A New Ordered Weighted Averaging Operator to Obtain the Associated Weights Based on the Principle of Least Mean Square Errors

Bai, Chengzu; Zhang, Ren; Song, Chenyang; Wu, Yaning

doi:10.1002/int.21838

Cited by 8 publications

(8 citation statements)

References 24 publications

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“…, the computational complexities of their proposed approach are higher. Therefore, applying the aggregation operators on IVPLTSs and the possibility degree formula , we propose an efficient ranking method of the alternatives as follows: If an importance weighting vector,

w = {(w_{1}, w_{2}, \dots . w_{n})}^{T}

with

w_{j} \geq 0

and

0true \sum_{j = 1}^{n} w_{j} = 1

, of criteria is known, then we use the IVPLWA operator to aggregate IVPLTSs of alternatives

x_{i} false(i = 1, 2, \dots, m false)

.If the importance weights of criteria are unknown, the weighting vector

w = {(w_{1}, w_{2}, \dots . w_{n})}^{T}

can be determined by the proposed techniques of the OWA operator . Then the overall aggregation values

{\tilde{L}}_{i}

can be derived using IVPLWA operator.…”

Section: Mcgdm With Interval‐valued Probabilistic Linguistic Term Setsmentioning

confidence: 99%

“…If the importance weights of criteria are unknown, the weighting vector

w = {(w_{1}, w_{2}, \dots . w_{n})}^{T}

can be determined by the proposed techniques of the OWA operator . Then the overall aggregation values

{\tilde{L}}_{i}

can be derived using IVPLWA operator.…”

Section: Mcgdm With Interval‐valued Probabilistic Linguistic Term Setsmentioning

confidence: 99%

“…can be determined by the proposed techniques of the OWA operator. 20,32,33 Then the overall aggregation values̃can be derived using IVPLWA operator. In addition, if the initial information represents some rates, then IVPLWG operator can be used.…”

Section: Mcgdm With Interval-valued Probabilistic Linguistic Term Setsmentioning

confidence: 99%

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Interval-valued probabilistic linguistic term sets in multi-criteria group decision making

Bai

Ren

Shen

et al. 2018

Int. J. Intell. Syst.

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The theory of probabilistic linguistic term sets (PLTSs) is very useful in objectively dealing with the multi‐criteria group decision making (MCGDM) problems in which there is hesitancy in providing linguistic assessments; and PLTSs allow experts to express their preferences on one linguistic term over another. In order to reflect the uncertainty and inconsistency of decision‐makers and handle incomplete linguistic information, we propose a new PLTS called interval‐valued probabilistic linguistic term set (IVPLTS). In addition, the existing approaches associated with PLTSs are limited or highly complex in real applications. Therefore, new operations, comparison laws, and aggregation operators are developed for IVPLTS. Furthermore, we establish an efficient framework for MCGDM problems based on the proposed comparison method and the fuzzy preference relation. Then we apply it to a real‐life case under linguistic environment. The extended TOPSIS methods combined with PLTSs by using different operational laws are also included for comparison. The final results demonstrate the efficiency and practicality of the new framework.

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w = {(w_{1}, w_{2}, \dots . w_{n})}^{T}

with

w_{j} \geq 0

and

0true \sum_{j = 1}^{n} w_{j} = 1

, of criteria is known, then we use the IVPLWA operator to aggregate IVPLTSs of alternatives

x_{i} false(i = 1, 2, \dots, m false)

.If the importance weights of criteria are unknown, the weighting vector

w = {(w_{1}, w_{2}, \dots . w_{n})}^{T}

can be determined by the proposed techniques of the OWA operator . Then the overall aggregation values

{\tilde{L}}_{i}

can be derived using IVPLWA operator.…”

Section: Mcgdm With Interval‐valued Probabilistic Linguistic Term Setsmentioning

confidence: 99%

“…If the importance weights of criteria are unknown, the weighting vector

w = {(w_{1}, w_{2}, \dots . w_{n})}^{T}

can be determined by the proposed techniques of the OWA operator . Then the overall aggregation values

{\tilde{L}}_{i}

can be derived using IVPLWA operator.…”

Section: Mcgdm With Interval‐valued Probabilistic Linguistic Term Setsmentioning

confidence: 99%

See 1 more Smart Citation

Interval-valued probabilistic linguistic term sets in multi-criteria group decision making

Bai

Ren

Shen

et al. 2018

Int. J. Intell. Syst.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Two of the most popular particular cases of Choquet integral are the weighted means and the OWA operators. 1 19 Liu, 20 Wang, 21 and Bai 22 ).…”

Section: B a ⊆mentioning

confidence: 99%

“…It is worth noting that the choice of the weight distribution has generated a large literature (in the case of OWA operators, see, for instance, Llamazares, Liu, Wang, and Bai).…”

mentioning

confidence: 99%

SUOWA operators: A review of the state of the art

Llamazares

2018

Int J Intell Syst

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SUOWA operators are a particular case of Choquet integral that simultaneously generalize weighted means and OWA operators. Because they are constructed by using normalized capacities, they possess properties such as continuity, monotonicity, idempotency, compensativeness, and homogeneity of degree 1. Besides these ones, some articles published in recent years have shown that SUOWA operators also exhibit other interesting properties. So, we think that the time has come to summarize existing knowledge of these operators. The aim of this paper is to collect the main results obtained so far on SUOWA operators. Moreover, we also introduce some new results and illustrate the usefulness of SUOWA operators by using an example given by Beliakov (2018).

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Construction of Choquet integrals through unimodal weighting vectors

Llamazares

2018

Int. J. Intell. Syst.

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Semiuninorm-based ordered weighted averaging (SUOWA) operators are a specific case of Choquet integrals that allow us to generalize simultaneously weighted means and ordered weighting averaging (OWA) operators. Although SUOWA operators possess some very interesting properties, their main weakness is that, sometimes, the game used in their construction is not monotonic and it is necessary to calculate its monotonic cover. In this paper, we introduce a new family of weighting vectors, called unimodal weighting vectors, which embrace some of the most outstanding weighting vectors used in the framework of OWA operators, and we show that when using these weighting vectors and a specific semiuninorm we directly get normalized capacities. Moreover, we also show that these operators satisfy some properties which are very useful in practice.Int J Intell Syst. 2018;33:771-790. wileyonlinelibrary.com/journal/int

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A New Ordered Weighted Averaging Operator to Obtain the Associated Weights Based on the Principle of Least Mean Square Errors

Cited by 8 publications

References 24 publications

Interval-valued probabilistic linguistic term sets in multi-criteria group decision making

Interval-valued probabilistic linguistic term sets in multi-criteria group decision making

SUOWA operators: A review of the state of the art

Construction of Choquet integrals through unimodal weighting vectors

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