Some Induced Aggregating Operators with Fuzzy Number Intuitionistic Fuzzy Information and their Applications to Group Decision Making

Wei, Guiwi; Zhao, Xiaofei; Lin, Rui

doi:10.2991/ijcis.2010.3.1.8

Cited by 23 publications

(6 citation statements)

References 17 publications

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“…Based on equations (7) and (8), ranking laws between two TrNZNs are given by the following definition.…”

Section: ((I V11 I V21 I V12 I V22 I V13 I V23 I V14 I V24 ) (mentioning

confidence: 99%

“…en, triangular and trapezoidal fuzzy numbers are usually used for real decision-making problems because they can be depicted by the continuous fuzzy numbers of membership functions rather than exact/discrete fuzzy values. Hence, some researchers extended triangular fuzzy numbers to intuitionistic fuzzy sets (IFSs) and presented triangular intuitionistic fuzzy sets (TIFSs), where the values of the membership and nonmembership functions are triangular fuzzy numbers, and some triangular intuitionistic fuzzy aggregation operators for multicriteria decision-making (MDM) problems with triangular intuitionistic fuzzy information [4][5][6][7]. As the extension of TIFSs, Ye [8] introduced a trapezoidal intuitionistic fuzzy set (TrIFS), in which the values of its membership and nonmembership functions are trapezoidal fuzzy numbers rather than triangular fuzzy numbers, and some prioritized weighted aggregation operators of trapezoidal intuitionistic fuzzy numbers (TrIFNs) for MDM problems with TrIFNs.…”

Section: Introductionmentioning

confidence: 99%

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Multicriteria Decision-Making Method and Application in the Setting of Trapezoidal Neutrosophic Z-Numbers

Rui

2021

Journal of Mathematics

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The information expression and modeling of decision-making are critical problems in the fuzzy decision theory and method. However, existing trapezoidal neutrosophic numbers (TrNNs) and neutrosophic Z-numbers (NZNs) and their multicriteria decision-making (MDM) methods reveal their insufficiencies, such as without considering the reliability measures in TrNN and continuous Z-numbers in NZN. To overcome the insufficiencies, it is necessary that one needs to propose trapezoidal neutrosophic Z-numbers (TrNZNs), their aggregation operations, and an MDM method for solving MDM problems with TrNZN information. Hence, this study first proposes a TrNZN set, some basic operations of TrNZNs, and the score and accuracy functions of TrNZN and their ranking laws. Then, the TrNZN weighted arithmetic averaging (TrNZNWAA) and TrNZN weighted geometric averaging (TrNZNWGA) operators are presented based on the operations of TrNZNs. Next, an MDM approach using the proposed aggregation operators and score and accuracy functions is established to carry out MDM problems under the environment of TrNZNs. In the end, the established MDM approach is applied to an MDM example of software selection for revealing its rationality and efficiency in the setting of TrNZNs. The main advantage of this study is that the established approach not only makes assessment information continuous and reliable but also strengthens the decision rationality and efficiency in the setting of TrNZNs.

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“…Based on equations (7) and (8), ranking laws between two TrNZNs are given by the following definition.…”

Section: ((I V11 I V21 I V12 I V22 I V13 I V23 I V14 I V24 ) (mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multicriteria Decision-Making Method and Application in the Setting of Trapezoidal Neutrosophic Z-Numbers

Rui

2021

Journal of Mathematics

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“…Note that many other group decision-making models have been discussed in the literature (Merigó, Casanovas 2011b;Wei et al 2010;Xu 2010;Zhou, Chen 2011). However, in this paper we focus on a multi-person decision-making problem under risk and uncertainty "ex-ante".…”

Section: Multi-person Decision-making Processmentioning

confidence: 99%

Decision-Making Under Risk and Uncertainty and Its Application in Strategic Management

Merigó

2014

Journal of Business Economics and Management

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We introduce a new decision-making model that unifies risk and uncertain environments in the same formulation. For doing so, we present the induced probabilistic ordered weighted averaging (IPOWA) operator. It is an aggregation operator that unifies the probability with the OWA operator in the same formulation and considering the degree of importance of each concept in the aggregation. Moreover, it also uses induced aggregation operators that provide a more general representation of the attitudinal character of the decision-maker. We study its applicability and we see that it is very broad because all the previous studies that use the probability or the OWA operator can be revised and extended with this new approach. We briefly analyze some basic applications in statistics such as the implementation of this approach with the variance, the covariance, the Pearson coefficient and in a simple linear regression model. We focus on a multi-person decision-making problem in strategic management. Thus, we are able to construct a new aggregation operator that we call the multi-person IPOWA operator. Its main advantage is that it can deal with the opinion of several persons in the analysis so we can represent the information in a more complete way.

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“…Merigó and Gil-Lafuente (2009) extended the previous approaches by using induced aggregation operators. Other extensions have considered problems with imprecise information in the analysis by using interval numbers (Merigó, Casanovas 2011a, b), fuzzy numbers (Liu 2011;Wei et al 2010;Zhao et al 2010) and linguistic variables (Wei 2011). Other developments have considered the use of distance measures in the aggregation process (Merigó, Gil-Lafuente 2010;Zeng, Su 2011).…”

Section: Introductionmentioning

confidence: 99%

Decision Making With Dempster-Shafer Belief Structure and the Owawa Operator

Merigó

Engemann

Palacios‐Marqués

2014

Technological and Economic Development of Economy

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A new decision making model that uses the weighted average and the ordered weighted averaging (OWA) operator in the Dempster-Shafer belief structure is presented. Thus, we are able to represent the decision making problem considering objective and subjective information and the attitudinal character of the decision maker. For doing so, we use the ordered weighted averaging – weighted average (OWAWA) operator. It is an aggregation operator that unifies the weighted average and the OWA in the same formulation. This approach is generalized by using quasi-arithmetic means and group decision making techniques. An application of the new approach in a group decision making problem concerning political management of a country is also developed.

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Some Induced Aggregating Operators with Fuzzy Number Intuitionistic Fuzzy Information and their Applications to Group Decision Making

Cited by 23 publications

References 17 publications

Multicriteria Decision-Making Method and Application in the Setting of Trapezoidal Neutrosophic Z-Numbers

Multicriteria Decision-Making Method and Application in the Setting of Trapezoidal Neutrosophic Z-Numbers

Decision-Making Under Risk and Uncertainty and Its Application in Strategic Management

Decision Making With Dempster-Shafer Belief Structure and the Owawa Operator

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