The sufficient and necessary condition for chance distribution of bifuzzy variable

Qin, Zhongfeng; Li, Xiang

doi:10.1007/s00500-010-0567-1

Cited by 2 publications

(2 citation statements)

References 20 publications

(16 reference statements)

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“…As a continuation of [5], Zhou and Liu [6,7] investigated some mathematical properties of this kind of variable, such as chance distribution and expected value operator. Afterwards, Qin and Li [8] gave and proved a sufficient and necessary condition for the chance distribution of the bifuzzy variable.…”

Section: Introductionmentioning

confidence: 99%

The Scalar Mean Chance and Expected Value of Regular Bifuzzy Variables

2021

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As a natural extension of the fuzzy variable, a bifuzzy variable is defined as a mapping from a credibility space to the collection of fuzzy variables, which is an appropriate tool to model the two-fold fuzzy phenomena. In order to enrich its theoretical foundation, this paper explores some important measures for regular bifuzzy variables, the most commonly used type of bifuzzy variables. Firstly, we introduce the regular bifuzzy variables’ mean chance measure and some properties, including self-duality and its calculation formulas. Furthermore, we also investigate the mean chance distribution for strictly monotone functions of regular bifuzzy variables based on the proposed operational law. Finally, we present the expected value operator as well as equivalent analytical formulas of the expected value of regular bifuzzy variables and their strictly monotone functions.

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Section: Introductionmentioning

confidence: 99%

The Scalar Mean Chance and Expected Value of Regular Bifuzzy Variables

2021

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“…Qin and Li [16] presented a necessary and sufficient condition for a chance distribution of the bifuzzy variable. Xu and Yan [23] not only presented a multi-objective decision making model for a vendor selection problem under a bifuzzy environment and then provided its generalization, but also transformed this bifuzzy uncertainty model into a deterministic one.…”

Section: Introductionmentioning

confidence: 99%

Imprecise data envelopment analysis model with bifuzzy variables

Paryab

Shiraz

Jalalzadeh

et al. 2014

Journal of Intelligent &Amp; Fuzzy Systems

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Data envelopment analysis (DEA) is a non-parametric approach for measuring and evaluating the relative efficiencies of a set of entities with common crisp inputs and outputs. Whereas crisp input-output data are required in the traditional DEA evaluation process, the observed input-output data in real-world performance evaluation problems are quite often imprecise or vague. The impreciseness and vagueness related to the input-output data in DEA can be represented by fuzzy variables. The purpose of this paper is three-fold. First, the current study introduces a non-deterministic chance constrained DEA model, which solves the Charnes, Cooper and Rhodes (CCR) model by treating the input-output data as bifuzzy variables which are fuzzy variables with fuzzy parameters. Second, by assuming that decision making units operate in a bifuzzy environment, the study derives a deterministic model equivalent to the chance constrained model. Finally, two numerical examples are presented to demonstrate the applicability of the proposed framework.

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The sufficient and necessary condition for chance distribution of bifuzzy variable

Cited by 2 publications

References 20 publications

The Scalar Mean Chance and Expected Value of Regular Bifuzzy Variables

The Scalar Mean Chance and Expected Value of Regular Bifuzzy Variables

Imprecise data envelopment analysis model with bifuzzy variables

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