A context-dependent method for ordering fuzzy numbers using probabilities

Yager, Ronald R.; Detyniecki, Marcin; Bouchon‐Meunier, Bernadette

doi:10.1016/s0020-0255(01)00132-3

Cited by 67 publications

(32 citation statements)

References 11 publications

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“…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. For instance, the approach of Yager et al [45] that consists in using statistical preference induced by the independent probability distributions p X (x) = π X (x) /∑ x π X (x ) and p Y (y) = π Y (y) /∑ y π Y (y ), yet we may have that p X ∈ P(Π X ) and p Y ∈ P(Π Y ), hence its links with the current view are unclear (if any). A similar argument can be advanced for methods that are based on areas under distributions π Y , π X and their combinations, such as the one of Nakamura [33].…”

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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“…The normal probability distribution is used extensively in that it can well model the additive effect of many independent factors [38][39][40][41][42]. In the following, a case that continuous probability distributions are normal ones was analyzed [35].…”

Section: Definition 4 (Stochastic Dominance Relation Between Two Normmentioning

confidence: 99%

Attribute Reduction in Stochastic Information Systems Based on α-Dominance

Aydoğan

Özmen

2017

Bilişim Teknolojileri Dergisi

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Abstract-Rough set has been commonly taken part in literature to examine inadequate and incomplete information systems. The efficiency of rough set with stochastic data observed for developing convenience and scalability. In this study, we use a ranking approach for attribute reduction in stochastic information systems and generalized this via presenting a dominance relation. We obtained the rough set approach of attribute reduction in stochastic information systems by establishing the dominance degrees. Furthermore, attribute reduction methods are studied by considering discernibility matrix and this approach is applied to explanatory examples to demonstrate its validity. Also this research proposes many research fields and new application areas show a tendency to concerning rough set approach to stochastic information systems.

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“…Recent studies have also developed numerous statistical analysis methods and concepts for fuzzy theory (Fan, 2010;Hsu, Tsai & Chiang, 2009;Ravi, Shankar, Sireesha, Rao & Vani, 2010;Sun & Wu, 2007;Wang & Chen, 2010;Wu & Lin, 2002). The second part involves the examining of the interval fuzzy number method to expand the applicability of the theory (Chu & Lin, 2009;Hung, Vladik, Wu & Gang, 2011;Lin & Chen, 2004;Sengupta & Pal, The Study of Taiwan's New Immigrant Children's Mathematics Achievement 37 2000; Yager, Detyniecki & Bouchon-Meunier, 2001). The third part includes research documents on the sorting of fuzzy numbers.…”

Section: Studies On the Application Of Fuzzy Statistics And Interval mentioning

confidence: 99%