Some novel inequalities for fuzzy variables on the variance and its rational upper bound

Yi, Xiajie; Miao, Yunwen; Zhou, Jian; Wang, Yujie

doi:10.1186/s13660-016-0975-6

Cited by 8 publications

(8 citation statements)

References 18 publications

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“…Then, the triplet (Θ, P, Pos) is known as a possibility space. A fuzzy variable is a mapping from possibility space (Θ, P, Pos) to the set of real numbers [37,39].…”

Section: Preliminariesmentioning

confidence: 99%

“…Definition Let be a fuzzy variable defined on the credibility space (Θ, P, Pos) . Then its membership function (MF) defined from the credibility measure is given by [37,39] Definition The -cut of a fuzzy variable A is defined as…”

Section: Preliminariesmentioning

confidence: 99%

“…Yi et al [39] derived the concept of rational upper bounded of the variance (RUBV) along with some definitions and results in terms of credibility distribution and ICD.…”

Section: Rational Upper Bound Of the Variancementioning

confidence: 99%

“…Definition Let A be a fuzzy variable with credibility distribution Φ and finite expected value e. The RUBV is defined as [39] Definition Let A be a fuzzy variable with credibility distribution Φ . If the expected value is e, then RUBV is evaluated as [39] Corollary The RUBV of SEFV depends on the width h and it is 2h 2 3 .…”

Section: Rational Upper Bound Of the Variancementioning

confidence: 99%

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Mathematics of uncertainty: an exploration on semi-elliptic fuzzy variable and its properties

Dutta

2019

SN Appl. Sci.

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Uncertainty is more or less encountered in industrial and medical systems as well. Uncertainty theory is an upgraded theory which comprises of possibility measure, necessity measure and credibility measure plays significant role in modelling uncertainty. In connection with uncertainty modeling, a special and intricate fuzzy variable viz., semi-elliptic fuzzy variable (SEFV) is thrashed out here. Subsequently, an attempt has been made to derive possibility, necessity and credibility measure of the SEFV first. Later, some other properties such as expected value, variance, rational upper bound etc are presented and based on that mean and variance ranking of SEFVs are proposed. Afterwards reliability analysis and medical diagnosis cases are carried out which exhibit the efficiency and novelty of the derived SEFV. In this work done, it is observed that the present work has the capability to resolve problems under uncertain complex situations. better to treat uncertainty and further studied by acolyte researchers such as Dubois and Prade [26], Klir [27], Yager [28] etc. Furthermore, Dubois and Prade [29] studied mean value of fuzzy numbers, Ban [30] discussed fuzzy valued measure and conditional expectations of fuzzy numbers, Heilpern [31]studied expected value of fuzzy numbers, Carlsson and Fuller [32] developed possiblistic mean and variance of fuzzy numbers, Chen and Tan [33] further developed mean value and variance of multiplication of fuzzy numbers. Nevertheless in the absence of self duality measure the earlier studies lead to the exaggeration of the reality. keeping this in mind, Liu and Liu [34] initiated a concept termed as credibility theory. Li and Liu [35] presented a sufficient and necessary condition for credibility measures. Further Liu and Liu [36] systematically studied and developed credibility theory. After that some extended studies on credibility theory can be observed in Liu [37], Zhou et al. [38], Yi et al. [39], Garai et al. [40].Although various types of fuzzy variables are encountered, however, an exceptional and intricate fuzzy variable SEFV in terms of credibility theory is not deliberated yet. This paper presents an approach to derive possibility, necessity and credibility measure of the SEFV. Furthermore, expected value, variance, rational upper bound etc of SEFV are presented. Then ranking of SEFNs through expected value and variance is proposed. Finally, novelty and applicability has been exhibited by performing reliability analysis and medical diagnosis cases.

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“…Then, the triplet (Θ, P, Pos) is known as a possibility space. A fuzzy variable is a mapping from possibility space (Θ, P, Pos) to the set of real numbers [37,39].…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

“…Yi et al [39] derived the concept of rational upper bounded of the variance (RUBV) along with some definitions and results in terms of credibility distribution and ICD.…”

Section: Rational Upper Bound Of the Variancementioning

confidence: 99%

Section: Rational Upper Bound Of the Variancementioning

confidence: 99%

See 2 more Smart Citations

Mathematics of uncertainty: an exploration on semi-elliptic fuzzy variable and its properties

Dutta

2019

SN Appl. Sci.

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“…So, the concept of a LR -type fuzzy interval and the concept of a LR -type fuzzy number must be defined in the first place. These concepts were described, for example, in [5] and [9].…”

Section: Fuzzy Numbersmentioning

confidence: 99%

Estimation of Bounds of the Set of Potential Number of Fuzzy Clusters in a Sought Clustering Structure

Dmitri¹,

Yaroma²,

Damaratski³

2016

CAE

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In this paper, an approach to constructing the set of values of the most possible number of fuzzy clusters in a sought clustering structure is proposed. The proposed approach is based on heuristic possibilistic clustering and fuzzy numbers. For the purpose, fuzzy numbers are described and algorithms of the heuristic approach to possibilistic clustering are considered in brief. A procedure for constructing the set of values of the most possible number of fuzzy clusters is described for the object data set. An application of the proposed technique to the Anderson's iris data set is provided and some concluding remarks are stated.

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Solution of a transshipment problem with uncertain parameters under impaired and enhanced flow

Sarkar,

Kar,

Basu

et al. 2023

J Anal

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Some novel inequalities for fuzzy variables on the variance and its rational upper bound

Cited by 8 publications

References 18 publications

Mathematics of uncertainty: an exploration on semi-elliptic fuzzy variable and its properties

Mathematics of uncertainty: an exploration on semi-elliptic fuzzy variable and its properties

Estimation of Bounds of the Set of Potential Number of Fuzzy Clusters in a Sought Clustering Structure

Solution of a transshipment problem with uncertain parameters under impaired and enhanced flow

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