Ranking of fuzzy intervals seen through the imprecise probabilistic lens

Destercke, Sébastien; Couso, Inés

doi:10.1016/j.fss.2014.12.009

Cited by 23 publications

(9 citation statements)

References 45 publications

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“…Additionally, ≤ E coincides with several other ranking methods from the literature as highlighted in [47]. It is also possible to establish a relation with classical interval comparison in the light of imprecise probabilities, with ≤ E coming down to using Hurwicz criterion on upper and lower expectations derived from the fuzzy number [12]. This provides us with an interpretation for comparisons based on ≤ E as those corresponding to a decision maker who keeps an equilibrium between pessimism and optimism.…”

Section: Ordering Of Tfnssupporting

confidence: 55%

Benchmarks for fuzzy job shop problems

Palacios

Puente

Vela

et al. 2016

Information Sciences

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Highlights• The fuzzy job shop scheduling problem with makespan minimization is revised• We survey existing metaheuristic methods and test beds for the problem • More challenging benchmark instances with LBs and competitive results are proposed• We publish old and new test beds to facilitate reproducibility and future research 1 AbstractThe fuzzy job shop scheduling problem with makespan minimisation is a problem with a significant presence in the scientific literature. However, a common meaningful comparison base is missing for such problem. This work intends to fill the gap in this domain by reviewing existing benchmarks as well as proposing new benchmark problems. First, we shall survey the existing test beds for the fuzzy job shop, analysing whether they are sufficiently varied and, most importantly, whether there is room for improvement on these instances -an essential requirement if the instances are to be useful for the scientific community in order to compare and develop new solving strategies. In the light of this analysis, we shall propose a new family of more challenging benchmark problems and provide lower bounds for the expected makespan of each instance as well as reference makespan values obtained with a memetic algorithm from the literature. The resulting benchmark will be made available so as to facilitate experiment reproducibility and encourage research competition.

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Section: Ordering Of Tfnssupporting

confidence: 55%

Benchmarks for fuzzy job shop problems

Palacios

Puente

Vela

et al. 2016

Information Sciences

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“…FPR is one of the most commonly used preference models . It specifies the degree to which each alternative

x_{i} \in X

is at least as good as any other alternative

x_{j}

by means of a fuzzy relation P , that is, a fuzzy set on

X \times X

with a membership function

μ_{P} : X \times X \to false[0, 1 false]

such that:

μ_{P} (x_{i}, x_{j}) = \{\begin{matrix} left 1 & left if x_{i} is definitely preferred to x_{j}, \\ left a \in ((), 0.5, 1) & left if x_{i} is slightly preferred to x_{j}, \\ left 0.5 & left if x_{i} and x_{j} are evenly preferred, \\ left b \in ((), 0, 0.5) & left if x_{j} is slightly preferred to x_{i}, \\ left 0 & left if x_{j} is definitely preferred to x_{i} . \end{matrix}

…”

Section: Background Concepts On Gdmmentioning

confidence: 99%

Fuzzy rankings for preferences modeling in group decision making

Capuano

Chiclana

Herrera‐Viedma

et al. 2018

Int. J. Intell. Syst.

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Although fuzzy preference relations (FPRs) are among the most commonly used preference models in group decision making (GDM), they are not free from drawbacks. First of all, especially when dealing with many alternatives, the definition of FPRs becomes complex and time consuming. Moreover, they allow to focus on only two options at a time. This facilitates the expression of preferences but let experts lose the global perception of the problem with the risk of introducing inconsistencies that impact negatively on the whole decision process. For these reasons, different preference models are often adopted in real GDM settings and, if necessary, transformation functions are applied to obtain equivalent FPRs. In this paper, we propose fuzzy rankings, a new approximate preference model that offers a higher level of user‐friendliness with respect to FPRs while trying to maintain an adequate level of expressiveness. Fuzzy rankings allow experts to focus on two alternatives at a time without losing the global picture so reducing inconsistencies. Conversion algorithms from fuzzy rankings to FPRs and backward are defined as well as similarity measures, useful when evaluating the concordance between experts’ opinion. A comparison of the proposed model with related works is reported as well as several explicative examples.

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“…(13) . Thus, in order to compare any pair of models, we will combine a stochastic ordering with an ordering between intervals, leading to a generalized stochastic ordering in the sense of Couso and Dubois [3] and Destercke and Couso [10] .…”

Section: Set-valued Datamentioning

confidence: 99%