Fuzzy Belief Research Articles

A novel evidential FMEA method by integrating fuzzy belief structure and grey relational projection method

Failure mode and effects analysis (FMEA) has been applied extensively in reliability engineering domain. Risk priority number (RPN), which is the product of occurrence (O), severity (S) and detection (D) of a failure is the most important measure used in FMEA for prioritizing risk. In this paper, a novel evidential FMEA integrating fuzzy belief structure and grey relational projection method(GRPM) is presented to avoid the use of traditional RPN, for it has been criticized with some weaknesses. First, a new distribution form of assessments applying fuzzy belief structure to represent the experts’ opinions in a more flexible and reasonable manner is constructed. Second, a new method to transform the experts’ fuzzy opinions into basic probability assignments (BPAs) is proposed. Third, to address the problems existing in conflicting evidence combination, the differences of experts’ authorities are taken into consideration, which is represented by the discounting coefficient. Besides, GPRM is adopted to address a more comprehensive assessments by fusing the 3 diverse criterion with weights respectively, which can overcome the limitations in traditional FMEA. An example is illustrated to show the practical application of the proposed FMEA methodology in engineering area.

A Family of Graded Epistemic Logics

Multi-Agent Epistemic Logic has been investigated in Computer Science [Fagin, R., J. Halpern, Y. Moses and M. Vardi, “Reasoning about Knowledge,” MIT Press, USA, 1995] to represent and reason about agents or groups of agents knowledge and beliefs. Some extensions aimed to reasoning about knowledge and probabilities [Fagin, R. and J. Halpern, Reasoning about knowledge and probability, Journal of the ACM 41 (1994), pp. 340–367] and also with a fuzzy semantics have been proposed [Fitting, M., Many-valued modal logics, Fundam. Inform. 15 (1991), pp. 235–254; Maruyama, Y., Reasoning about fuzzy belief and common belief: With emphasis on incomparable beliefs, in: IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16–22, 2011, 2011, pp. 1008–1013]. This paper introduces a parametric method to build graded epistemic logics inspired in the systematic method to build Multi-valued Dynamic Logics introduced in [Madeira, A., R. Neves and M. A. Martins, An exercise on the generation of many-valued dynamic logics, J. Log. Algebr. Meth. Program. 85 (2016), pp. 1011–1037. URL http://dx.doi.org/10.1016/j.jlamp.2016.03.004; Madeira, A., R. Neves, M. A. Martins and L. S. Barbosa, A dynamic logic for every season, in: C. Braga and N. Martí-Oliet, editors, Formal Methods: Foundations and Applications – 17th Brazilian Symposium, SBMF 2014, Maceió, AL, Brazil, September 29-October 1, 2014. Proceedings, Lecture Notes in Computer Science 8941 (2014), pp. 130–145. URL http://dx.doi.org/10.1007/978-3-319-15075-8_9]. The parameter in both methods is the same: an action lattice [Kozen, D., On action algebras, Logic and Information Flow (1994), pp. 78–88]. This algebraic structure supports a generic space of agent knowledge operators, as choice, composition and closure (as a Kleene algebra), but also a proper truth space for possible non bivalent interpretation of the assertions (as a residuated lattice).

A risk-based fuzzy evidential framework for FMEA analysis under uncertainty: An interval-valued DS approach

Failure Modes and Effects Analysis (FMEA) is a common technique used in several manufacturing and service industries for eliminating failures and potential problems using the evaluation of failure modes of a new or an existing product, process, or system. The risk analysis is carried out by calcula ting the Risk Priority Number (RPN), which is a product of three factors, Occurrence (O), Severity (S), and Detection (D). In the literature, modeling uncertainties are used to improve the FMEA process and overcome the inefficiencies of traditional RPN. One of the common uncertainties in FMEA is the epistemic uncertainty that is essentially modeled using the Dempster-Shafer theory (DST). In this study, a novel risk-based fuzzy evidential approach is proposed by using interval-valued DST and fuzzy axiomatic design (FAD) to assess the risk of failure modes with fuzzy belief structures. The efficiency of the proposed model was investigated with the help of an example and the results are compared with riskless evaluations. Reviewing the results shows the information content of failure modes decrease relatively when risk is taken into account, in fact failure modes become relatively more critical than those in the case where no risk is considered.

The Reliability Estimation for the Open Function of Cabin Door Affected by the Imprecise Judgment Corresponding to Distribution Hypothesis

With the development of artificial intelligence, more and more reliability experts have noticed the roles of subjective information in the reliability design of complex system. Therefore, based on the certain numbers of experiment data and expert judgments, we have divided the reliability estimation based on distribution hypothesis into cognition process and reliability calculation. Consequently, for an illustration of this modification, we have taken the information fusion based on intuitional fuzzy belief functions as the diagnosis model of cognition process, and finished the reliability estimation for the open function of cabin door affected by the imprecise judgment corresponding to distribution hypothesis.

Reliability analysis of non-repairable weighted <i>k</i>-out-of-<i>n</i> system using belief universal generating function

In this study reliability analysis of non-repairable weighted k-out-of-n: G (F) systems by incorporating uncertainties namely aleatory and epistemic have been considered. To remove these uncertainties the combination of mass distribution, fuzzy exponential distribution and belief universal generating function have been used. The failure rate (λ) of each component is taken as trapezoidal fuzzy number. Using the proposed method fuzzy reliability function of each component have been calculated and then distributed masses among the components. With the help of these masses reliability and MTTF of the proposed system have been obtained. Lastly, a numerical example is taken to understand the proposed method.

Scientism and Scientific Thinking

The move from respecting science to scientism, i.e., the idealization of science and scientific method, is simple: We go from acknowledging the sciences as fruitful human activities to oversimplifying the ways they work, and accepting a fuzzy belief that Science and Scientific Method, will give us a direct pathway to the true making of the world, all included. The idealization of science is partly the reason why we feel we need to impose the so-called scientific terminologies and methodologies to all aspects of our lives, education too. Under this rationale, educational policies today prioritize science, not only in curriculum design, but also as a method for educational practice. One might expect that, under the scientistic rationale, science education would thrive. Contrariwise, I will argue that scientism disallows science education to give an accurate image of the sciences. More importantly, I suggest that scientism prevents one of science education’s most crucial goals: help students think. Many of my arguments will borrow the findings and insights of science education research. In the last part of this paper, I will turn to some of the most influential science education research proposals and comment on their limits. If I am right, and science education today does not satisfy our most important reasons for teaching science, perhaps we should change not just our teaching strategies, but also our scientistic rationale. But that may be a difficult task.

A New Compromise Solution Model Based on Dantzig–Wolfe Decomposition for Solving Belief Multi-Objective Nonlinear Programming Problems with Block Angular Structure

This paper presents an integrated model based on a compromised solution method to solve fuzzy belief multi-objective large-scale nonlinear programming (FBMOLSNLP) problem with block angular structure. A new method is proposed to transfer each belief decision-making problem into some fuzzy problems. Furthermore, we propose a new compromise method of decision-making as one of the most efficient methods based on the particular measure of closeness to the ideal solution to aggregate multi-objective decision-making (MODM) problems into a single problem. The decomposition algorithm based on Dantzig–Wolfe is utilized to reduce the large-dimensional objective space into a two-dimensional space. Then, Zimmerman method is applied to transfer each bi-objective to a single-objective. Moreover, TOPSIS and VIKOR are utilized as two independent solution methods to aggregate each multi-objective sub-problem. Finally, a new single-objective nonlinear programming problem is solved to find the final solution. To justify the proposed model, two illustrative examples are provided, and the results of three decision methods are compromised.

FUZZY BELIEF STRUCTURE BASED VIKOR METHOD: AN APPLICATION FOR RANKING DELAY CAUSES OF TEHRAN METRO SYSTEM BY FMEA CRITERIA

Public transport is a critical part of civilization in this decade. The amount of money invested and the criticality of transferring people in an acceptable time and without any conflict made it a challenging problem for managers, especially in metropolises. Absolutely, making effective decisions in this area requires considering different aspects. Waiting time is a key criterion in apprising quality of public transport. In this paper, a real world case study of ranking causes of delay in Tehran (Iran) metro system is solved by developing multi attribute group decision-making VIšeKriterijumska Optimizacija I KOmpromisno Rešenje (in Serbian, VIKOR) method under uncertainty, where this uncertainty is captured by Fuzzy Belief Structures (FBS). The obtained results are then compared with a previously proposed Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method with FBSs. The results show that human related issues, along with the problems related to line and transportation system are the most important causes of delay. The obtained results of the problem seem acceptable for decision makers.

Failure mode and effects analysis method based on fuzzy TOPSIS

Aiming at the defect of traditional failure mode and effects analysis( FMEA) in evaluating the effect factors of the failure mode and calculating the risk priority number,a FMEA method based on fuzzy technique for order preference by similarity to ideal solution( TOPSIS) is proposed. This method uses fuzzy belief structure to express the evaluation of the effect factors,and adopts defuzzification and the weighted average to establish the clear belief matrix. Moreover,considering the importance of the weights of the effect factors on analysis result,the weights are determined by the combination the subjective weighting method and the objective weighting method,then the weighted normalized matrix can be constructed,and the risk level of each failure mode is ranked in the order of the relative closeness. An example is taken to validate feasibility and effectiveness of the method.

Constrained fuzzy evidential multivariate model identified by EM algorithm: a soft sensor to monitoring imprecise and uncertain process parameters

This paper focuses on the problem of monitoring/estimating process parameters in the insufficient case when only imprecise and uncertain information can be obtained, possibly due to limited precision and reliability of sensors in industries. To solve this problem, a constrained fuzzy evidential multivariate model is proposed as a soft sensor to monitor imprecise and uncertain process parameters. The most challenging task involved in the modeling is how to identify structure parameters of the monitor model, especially under sets of constraints. To tackle this challenge, we represent the imprecise and uncertain information as fuzzy belief functions in the evidence theory framework, and then propose a restricted fuzzy evidential Expectation-Conditional Maximization algorithm (RFE2CM) for maximum likelihood estimation from fuzzy belief functions under linear inequality constraints. Also, the convergence property of the restricted fuzzy evidential EM algorithm is discussed. In order to validate the performance of the proposed model and algorithm, some numerical simulations are conducted as well as an experimental simulation on a real ball mill in a power plant. The numerical and experimental simulation results show that the proposed model and algorithm can not only be feasibly applicable to monitor the process parameters in insufficient informatics cases, but also have high prediction accuracy with small mean square errors.

A distance measure between intuitionistic fuzzy belief functions

Intuitionistic fuzzy (IF) evidence theory, as an extension of Dempster–Shafer theory of evidence to the intuitionistic fuzzy environment, is exploited to process imprecise and vague information. Since its inception, much interest has been concentrated on IF evidence theory. Many works on the belief functions in IF information systems have appeared. However, there is little research on the distance measure between IF belief functions despite the fact that distance measure in classical belief functions has received close attention. In this paper we mainly investigated the distance measure between IF belief functions based on the Euclidean distance between two column vectors. The similarity between focal elements is also taken into account. The distance and similarity measures between IF sets are investigated firstly. A new similarity measure between IF sets along with its properties and proofs is proposed. The positive definiteness of similarity matrix is investigated to guarantee the metric properties of the distance measure. Then a distance measure between IF belief functions is proposed. It is proved that the proposed distance measure is a metric distance. As is illustrated by examples, the distance measure is sensitive to the change of focal elements. Moreover, its applicability for classical belief functions is also demonstrated.

Constructing T–S fuzzy model from imprecise and uncertain knowledge represented as fuzzy belief functions

The classical Takagi–Sugeno (T–S) fuzzy model is an effective tool used to approximate the behaviors of nonlinear systems on the basis of precise and certain input and output observations. In many real-life situations, however, the knowledge of our interest, i.e., the output observations, can only be imprecise, uncertain, or both. This paper presents a method used to construct T–S fuzzy model when the output is imprecise and uncertain, represented as fuzzy belief function, and then proposes the so-called Evidential knowledge-based T–S regression model (ETS). The consequents of ETS are identified by using maximum likelihood estimate strategy, in which, a novel fuzzy evidential Expectation-Maximization (EM) algorithm is proposed to iteratively maximize the likelihood. The antecedents of ETS are automatically constructed by using a data-driven strategy, considering both the accuracy and complexity of the produced ETS. The performance of ETS was validated by using some unreliable sensor experiments and comparing with other similar methods in the literature. The numerical simulations suggest that the ETS can be used to approximate nonlinear systems with high accuracy when the outputs of systems are imprecisely and uncertainly observed. Correspondingly, the investigations on T–S fuzzy regression of fuzzy output and point-valued output, called Fuzzy knowledge-based T–S regression model (FTS) and classical data based T–S fuzzy regression model, respectively, are covered, when the output fuzzy belief functions degenerate to be fuzzy functions and point-valued data, respectively.

Probability Estimation in the Framework of Intuitionistic Fuzzy Evidence Theory

Intuitionistic fuzzy (IF) evidence theory, as an extension of Dempster-Shafer theory of evidence to the intuitionistic fuzzy environment, is exploited to process imprecise and vague information. Since its inception, much interest has been concentrated on IF evidence theory. Many works on the belief functions in IF information systems have appeared. Although belief functions on the IF sets can deal with uncertainty and vagueness well, it is not convenient for decision making. This paper addresses the issue of probability estimation in the framework of IF evidence theory with the hope of making rational decision. Background knowledge about evidence theory, fuzzy set, and IF set is firstly reviewed, followed by introduction of IF evidence theory. Axiomatic properties of probability distribution are then proposed to assist our interpretation. Finally, probability estimations based on fuzzy and IF belief functions together with their proofs are presented. It is verified that the probability estimation method based on IF belief functions is also potentially applicable to classical evidence theory and fuzzy evidence theory. Moreover, IF belief functions can be combined in a convenient way once they are transformed to interval-valued possibilities.

Multi-level information fusion for spatiotemporal monitoring in water distribution networks

This paper deals with online water quality monitoring in distribution networks based on surrogate water quality parameters (WQPs). The present strategy is based on multi-level information fusion using hierarchical belief rule-based (BRB) systems. Networked fuzzy belief rule-based (NF-BRB) and high-level BRB systems are introduced for information fusion at the feature level. Primary and secondary features are extracted from online WQP signals. Primary features are analyzed using the NF-BRB system that is built through knowledge elicitation from experts. Secondary features are interpreted through the high-level BRB system that employs a fuzzy partitioning on the feature sets and a hybrid learning strategy for its rule base construction. Finally, the dynamic fuzzy evidential fusion is introduced to aggregate the local and spatial assessments in each analysis window. As an important contribution of this paper, we propose a new validation method for event detection in the water distribution network (WDN) based on adaptive projection of the signal patterns attributed to anomaly events, obtained through contamination experiments in a pilot facility, to the real WQP signals measured across the WDN. Single and composite contamination events based on several biological and chemical contaminants are simulated to evaluate the performance of the proposed framework in event detection. The proposed multi-level information fusion framework obtains a high detection rate and a reduced number of false negative and positive results.

A new FMEA method by integrating fuzzy belief structure and TOPSIS to improve risk evaluation process

Failure mode and effect analysis (FMEA) model is a technique used to evaluate the risk. This paper aimed to propose a new FMEA model combining technique for order of preference by similarity to ideal solution (TOPSIS) and belief structure to overcome the shortcomings of the traditional index of FMEA. In this paper, the fuzzy belief TOPSIS method is combined with FMEA to introduce a belief structure FMEA to describe the expert knowledge by a number of linguists as a grammatical phenomenon. Moreover, the weights of components in FMEA index can be different from each other. Therefore, the flexibility of assigning weight to each factor in this method is more compatible to the real decision-making situation. In other word, TOPSIS method is applied to determine the preference of alternatives versus risk criteria. Using linguistic terms in the fuzzy belief approach, the risk factors described a more meaningful value and decision-makers’ judgment is assigned with belief degrees through evaluation of factors. Finally, a numerical case study about the preference of cause failures of steel production process is provided to illustrate the process of proposed method, and then result and discussion is performed for each case.

An Integrated Risk Assessment Model of Township‐Scaled Land Subsidence Based on an Evidential Reasoning Algorithm and Fuzzy Set Theory

Land subsidence risk assessment (LSRA) is a multi-attribute decision analysis (MADA) problem and is often characterized by both quantitative and qualitative attributes with various types of uncertainty. Therefore, the problem needs to be modeled and analyzed using methods that can handle uncertainty. In this article, we propose an integrated assessment model based on the evidential reasoning (ER) algorithm and fuzzy set theory. The assessment model is structured as a hierarchical framework that regards land subsidence risk as a composite of two key factors: hazard and vulnerability. These factors can be described by a set of basic indicators defined by assessment grades with attributes for transforming both numerical data and subjective judgments into a belief structure. The factor-level attributes of hazard and vulnerability are combined using the ER algorithm, which is based on the information from a belief structure calculated by the Dempster-Shafer (D-S) theory, and a distributed fuzzy belief structure calculated by fuzzy set theory. The results from the combined algorithms yield distributed assessment grade matrices. The application of the model to the Xixi-Chengnan area, China, illustrates its usefulness and validity for LSRA. The model utilizes a combination of all types of evidence, including all assessment information--quantitative or qualitative, complete or incomplete, and precise or imprecise--to provide assessment grades that define risk assessment on the basis of hazard and vulnerability. The results will enable risk managers to apply different risk prevention measures and mitigation planning based on the calculated risk states.

The Software to Analyze the States of Complex Systems under Uncertainty based on Fuzzy Belief Network Models

We propose the fundamentals of the software for the analysis of states of complex systems by probabilistic inference methods based on fuzzy belief network models and their extensions. We introduce the concepts of fuzzy potentials and operations on them, develop mathematical tools of two-phase exact probabilistic inference and the procedure for evaluating and predicting the states of the system under study, and describe the architectural aspects of the computer implementation of the relevant information technology.

Parametric regression analysis of imprecise and uncertain data in the fuzzy belief function framework

In this paper, parametric regression analyses including both linear and nonlinear regressions are investigated in the case of imprecise and uncertain data, represented by a fuzzy belief function. The parameters in both the linear and nonlinear regression models are estimated using the fuzzy evidential EM algorithm, a straightforward fuzzy version of the evidential EM algorithm. The nonlinear regression model is derived by introducing a kernel function into the proposed linear regression model. An unreliable sensor experiment is designed to evaluate the performance of the proposed linear and nonlinear parametric regression methods, called parametric evidential regression (PEVREG) models. The experimental results demonstrate the high prediction accuracy of the PEVREG models in regressions with crisp inputs and a fuzzy belief function as output.

Fuzzy Failure Mode and Effects Analysis Using Fuzzy Evidential Reasoning and Belief Rule-Based Methodology

The main objective of this paper is to propose a new risk priority model for prioritizing failures in failure mode and effects analysis (FMEA) on the basis of fuzzy evidential reasoning (FER) and belief rule-based (BRB) methodology. The technique is particularly intended to resolve some of the shortcomings in fuzzy FMEA (i.e., fuzzy rule-based) approaches. In the proposed approach, risk factors like occurrence (O), severity (S), and detection (D), along with their relative importance weights, are described using fuzzy belief structures. The FER approach is used to capture and aggregate the diversified, uncertain assessment information given by the FMEA team members; the BRB methodology is used to model the uncertainty, and nonlinear relationships between risk factors and corresponding risk level; and the inference of the rule-based system is implemented using the weighted average-maximum composition algorithm. The Dempster rule of combination is then used to aggregate all relevant rules for assessing and prioritizing the failure modes that have been identified in FMEA. A case study concerning an ocean going fishing vessel in a marine industry is provided and conducted using the proposed model to illustrate its potential applications and benefits.

A prototype for web services reliability prediction

In this paper, we introduce a new prototype for web services reliability prediction based on a fuzzy belief Petri network FBPN. Since software reliability becomes a high interest research field and the growth of web services in the last years shows an exponential rate, the need of models for web services reliability prediction increased. We also make a review of similar Petri and fuzzy models to show how this idea came to life.