Reasonable properties for the ordering of fuzzy quantities (II)

Wang, Xuzhu; Kerre, Etienne

doi:10.1016/s0165-0114(99)00063-9

Cited by 407 publications

(142 citation statements)

References 13 publications

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“…Note that our purpose is not to perform an extensive review of existing fuzzy rankings, as such reviews are already available [5,42,43]. We also decided to include only those fuzzy rankings that had a clear link with the imprecise probabilistic approach: other fuzzy ranking methods could perhaps be given a complex imprecise probabilistic interpretation, however this goes beyond the scope of this paper.…”

Section: Reinterpreting Some Classical Fuzzy Ranking Methodsmentioning

confidence: 99%

Ranking of fuzzy intervals seen through the imprecise probabilistic lens

Destercke

Couso

2015

Fuzzy Sets and Systems

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Ranking of fuzzy intervals seen through the imprecise probabilistic lensSébastien Destercke, Inés Couso To cite this version:Sébastien Destercke, Inés Couso. Ranking of fuzzy intervals seen through the imprecise probabilistic lens. AbstractWithin the fuzzy literature, the issue of ranking fuzzy intervals has been addressed by many authors, who proposed various solutions to the problem. Most of these solutions intend to find a total order on a given collection of fuzzy intervals. However, if one sees fuzzy intervals as descriptions of uncertain quantities, an alternative to rank them is to use ranking rules issued from the imprecise probabilistic literature. In this paper, we investigate ranking rules based on different statistical features (mean, median) and orderings, and relate the obtained (partial) orders to some classical proposals. In particular, we propose a generic expression of stochastic orderings, and then use it to systematically investigate extensions of the most usual stochastic orderings to fuzzy intervals. We also show some relations between those extensions, and explore their relation with existing fuzzy ranking proposals.

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Section: Reinterpreting Some Classical Fuzzy Ranking Methodsmentioning

confidence: 99%

Ranking of fuzzy intervals seen through the imprecise probabilistic lens

Destercke

Couso

2015

Fuzzy Sets and Systems

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“…According to [29], this approach is the only one which satisfies all the reasonable properties proposed in [42,43] for ordering fuzzy quantities.…”

Section: Ranking Fuzzy Makespan Valuesmentioning

confidence: 99%

Coevolutionary makespan optimisation through different ranking methods for the fuzzy flexible job shop

Palacios

González-Rodríguez

Vela

et al. 2015

Fuzzy Sets and Systems

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In this paper we tackle a variant of the flexible job shop scheduling problem with uncertain task durations modelled as fuzzy numbers. To minimise the schedule's makespan, we consider different ranking methods for fuzzy numbers. We then propose a cooperative co-evolutionary algorithm with two different populations evolving the two components of a solution: machine assignment and task relative order. Additionally, we incorporate a specific local search method for each population. The resulting hybrid algorithm is then evaluated on existing benchmark instances, comparing favourably with the state-of-theart methods. The experimental results also serve to analyse the influence in the robustness of the resulting schedules of the chosen ranking method.

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“…However, it seems that fuzzy sets, considering their mathematical properties and their ability to deal with vagueness and uncertainty (characteristics present in Natural Languages) are well-equipped to model sentiment-related problems. As it is well known, fuzzy relations have been extensively used in disciplines as dissimilar as linguistics [15], clustering [46] and decision-making [62], among many others. Thus, a combination of techniques -which would fit the concept of hybrid -could be successful at addressing the SA challenges by exploiting the best in each technique.…”

Section: Introductionmentioning

confidence: 99%