economy of mine ventilators, in view of early detection and effective fault diagnosis of mechanical faults which could prevent unscheduled downtime and minimize maintenance fees, it is imperative to construct some viable mathematical models for mine ventilator fault diagnosis. In this article, we plan to establish a (...) data-based mine ventilator fault diagnosis method to handle situations where engineers are absent or they are incapable of coming to a conclusion from multisource data. In the process of building the mine ventilator fault diagnosis model, considering that probabilistic rough sets could reduce the errors triggered by incompleteness, inconsistency, and inaccuracy without needing any additional assumptions and Pythagorean fuzzy multigranulation rough sets over the two universes’ model could effectively handle data representation, fusion, and analysis issues, we generalize the existing PF MGRSs over the two universes’ model to the PRS setting, as well as to further establish a novel model named Pythagorean fuzzy multigranulation probabilistic rough sets over two universes. In the granular computing paradigm, three types of PF MG-PRSs over two universes based on the risk attitude of engineers are proposed at first. Afterwards, several basic propositions of the newly proposed model are explored. Moreover, a PF multigranulation probabilistic model for mine ventilator fault diagnosis based on PF MG-PRSs over two universes is investigated. At last, a real-world case study of dealing with a mine ventilator fault diagnosis problem is given to illustrate the practicality of the presented model, and a validity test, a sensitivity analysis, and a comparison analysis are further explored to demonstrate the effectiveness of the presented model. (shrink)