Prioritized Aggregation Operators and Correlated Aggregation Operators for Hesitant 2-Tuple Linguistic Variables

Lidong Wang,Xiaodong Liu,Yanjun Wang

doi:10.3390/sym10020039

Lidong Wang, Xiaodong Liu + Show 1 more

Open Access

https://doi.org/10.3390/sym10020039

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Abstract

The aggregation operator is a potential tool to fuse the information derived from multisources, which has been applied in group decision, combination classification and scheduling clusters successfully. To better characterize complex decision situations and capture complex opinions of decision-makers (DMs), aggregation operators are required to be explored from different viewpoints. In view of information fusion of hesitant 2-tuple linguistic variables, this paper establishes four new aggregation operators, which are called the hesitant 2-tuple linguistic prioritized weighted averaging (H2TLPWA) aggregation operator, hesitant 2-tuple linguistic prioritized weighted geometric (H2TLPWG) aggregation operator, hesitant 2-tuple linguistic correlated averaging (H2TLCA) aggregation operator, and hesitant 2-tuple linguistic correlated geometric (H2TLCG) aggregation operator, respectively. The H2TLPWA aggregation operator and H2TLPWG aggregation operator can characterize the prioritization relationship of the aggregated arguments. The H2TLCA aggregation operator and H2TLCG aggregation operator can describe dependencies between criteria in decision-making problem solving. Moreover all aggregation operation operators have the properties of idempotency, boundedness and monotonicity, and the H2TLCA aggregation operator and H2TLCG aggregation operator are also verified to be symmetric functions. In addition, the H2TLPWA aggregation operator and H2TLCA aggregation operator are employed to settle multicriteria decision-making problems with hesitant 2-tuple linguistic terms. By virtue of predefining discrete initial linguistic labels with symmetrical distribution, the detailed steps of the decision-making process with an example are given to illustrate their practicality and effectiveness.

Highlights

Decision-making is a cognitive process to identify the desirable choice among several alternatives.Everyone makes decisions in his/her daily life, such as choosing a suitable car, recruiting excellent staff, choosing a tourist site for enjoying a summer holiday, and so on
We propose the hesitant 2-tuple linguistic prioritized weighted averaging (H2TLPWA) aggregation operator, the hesitant 2-tuple linguistic prioritized weighted geometric (H2TLPWG) aggregation operator, the hesitant 2-tuple linguistic correlated averaging (H2TLCA) aggregation operator and the hesitant 2-tuple linguistic correlated geometric (H2TLCG) aggregation operator
On the basis of the prioritized averaging (PA) operator, we present the H2TLPWA aggregation operator and H2TLPWG

Summary

Introduction

Decision-making is a cognitive process to identify the desirable choice among several alternatives. The decision table involves a mixture of quantitative and qualitative uncertain terms; fuzzy sets and probability theory are widely employed to deal with both the subjective imprecision of human perception-based information described in natural language and the objective uncertainty of randomness universally existing in the real world It is the most common situation for experts to reflect their information preferences with a linguistic term, which is introduced to simulate the human decision process on the basis of the expression of cognitive information [2,3,4,5]. Xue proposed an integrated model and extended the QUALIFLEX (qualitative flexible multiple criteria method) approach to handle robot selection problems on the basis of the hesitant 2-tuple linguistic term sets [46].

Preliminaries

New Hesitant 2-Tuple Linguistic Aggregation Operators

Hesitant 2-Tuple Linguistic Prioritized Weighted Aggregation Operator

Hesitant 2-Tuple Linguistic Correlated Aggregation Operator

An Illustrative Example

Conclusions