Ranking fuzzy numbers by distance minimization

Asady, B.; Zendehnam, Akbar

doi:10.1016/j.apm.2006.10.018

Cited by 214 publications

(127 citation statements)

References 29 publications

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“…Note that this proposal has also been made by Liou and Wang [30], and that the special case of β = 1 /2 has been proposed by many authors [44,25,46,2] with different justifications. To our knowledge, there are no existing proposal in the fuzzy literature corresponding to the extension of interval dominance, weak ordering and lattice ordering of lower and upper expectations.…”

Section: Campos and González Approachmentioning

confidence: 96%

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: Campos and González Approachmentioning

confidence: 96%

Ranking of fuzzy intervals seen through the imprecise probabilistic lens

Destercke

Couso

2015

Fuzzy Sets and Systems

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“…For the special case of β = 1 2 , E 1 2 has been proposed by many authors, among others, as the the neutral scalar substitute of a fuzzy interval in [33], as the expected value of a fuzzy number in [34], using the area compensation method in [35], as the generative expected value induced by the evidence X [36], as the credibilistic expectation of a fuzzy variable [37] or as the middle point of a fuzzy number defined for ranking by distance minimisation [38]. It is also the centre of the mean value of a fuzzy number as defined in [39] and the expected value of the so-called pignistic probability distribution, which is found as the centroid of the set of probabilities dominated by the possibility measure associated with X, P(Π X ) (cf.…”

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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“…This method is also a distance minimization technique, developed and tested by Asady and Zendehnam (2007). In this, the V ijk is converted into a crisp number using equation…”

Section: Methodsmentioning

confidence: 99%

Comparative Study of Leanness Index Methods for Manufacturing Organizations

2017

IJAERD

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Abstract-The Purpose of this paper is to identify the leanness index of the organizations using multiple models.The leanness index of three SME's are identified using the predefined models.It is identified that the results obtained through these models are in line with each other. The case study has been conducted only by taking qualitative and benefit factor. Only SME's are selected for a case study.The comparative study between the three predefined models and development of proposed model followed by a real-world case study is the original contributions under this paper.

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Ranking fuzzy numbers by distance minimization

Cited by 214 publications

References 29 publications

Ranking of fuzzy intervals seen through the imprecise probabilistic lens

Ranking of fuzzy intervals seen through the imprecise probabilistic lens

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

Comparative Study of Leanness Index Methods for Manufacturing Organizations

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