A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory

Jorba, Lambert; Adillon, Romà J.

doi:10.3390/sym9100198

Cited by 7 publications

(9 citation statements)

References 48 publications

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“…In this regard, we can point out [23] in a non-life insurance context, [24] to interpret the parameter that quantifies the dependence in a Farlie-Gumbel-Morgestein copula, and [25][26][27][28] in life insurance pricing. Since any interval can be seen as the -cut of a FN, even in the case of improper intervals ( [29]), in this work we consider that is fitted by means of a FN and, more particularly, by a triangular fuzzy number (TFN). So, this paper builds up a framework to model Markovian BMSs that embed the standard case, where the risk parameter is crisp, but also the method developed in [11] that quantifies this parameter as a modal interval.…”

Section: Noveltiesmentioning

confidence: 99%

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Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

2021

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Markov chains (MCs) are widely used to model a great deal of financial and actuarial problems. Likewise, they are also used in many other fields ranging from economics, management, agricultural sciences, engineering or informatics to medicine. This paper focuses on the use of MCs for the design of non-life bonus-malus systems (BMSs). It proposes quantifying the uncertainty of transition probabilities in BMSs by using fuzzy numbers (FNs). To do so, Fuzzy MCs (FMCs) as defined by Buckley and Eslami in 2002 are used, thus giving rise to the concept of Fuzzy BMSs (FBMSs). More concretely, we describe in detail the common BMS where the number of claims follows a Poisson distribution under the hypothesis that its characteristic parameter is not a real but a triangular FN (TFN). Moreover, we reflect on how to fit that parameter by using several fuzzy data analysis tools and discuss the goodness of triangular approximates to fuzzy transition probabilities, the fuzzy stationary state, and the fuzzy mean asymptotic premium. The use of FMCs in a BMS allows obtaining not only point estimates of all these variables, but also a structured set of their possible values whose reliability is given by means of a possibility measure. Although our analysis is circumscribed to non-life insurance, all of its findings can easily be extended to any of the abovementioned fields with slight modifications.

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Section: Noveltiesmentioning

confidence: 99%

“…Equations (26), (29) and (30) do not give a TFN. However, can be approximated as a TFN simply by using Equation (18).…”

Section: Implementing a Markovian Fuzzy Bonus-malus System Governed Bmentioning

confidence: 99%

Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

2021

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“…Definition 1 (see [14]). There are two trapezoidal fuzzy numbers a = a 1 , a 2 , a 3 Definition 2 (see [14]).…”

Section: Trapezoidal Fuzzy Number and Language Evaluation Phrasesmentioning

confidence: 99%

“…Definition 1 (see [14]). There are two trapezoidal fuzzy numbers a = a 1 , a 2 , a 3 Definition 2 (see [14]). There are two trapezoidal fuzzy numbers a = a 1 , a 2 , a 3 , a 4…”

Section: Trapezoidal Fuzzy Number and Language Evaluation Phrasesmentioning

confidence: 99%

Optimal Allocation Method of Discrete Manufacturing Resources for Demand Coordination between Suppliers and Customers in a Fuzzy Environment

2018

Complexity

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Discrete manufacturing products are often assembled from multiple parts through a series of discrete processes. How to effectively configure resources in a discrete manufacturing environment is an important research topic worthy of attention. Based on an in-depth analysis of the discrete manufacturing operation model and the manufacturing resource allocation process, this paper fully considers the uncertainty factors of the manufacturing resource customers and the interests of the manufacturing resource suppliers and proposes a bilevel planning model under a fuzzy environment that comprehensively considers the customers’ expectation bias and the suppliers’ profit maximization. The method firstly uses a language phrase to collect the language evaluation of the customers and suppliers for manufacturing tasks and uses a trapezoidal fuzzy number to convert the language evaluation phrase into a value that can be calculated. Then, we use the prospect theory to optimize the constraint indicators based on the language evaluation of customers and suppliers. Next, the bilevel planning model for optimal configuration of manufacturing resources in discrete manufacturing environment is established under the consideration of the respective interests of both the customers and the suppliers, and the fast nondominated sorting genetic algorithm (NSGA-II) is used to solve the model. Finally, an example is given to verify the validity and feasibility of the model.

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“…Such deviations in subjective estimations can lead to fuzziness being inherent in the real-world decision problems (e.g., vagueness and/or impreciseness in the outcomes of a water pollution control sample), neglect of which can cause the solutions of problems deviating greatly from their true values. Fuzzy mathematic programming (FMP), based on fuzzy sets theory, can facilitate the analysis of system associated with uncertainties being derived from vagueness and imprecision [6,7]. FMP is capable of handling decision problems under fuzzy goal and constraints and tackling ambiguous coefficients in the objective function and constraints.…”

Section: Introductionmentioning

confidence: 99%

A Recourse-Based Type-2 Fuzzy Programming Method for Water Pollution Control under Uncertainty

Liu

Huang

et al. 2017

Symmetry

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Abstract:In this study, a recourse-based type-2 fuzzy programming (RTFP) method is developed for supporting water pollution control of basin systems under uncertainty. The RTFP method incorporates type-2 fuzzy programming (TFP) within a two-stage stochastic programming with recourse (TSP) framework to handle uncertainties expressed as type-2 fuzzy sets (i.e., a fuzzy set in which the membership function is also fuzzy) and probability distributions, as well as to reflect the trade-offs between conflicting economic benefits and penalties due to violated policies. The RTFP method is then applied to a real case of water pollution control in the Heshui River Basin (a rural area of China), where chemical oxygen demand (COD), total nitrogen (TN), total phosphorus (TP), and soil loss are selected as major indicators to identify the water pollution control strategies. Solutions of optimal production plans of economic activities under each probabilistic pollutant discharge allowance level and membership grades are obtained. The results are helpful for the authorities in exploring the trade-off between economic objective and pollutant discharge decision-making based on river water pollution control.

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A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory

Cited by 7 publications

References 48 publications

Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

Optimal Allocation Method of Discrete Manufacturing Resources for Demand Coordination between Suppliers and Customers in a Fuzzy Environment

A Recourse-Based Type-2 Fuzzy Programming Method for Water Pollution Control under Uncertainty

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