Geometric Heronian Mean Operator Research Articles

A new three-way group decision-making model based on geometric heronian mean operators with q-rung orthopair uncertain linguistic information

As an effective tool for three-way decisions (3WD) problems, decision-theoretic rough sets (DTRSs) have raised increasing attention recently. In view of the advantages of q-rung orthopair uncertain linguistic variables (q-ROULVs) in depicting uncertain information, a new DTRSs model based on q-ROULVs is proposed to solve three-way group decision-making (3WGDM) problems. Firstly, the loss function of DTRSs is depicted by q-ROULVs and a q-rung orthopair uncertain linguistic DTRSs model is constructed subsequently. Secondly, to aggregate different experts’ evaluation results on loss function in group decision-making (GDM) scenario, the q-rung orthopair uncertain linguistic geometric Heronian mean (q-ROULGHM) operator and the q-rung orthopair uncertain linguistic weighted geometric Heronian mean (q-ROULWGHM) operator are presented. Related properties of the proposed operators are investigated. Thirdly, to compare the expected loss of each alternative, a new score function of q-ROULVs is defined and the corresponding decision rules for 3WGDM are deduced. Finally, an illustrative example of venture capital in high-tech projects is provided to verify the rationality and effectiveness of our method. The influence of different conditional probabilities and parameter values on decision results is comprehensively discussed.

A method to multi-attribute decision making problems by using heronian mean operators based on linear diophantine uncertain linguistic settings

In the real decision process, an important problem is how to express the attribute value more efficiently and accurately. In the real world, because of the complexity of decision-making problems and the fuzziness of decision-making environments, it is not enough to express attribute values of alternatives by exact values. For this managing with such sorts of issues, the principle of Linear Diophantine uncertain linguistic set is a valuable and capable technique to manage awkward and inconsistent information in everyday life problems. In this manuscript, we propose the original idea of Linear Diophantine uncertain linguistic set and elaborated their essential laws. Additionally, to determine the association among any numbers of attributes, we elaborated the Linear Diophantine uncertain linguistic arithmetic Heronian mean operator, Linear Diophantine uncertain linguistic weighted arithmetic Heronian mean operator, Linear Diophantine uncertain linguistic geometric Heronian mean operator, Linear Diophantine uncertain linguistic weighted geometric Heronian mean operator, and their properties are also discovered. By using these operators, we utilize the multi-attribute decision-making procedure by using elaborated operators. To determine the consistency and validity of the elaborated operators, we illustrate some examples by using explored operators. Finally, the superiority and comparative analysis of the elaborated operators with some existing operators are also determined and justified with the help of a graphical point of view.

Archimedean geometric Heronian mean aggregation operators based on dual hesitant fuzzy set and their application to multiple attribute decision making

Fuzzy set, intuitionistic fuzzy set, hesitant fuzzy set can be regarded as a special case of dual hesitant fuzzy set. Therefore, dual hesitant fuzzy set is a more comprehensive set. Further, Archimedean t-norm and t-conorm provides generalized operational rules for dual hesitant fuzzy set. And geometric Heronian mean have advantages when considering the interrelationship of aggregation arguments. Thus, it is necessary to extend the geometric Heronian mean operator to the dual hesitant fuzzy environment based on Archimedean t-norm and t-conorm. Comprehensive above, in this paper, the dual hesitant fuzzy geometric Heronian mean operator and dual hesitant fuzzy geometric weighted Heronian mean operator based on Archimedean t-norm and t-conorm are developed. Their properties and special case are investigated. Moreover, a multiple attribute decision making method is proposed. The effectiveness of our method and the influence of parameters on multiple attribute decision making are studied by an example. The superiority of our method is illustrated by comparing with other existing methods.

An Approach to Linguistic Multiple Attribute Decision-Making Based on Unbalanced Linguistic Generalized Heronian Mean Aggregation Operator.

This paper proposes an approach to linguistic multiple attribute decision-making problems with interactive unbalanced linguistic assessment information by unbalanced linguistic generalized Heronian mean aggregation operators. First, some generalized Heronian mean aggregation operators with unbalanced linguistic information are proposed, involving the unbalanced linguistic generalized arithmetic Heronian mean operator and the unbalanced linguistic generalized geometric Heronian mean operator. For the situation that the input arguments have different degrees of importance, the unbalanced linguistic generalized weighted arithmetic Heronian mean operator and the unbalanced linguistic generalized weighted geometric Heronian mean operator are developed. Then we investigate their properties and some particular cases. Finally, the effectiveness and universality of the developed approach are illustrated by a low-carbon tourist instance and comparison analysis. A sensitivity analysis is performed as well to test the robustness of proposed methods.

Dual hesitant fuzzy group decision making method and its application to supplier selection

The concept of dual hesitant fuzzy set arising from hesitant fuzzy set is generalized by including a function reflecting the decision maker’s fuzziness about the non-membership degree of the information provided. This paper studies some dual hesitant fuzzy information aggregation operators for aggregating dual hesitant fuzzy elements, such as dual hesitant fuzzy Heronian mean operator and dual hesitant fuzzy geometric Heronian mean operator. The research resulting dual hesitant fuzzy information aggregation operators finds an important role in group decision making (GDM) applications. It can fusion the experts’ opinion to the comprehensive ones and based on which an optimal decision making scheme can be determined. The properties of the proposed operators are studied and the application on GDM are investigated. The effectiveness of the GDM method is demonstrated on the case study about supplier selection.

Some two-dimensional uncertain linguistic Heronian mean operators and their application in multiple-attribute decision making

Heronian mean (HM) is an important aggregation operator which has the characteristic of capturing the correlations of the aggregated arguments. In this paper, we first analyze the shortcomings of the existing weighted HM operators which do not feature reducibility and idempotency, and then, we propose the new weighted generalized Heronian mean operator and weighted generalized geometric Heronian mean operator, and prove that they can satisfy some desirable properties, such as reducibility, idempotency, monotonicity, and boundedness, and discuss some special cases of these operators. Further, because two-dimensional uncertain linguistic information can easily express the fuzzy information, we propose two-dimensional uncertain linguistic weighted generalized Heronian mean (2DULWGHM) operator and the two-dimensional uncertain linguistic weighted generalized geometric Heronian mean (2DULWGGHM) operator, and some desirable properties and special cases of 2DULWGHM and 2DULWGGHM operators are discussed. Moreover, for multiple-attribute decision-making problems in which attribute values take the form of two-dimensional uncertain linguistic variables, some approaches based on the developed operators are proposed. Finally, we gave an illustrative example to explain the steps of the developed methods and to discuss the influence of different parameters on the decision-making results.