Fuzzy Risk Analysis Research Articles

Application of non-normal p-norm trapezoidal fuzzy number in reliability evaluation of electrical substations

This paper presented a non-normal p-norm trapezoidal fuzzy number–based fault tree technique to obtain the reliability analysis for substations system. Due to uncertainty in the collected data, all the failure probabilities are represented by non-normal p-norm trapezoidal fuzzy number. In this paper, the fault tree incorporated with the non-normal p-norm trapezoidal fuzzy number and minimal cut sets approach are used for reliability assessment of substations. An example of 66/11 kV substation is given to demonstrate the method. Further, fuzzy risk analysis problems are described to find out the probability of failure of each components of the system using linguistic variables, which could be used for managerial decision making and future system maintenance strategy.

Fuzzy Risk Analysis based on a new approach of Ranking Fuzzy Numbers using Orthocenter of Centroids

this paper, a new approach of ranking fuzzy numbers using orthocenter of centroids of fuzzy numbers to its distance from original point is proposed. The proposed method can rank all types of fuzzy numbers including crisp numbers with different membership functions. We apply the proposed ranking method to develop a new method to deal with fuzzy risk analysis problems. The proposed method is more flexible than the existing methods.

Fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights

In this paper, we present a new method for fuzzy risk analysis based on the proposed new fuzzy ranking method for ranking generalized fuzzy numbers with different left heights and right heights. First, we present a fuzzy ranking method for ranking generalized fuzzy numbers with different left heights and right heights. The proposed method considers the areas of the positive side, the areas of the negative side and the centroid values of generalized fuzzy numbers as the factors for calculating the ranking scores of generalized fuzzy numbers with different left heights and right heights. It can overcome the drawbacks of the existing fuzzy ranking methods. Then, we propose a new method for fuzzy risk analysis based on the proposed fuzzy ranking method, where the evaluating values are represented by generalized fuzzy numbers. The proposed fuzzy risk analysis method provides us with a useful way for fuzzy risk analysis based on generalized fuzzy numbers with different left heights and right heights.

Fuzzy risk analysis of flood disasters based on diffused-interior-outer-set model

Floods are indeed one of the most serious natural hazards for human societies, especially in China. In this paper, we firstly introduce the interior-outer-set model (IOSM) based on information diffusion theory in detail. Then taking consideration its deficiencies, we represent the diffused-interior-outer-set model (DIOSM) to obtain the possibility–probability distribution (PPD). Based on the PPD, we analyze and calculate the risk results. To illustrate the procedure of the proposed method, we apply DIOSM to describe the flood disaster risk quantitatively in China by using statistical data respectively, such as the time of floods, the number of the deaths as well as the economic losses each year from 1990 to 2009. The outcomes of this research offer new insights and moreover new possibility to carry out an efficient way for various future flood disaster prevention and mitigation.

Credibilistic Value and Average Value at Risk in Fuzzy Risk Analysis

Decision making in real world is usually made in fuzzy environment and subject to fuzzy risks. The value at risk (VaR) is a widely used tool in risk management and the average value at risk (AVaR) is a risk measure which is a superior alternative to VaR. In this paper, we present a methodology for fuzzy risk analysis based on credibility theory. First, we present the new concepts of the credibilistic VaR and credibilistic AVaR. Next, we examine some properties of the proposed credibilistic VaR and credibilistic AVaR. After that, a kind of fuzzy simulation algorithms are given to show how to calculate them. Finally, a numerical example is illustrated. The proposed credibilistic VaR and credibilistic AVaR are suitable for use in many real problems of fuzzy risk analysis.

An aggregative fuzzy risk analysis for flood incident management

Mitigation of loss or damage is the prime focus in flood incident management (FIM). Emergency response program, a key element in flood incident management can fail in multiple ways; however it can be mainly attributed to failure of infrastructure and/or failure of human institutions. Characterization and quantification of various risk factors in emergency response is a difficult task because responses to floods are complex and dynamic in nature. For these reasons, high level of uncertainties are inherent in the estimation of risk associated with the emergency response and may warrant the usage of a quantitative–qualitative risk assessment framework. In this paper, a multi-stage hierarchical model is developed to estimate the aggregative risk associated with the failure of emergency response system in case of flood. Each risk item is defined by the product of the likelihood of a failure event and associated consequences. Both likelihood and the consequences of a failure event are defined using fuzzy numbers to capture vagueness in the concept of relevant risk factors. An analytic hierarchy process is used for estimating the priority matrix (weights) for grouping risk attributes. Utility of a proposed model is demonstrated through a simplified risk hierarchy representing emergency response system failure of a FIM.

A new approach for ranking of L– R type generalized fuzzy numbers

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. Cheng (Cheng, C. H. (1998). A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems, 95, 307–317) pointed out that the proof of the statement “Ranking of generalized fuzzy numbers does not depend upon the height of fuzzy numbers” stated by Liou and Wang (Liou, T. S., & Wang, M. J. (1992). Ranking fuzzy numbers with integral value. Fuzzy Sets and Systems, 50, 247–255) is incorrect. In this paper, by giving an alternative proof it is proved that the above statement is correct. Also with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Chen, S. M., & Chen, J. H. (2009). Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Systems with Applications, 36, 6833–6842) is incorrect. The main aim of this paper is to modify the Liou and Wang approach for the ranking of L– R type generalized fuzzy numbers. The main advantage of the proposed approach is that the proposed approach provide the correct ordering of generalized and normal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfy all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Wang, X., & Kerre, E. E. (2001). Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems, 118, 375–385).

An improved fuzzy risk analysis based on a new similarity measures of generalized fuzzy numbers

This paper presents a novel method of fuzzy risk analysis based on a new similarity measure of generalized fuzzy numbers. This similarity measure considers many features of generalized fuzzy numbers such as the area, perimeter, height and geometric distance of these kinds of fuzzy numbers. Using some sets of generalized fuzzy numbers, we show the power of this similarity measurement method to overcome the drawbacks that other methods are suffering. Applying the proposed method, we present an improved fuzzy risk analysis method which develops the capability of fuzzy risk analysis methods to deal with sophisticated problems. In the proposed method we use new factors such as probability of failure detection and economic disbenefits of failure occurrence which have not been used in fuzzy risk analysis methods before.

Analyzing fuzzy risk based on similarity measures between interval-valued fuzzy numbers

In this paper, we present a new method for handling fuzzy risk analysis problems based on the proposed new similarity measure between interval-valued fuzzy numbers. First, we present a new similarity measure between interval-valued fuzzy numbers. It considers the degrees of closeness between interval-valued fuzzy numbers on the X-axis and the degrees of differences between the shapes of the interval-valued fuzzy numbers on the X-axis and the Y-axis, respectively. We also prove three properties of the proposed similarity measure. Then, we make an experiment to compare the experimental results of the proposed method with the existing similarity measures between interval-valued fuzzy numbers. The proposed method can overcome the drawbacks of the existing methods. Finally, based on the proposed similarity measure between interval-valued fuzzy numbers, we present a new fuzzy risk analysis algorithm for dealing with fuzzy risk analysis problems. Because the proposed method allows the evaluating values of sub-components to be represented by interval-valued fuzzy numbers, it is more flexible than Chen and Chen’s method (2003).

A New Fuzzy Risk Analysis Method based on Generalized Fuzzy Numbers

Risk analysis plays an important role in many application systems. The current researches prefer to use fuzzy set theory for risk analysis. In this paper, we present a new fuzzy risk analysis method based on generalized fuzzy numbers. Firstly, we define new arithmetic operations between generalized fuzzy numbers. Then, we propose a new method to measure the degree of similarity between generalized fuzzy numbers. Finally, we apply the new arithmetic operations between generalized fuzzy numbers and proposed similarity measure to develop a new method to deal with fuzzy risk analysis problems. The greatest advantage of the new method is that it has less computational complexity. When dealing with the risk analysis problems, the predominance of new method has been showed: easier and more useful.

A modified similarity measure of generalized fuzzy numbers

In this paper, a new similarity measure between generalized fuzzy numbers is presented. It combines the concepts of the center of gravity, the area, the perimeter and the height of generalized fuzzy numbers for calculating the degree of similarity between generalized fuzzy numbers. Eighteen sets of generalized fuzzy numbers are used to compare the proposed method with the existing similarity measures. The proposed method can overcome the drawbacks of the existing similarity measures. The proposed method provides a useful way to handle pattern recognition problems and fuzzy risk analysis problems.

Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers

In this paper, we present a new method for analyzing fuzzy risk based on a new method for ranking generalized fuzzy numbers. First, we present a new method for ranking generalized fuzzy numbers. It considers the areas on the positive side, the areas on the negative side and the heights of the generalized fuzzy numbers to evaluate ranking scores of the generalized fuzzy numbers. The proposed method can overcome the drawbacks of some existing methods for ranking generalized fuzzy numbers. Then, we apply the proposed method for ranking generalized fuzzy numbers to develop a new method for dealing with fuzzy risk analysis problems. The proposed method provides us with a useful way to deal with fuzzy risk analysis problems based on generalized fuzzy numbers.

Practical Research on Fuzzy Risk of Water Resources in Jinhua City, China

A fuzzy expected value of the possibility-probability distribution is a set with \(\underline{E}_{\alpha}(x)\) and \(\overline{E}_{\alpha}(x)\) as its boundaries. The fuzzy expected values \(\underline{E}_{\alpha}(x)\) and \(\overline{E}_{\alpha}(x)\) of a possibility-probability distribution represent the fuzzy risk values being calculated. Using these values under a given α level, three risk values can be calculated: a conservative risk value, a venture risk value, and a maximum probability risk value. Calculation of the fuzzy expected value of Jinhua City’s water resource risk has been performed based on the interior-exterior set model. This model is first used to evaluate the risk of water resources in Jinhua City: it not only solves an imprecise probability estimation, which results from small samples and unclear risk relationship, but it also explores the implicit risk information of the raw data as much as possible. Both of these achievements can make analyses more objective and comprehensive, which makes it easy to regulate options for policy-makers. Hence, the fuzzy risk analysis provides a new way to assess water resources.

Integrated fuzzy framework to incorporate uncertainty in risk management

Integrated Fuzzy Relation Analysis (IFRA) model is proposed for risk assessment involving multiple criteria. The model is an integrated view on uncertainty techniques based on multi-valued mappings, fuzzy relations and fuzzy analytical hierarchical process. Integration of system simulation and risk analysis using fuzzy approach allowed incorporating system modelling uncertainty and subjective risk criteria. The model is demonstrated for a multi-components groundwater contamination problem. Results reflect uncertainties presented as fuzzy numbers for different modelling inputs obtained from fuzzy system simulation. It has been shown that uncertainty can be propagated in complete risk management chain through a broad integration of fuzzy system simulation, and fuzzy risk analysis is possible.

A method for fuzzy risk analysis based on the new similarity of trapezoidal fuzzy numbers

At present, some researchers provide a type of fuzzy risk analysis algorithms for dealing with fuzzy risk analysis problems, where the values of the evaluating items are represented by trapezoidal fuzzy numbers. In those algorithms, the main operations are two: one is arithmetic operators of the trapezoidal fuzzy numbers; the other is the similarity of the trapezoidal fuzzy numbers. However, the arithmetic operators of some algorithms do not satisfy some properties of the trapezoidal fuzzy numbers and the similarity of the trapezoidal fuzzy numbers does not coincide with the intuition of the human being. Due to this situation, in this paper, we present an efficient approach for fuzzy risk analysis based on some new arithmetic operators of the trapezoidal fuzzy numbers and propose a new similarity of the trapezoidal fuzzy numbers to deal with fuzzy risk analysis problems. At the same time, we make an experiment to use 30 sets of trapezoidal fuzzy numbers to compare the experimental results of our proposed approach with the existing similarity measures. At last, we use an example to illustrate the efficiency of the new approach.

Fuzzy risk analysis based on similarity measures between interval-valued fuzzy numbers and interval-valued fuzzy number arithmetic operators

In this paper, we present a new method for fuzzy risk analysis based on a new similarity measure between interval-valued fuzzy numbers and new interval-valued fuzzy number arithmetic operators. First, we present a new similarity measure between interval-valued fuzzy numbers. The proposed similarity measure considers the similarity of the gravities on the X-axis between upper fuzzy numbers, the difference of the spreads between upper fuzzy numbers, the heights of the upper fuzzy numbers, the degree of similarity on the X-axis between interval-valued fuzzy numbers, and the gravities on the Y-axis between interval-valued fuzzy numbers. We also present three properties of the proposed similarity measure between interval-valued fuzzy numbers. Then, we present new interval-valued fuzzy number arithmetic operators. Finally, we apply the proposed similarity measure between interval-valued fuzzy numbers and the proposed interval-valued fuzzy number arithmetic operators to propose a fuzzy risk analysis algorithm to deal with fuzzy risk analysis problems. The proposed method provides a useful way for handling fuzzy risk analysis problems based on interval-valued fuzzy numbers.

Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads

In this paper, we present a new method for fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. First, we present a new method for ranking generalized fuzzy numbers. The proposed method considers the defuzzified values, the heights and the spreads for ranking generalized fuzzy numbers. Based on the proposed method for ranking generalized fuzzy numbers, we propose a fuzzy risk analysis algorithm to deal with fuzzy risk analysis problems. The proposed method provides a useful way for handling the fuzzy risk analysis problems.

Fuzzy risk analysis based on ranking fuzzy numbers using [formula omitted]-cuts, belief features and signal/noise ratios

In this paper, we present a new approach for fuzzy risk analysis based on the ranking of fuzzy numbers. First, we propose a new method for ranking fuzzy numbers using the α-cuts, the belief feature and the signal/noise ratios, where α ∈ [0, 1]. The proposed method for ranking fuzzy numbers calculates the signal/noise ratio of each α-cut of a fuzzy number to evaluate the quantity and the quality of a fuzzy number, where the signal and the noise are defined as the middle-point and the spread of each α-cut of a fuzzy number, respectively. We use the value of α as the weight of the signal/noise ratio of each α-cut of a fuzzy number to calculate the ranking index of each fuzzy number. The proposed method can rank any kinds of fuzzy numbers with different kinds of membership functions. Then, we apply the proposed fuzzy ranking method to propose a fuzzy risk analysis algorithm to deal with fuzzy risk analysis problems. Because the proposed fuzzy risk analysis method considers the degrees of confidence of decision makers’ opinions, it is more flexible than the existing methods.

Fuzzy risk analysis based on interval-valued fuzzy numbers

In this paper, we present a new method for fuzzy risk analysis based on similarity measures between interval-valued fuzzy numbers. First, we present a new similarity measure between interval-valued fuzzy numbers. It combines the concepts of geometric distance, the perimeter, the height and the center-of-gravity-points of interval-valued fuzzy numbers for calculating the degree of similarity between interval-valued fuzzy numbers. We also prove some properties of the proposed similarity measure. We make an experiment to use nine sets of interval-valued fuzzy numbers to compare the experimental results of the proposed method with the existing similarity measures. The proposed method can overcome the drawbacks of the existing similarity measures. We also propose a new division operator and an interval-valued fuzzy number adjustment algorithm. Based on the proposed similarity measure, new division operator and adjustment algorithm, we present a new fuzzy risk analysis algorithm for dealing with fuzzy risk analysis problems, where the values of the evaluating items are represented by interval-valued fuzzy numbers. The proposed method provides a useful way to deal with fuzzy risk analysis problems.

A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers

In this paper, we present a new method for fuzzy risk analysis based on similarity measures between generalized fuzzy numbers. First, we present a new similarity measure between generalized fuzzy numbers. It combines the concepts of geometric distance, the perimeter and the height of generalized fuzzy numbers for calculating the degree of similarity between generalized fuzzy numbers. We also prove some properties of the proposed similarity measure. We make an experiment to use 15 sets of generalized fuzzy numbers to compare the experimental results of the proposed method with the existing similarity measures. The proposed method can overcome the drawbacks of the existing similarity measures. Based on the proposed similarity measure between generalized fuzzy numbers, we present a new fuzzy risk analysis algorithm for dealing with fuzzy risk analysis problems, where the values of the evaluating items are represented by generalized fuzzy numbers. The proposed method provides a useful way to deal with fuzzy risk analysis problems.