Generalizations of Hu-type inequalities and their applications

Tian, Jing-Feng; Yang, Zhen-Hang

doi:10.22436/jnsa.010.04.55

Cited by 4 publications

(3 citation statements)

References 13 publications

(17 reference statements)

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“…In FS theory, t-conorm (T * ) and t-norm (T) are very important to the generalization of intersection or union of fuzzy sets [34,42,46,[55][56][57][58][59][60][61].…”

Section: Hamacher T-norm and Hamacher T-conormmentioning

confidence: 99%

Some Normal Intuitionistic Fuzzy Heronian Mean Operators Using Hamacher Operation and Their Application

Zhang

Kong

2018

Symmetry

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Hamacher operation is a generalization of the algebraic and Einstein operation and expresses a family of binary operation in the unit interval [0,1]. Heronian mean can deal with correlations of different criteria or input arguments and does not bring out repeated calculation. The normal intuitionistic fuzzy numbers (NIFNs) can depict normal distribution information in practical decision making. A decision-making problem was researched under the NIFN environment in this study, and a new multi-criteria group decision-making (MCGDM) approach is herein introduced on the basis of Hamacher operation. Firstly, according to Hamacher operation, some operational laws of NIFNs are presented. Secondly, it is noted that Heronian mean not only takes into account mutuality between the attribute values once, but also considers the correlation between input argument and itself. Therefore, in order to aggregate NIFN information, we developed some operators and studied their properties. These operators include Hamacher Heronian mean (NIFHHM), Hamacher weighted Heronian mean (NIFHWHM), Hamacher geometric Heronian mean (NIFHGHM), and Hamacher weighted geometric Heronian mean (NIFHWGHM). Furthermore, we applied the proposed operators to the MCGDM problem and developed a new MCGDM approach. The characteristics of this new approach are that: (1) it is suitable for making a decision under the NIFN environment and it is more reasonable for aggregating the normal distribution data; (2) it utilizes Hamacher operation to provide an effective and powerful MCGDM algorithm and to make more reliable and more flexible decisions under the NIFN circumstance; (3) it uses the Heronian mean operator to deal with interrelations between the attributes or input arguments, and it does not bring about repeated calculation. Therefore, the proposed method can describe the interaction of the different criteria or input arguments and offer some reasonable and reliable MCGDM aggregation operators, which can open avenues for decision making and broaden perspectives of the decision experts. Lastly, an application is given for showing the effectiveness and feasibility of the approach presented in this paper.

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“…In FS theory, t-conorm (T * ) and t-norm (T) are very important to the generalization of intersection or union of fuzzy sets [34,42,46,[55][56][57][58][59][60][61].…”

Section: Hamacher T-norm and Hamacher T-conormmentioning

confidence: 99%

Some Normal Intuitionistic Fuzzy Heronian Mean Operators Using Hamacher Operation and Their Application

Zhang

Kong

2018

Symmetry

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“…Zhao et al [ 14 ] found that the Hölder inequality for the pan-integral holds if the monotone measurer is subadditive. Tian [ 15 – 18 ] gave some new properties and refinements of the Hölder and reverse Hölder inequalities. For more detail, the reader may consult [ 19 – 25 ].…”

Section: Introductionmentioning

confidence: 99%

Triple Diamond-Alpha integral and Hölder-type inequalities

Tian

2018

J Inequal Appl

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In this paper, we first introduce the definition of triple Diamond-Alpha integral for functions of three variables. Therefore, we present the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral on time scales, and then we obtain some new generalizations of the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral. Moreover, using the obtained results, we give a new generalization of the Minkowski inequality for the triple Diamond-Alpha integral on time scales.

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“…Steele et al [5] employed the Hölder inequality to place lower bounds on the sum of and 1.0 running masses. Tian et al [6][7][8][9][10][11][12][13] gave some new properties, generalizations, refinements, and applications of Hölder's inequalities. Wu [14,15] presented some new sharpened and generalized versions of Hölder's inequalities in classical real analysis.…”

Section: Introductionmentioning

confidence: 99%