On possibility-degree formulae for ranking interval numbers

Liu, Fang; Pan, Lijun; Liu, Zu-Lin; Peng, Ya-Nan

doi:10.1007/s00500-017-2509-7

Cited by 22 publications

(7 citation statements)

References 29 publications

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“…As described in Section 3.3, the expected value of the RPN for F n is interval [A n , A n ] . To compare two overlapping intervals, many methods have been proposed [49][50][51][52]. In this section, a simple and effective method of interval number ranking based on the possibility degree is used to order these interval RPNs.…”

Section: E Risk Prioritizationmentioning

confidence: 99%

An Area-Based Metrics to Evaluate Risk in Failure Mode and Effects Analysis Under Uncertainties

Yan

Suo

2022

IEEE Access

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Failure mode and effects analysis (FMEA) is a widely used, powerful tool to identify and assess potential failure modes in products and to make products more reliable. Due to the complexity of products and lack of knowledge, FMEA involves many uncertainties in practice. In previous studies, numerous modified FMEA methods based on fuzzy logic and Dempster-Shafer (D-S) evidence theory have been employed to address these uncertainties. These studies focus on how to handle uncertainties and to identify a more reliable prioritization of risk priority numbers (RPNs). However, studies have not sufficiently examined how many uncertainties are present in resulting RPNs. To better model and process various types of uncertainties in FMEA, two new area-based metrics are constructed in this paper. One is the interval area metric (IAM), which is used in RPN representation. The other is the dimensionless uncertainty metric (DUM), which is used to measure how many uncertainties there are in RPN. IAM is used to rank the risks in failure modes, and DUM is used to rank the uncertainties in failure modes. Then, an expert system is presented to qualitatively evaluate the DUM, which can help FMEA users intuitively judge whether further investigation should be performed to alleviate the epistemic uncertainties in each failure mode. Finally, a practical risk evaluation case regarding the grinding wheel system of a numerically controlled (NC) machine is provided to demonstrate the application and effectiveness of the proposed FMEA. The case study shows that the calculation programs of IAM and DUM do not require any assumptions or need to address conflict among experts. In addition, proposed method can not only give a more accurate rating of each failure mode, but also help designers intuitively see the uncertainty grade of each RPN, which is useful to help them understand FMEA results.INDEX TERMS failure mode and effects analysis, D-S evidence theory, area-based metrics; epistemic uncertainty metric, risk priority number.

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Section: E Risk Prioritizationmentioning

confidence: 99%

An Area-Based Metrics to Evaluate Risk in Failure Mode and Effects Analysis Under Uncertainties

Yan

Suo

2022

IEEE Access

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“…In Table 1 we have studies some typical examples of ranking methods for interval orders. However, it is clear that there are many others, which are very important and useful in some context as, for example, Liu (2009), Xia and Chen (2015) or Liu et al (2018). However, we are interested on total orders in L([0, 1]).…”

Section: Ordersmentioning

confidence: 99%

Convexity and level sets for interval-valued fuzzy sets

Huidobro

Alonso

Janiš

et al. 2022

Fuzzy Optim Decis Making

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Convexity is a deeply studied concept since it is very useful in many fields of mathematics, like optimization. When we deal with imprecision, the convexity is required as well and some important applications can be found fuzzy optimization, in particular convexity of fuzzy sets. In this paper we have extended the notion of convexity for interval-valued fuzzy sets in order to be able to cover some wider area of imprecision. We show some of its interesting properties, and study the preservation under the intersection and the cutworthy property. Finally, we applied convexity to decision-making problems.

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“…The objective (11) corresponds to the total cost minimization. Constraint ( 12) avoids going from a point to itself.…”

Section: Objective Functionmentioning

confidence: 99%

“…Let us have two solutions s X , s Y with their corresponding non-negative intervals X = [x l , x r ], Y = [y l , y r ] and x l , x r , y l , y r ∈ R + 0 . The possibility degree of s X being greater than s Y is stated in terms of P(X ≥ Y) as in [10] and considering a user with a neutral attitude is defined as follows [11]:…”

mentioning

confidence: 99%

The Role of Metaheuristics as Solutions Generators

2021

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Optimization problems are ubiquitous nowadays. Many times, their corresponding computational models necessarily leave out of consideration several characteristics and features of the real world, so trying to obtain the optimum solution can not be enough for a problem solving point of view. The aim of this paper is to illustrate the role of metaheuristics as solutions’ generators in a basic problem solving framework. Metaheuristics become relevant in two modes: firstly because every run (in the case of population based techniques) allows to obtain a set of potentially good solutions, and secondly, if a reference solution is available, one can set up a new optimization problem that allows to obtain solutions with similar quality in the objectives space but maximally different structure in the design space. Once a set of solutions is obtained, an example of an a posteriori analysis to rank them according with decision maker’s preferences is shown. All the problem solving framework steps, emphasizing the role of metaheuristics are illustrated with a dynamic version of the tourist trip design problem (for the first mode), and with a perishable food distribution problem (for the second one). These examples clearly show the benefits of the problem solving framework proposed. The potential role of the symmetry concept is also explored.

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On possibility-degree formulae for ranking interval numbers

Cited by 22 publications

References 29 publications

An Area-Based Metrics to Evaluate Risk in Failure Mode and Effects Analysis Under Uncertainties

An Area-Based Metrics to Evaluate Risk in Failure Mode and Effects Analysis Under Uncertainties

Convexity and level sets for interval-valued fuzzy sets

The Role of Metaheuristics as Solutions Generators

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