Hamacher Interactive Hybrid Weighted Averaging Operators under Fermatean Fuzzy Numbers

The decision-making activities of major public affairs are closely related to the public, so the decision results of such affairs must be supported by the public. The public must participate in decision-making activities to ensure their effectiveness, which further increases the complexity. In addition, attribute information and public opinion usually present different forms of expression in this type of problem, making decision-making more difficult. Therefore, a suitable decision approach must be chosen to deal with this type of decision problem. This paper addresses the decision-making characteristics of major public affairs and proposes a public-participation-based decision-making approach for mixed multiattribute decision-making problems in major public affairs. The proposed approach can work with entirely unknown attribute weights and decision-making values represented in multiple formats. First, the statistical distribution of public opinions is determined based on the expectation of the attributes, resulting in decision-making reference points for various attributes. The different forms of attributes and reference points are unified. Then, the values of the attributes and reference points are standardized. Afterward, the attribute prospect value for each alternative is calculated using the attribute value and corresponding reference points. The attribute weight intervals are determined based on the importance information of the attributes provided by the public. An optimization model is established to determine the attribute weights to maximize the alternative attribute deviation. Next, the comprehensive prospect value of each alternative is obtained to determine the ranking of the alternatives. Finally, a case analysis is conducted with a method comparison and sensitivity analysis, and the feasibility and effectiveness of the proposed approach are verified. In the proposed method, the reference points for each attribute are set according to the distribution characteristics and ambiguity of public expectations, guaranteeing that public expectations can be effectively reflected in the attribute reference points. In the process of attribute weighting, based on the information for the attribute importance given by the public, the range of attribute weights is determined. Then, we obtain the exact value of the attribute weights using an optimization model to maximize the alternative attribute deviation. The final result of the attribute weights ensures the full expression of public opinion and can improve the differentiation of decision results, which is convenient for ranking alternatives. During evaluation of the alternatives based on prospect theory, the expression forms of attributes and reference points are unified. Subsequently, the values of them are normalized, which satisfy the decision-making requirement of major public affairs.

Section: Introductionmentioning

confidence: 99%

A Public-Participation-Based Mixed Multiattribute Decision-Making Approach for Major Public Affairs

Cai

Luo

Zhu

et al. 2021

“…Recently, Aydemir and Gunduz [29] explained the Fermatean fuzzy TOPSIS (FF-TOPSIS) method consisting of Dombi AOs. Shahzadi et al [30] introduced the idea of Hamacher interactive hybrid weighted averaging operators under FFE. Feng et al [31] investigated membership grades of q− rung orthopair fuzzy sets geometrically.…”

Section: Introductionmentioning

confidence: 99%

Multiple-Attribute Decision-Making Using Fermatean Fuzzy Hamacher Interactive Geometric Operators

Shahzadi

Zafar

Alghamdi

2021

Self Cite

Fermatean fuzzy set (FFS) is a more efficient, flexible, and generalized model to deal with uncertainty, as compared to intuitionistic and Pythagorean fuzzy models. This research article presents a novel multiple-attribute decision-making (MADM) technique based on FFS. Aggregation operators (AOs), for example, Dombi, Einstein, and Hamacher, are frequently being used in the MADM process and are considered useful tools for evaluating the given alternatives. Among these, one of the most effective is the Hamacher operator. The salient feature of this operator is that it reduces the impact of negative information and provides more accurate results. Motivated by the primary characteristics of the Hamacher operator, we apply Hamacher interactive aggregation operators based on FFSs to determine the best alternative. Using Hamacher’s norm operations, we introduce some new geometric operators, namely, Fermatean fuzzy Hamacher interactive weighted geometric (FFHIWG) operator, Fermatean fuzzy Hamacher interactive ordered weighted geometric (FFHIOWG) operator, and Fermatean fuzzy Hamacher interactive hybrid weighted geometric (FFHIHWG) operator. Some important results and properties of the proposed AOs are discussed, and to achieve the optimal alternative, the proposed MADM technique is carried out in a real-life application of the medical field. An algorithm of the proposed technique is also developed. The significance of the proposed method is that Fermatean fuzzy Hamacher interactive geometric (FFHIG) operators deal with the relationship among belongingness degree (BD) and nonbelongingness degree (NBD) of the objects, which perform a crucial role in decision-making (DM). At last, to show the exactness and validity of the proposed work, a comparative analysis of the proposed model and the existing models is presented.

“…In addition, Akram et al [26] launched a novel hybrid model called m-polar fuzzy SESs and solved certain MAGDM problems. For more important terminologies, the readers are referred to [27][28][29][30][31][32][33][34][35][36][37][38][39]. e motivations of this research article are described as follows:…”

Section: Introductionmentioning

confidence: 99%

Ranking Effectiveness of COVID-19 Tests Using Fuzzy Bipolar Soft Expert Sets

Ali

Muhiuddin

Adeel

et al. 2021

Self Cite

The theory of fuzzy bipolar soft sets is an efficient extension of soft sets for depicting the bipolarity of uncertain fuzzy soft information; however, it is limited to a single expert. The present research article introduces the theory of an innovative hybrid model called the fuzzy bipolar soft expert sets, as a natural extension of two existing models (including fuzzy soft expert sets and fuzzy bipolar soft sets). The proposed model is highly suitable for describing the bipolarity of fuzzy soft information having multiple expert opinions. Some fundamental properties of the developed hybrid model are discussed, including subset, complement, union, intersection, AND operation, and OR operation. The proposed concepts are explained with detailed examples. Moreover, to demonstrate the applicability of our initiated model, an application of the proposed hybrid model is presented along with the developed algorithm to tackle the real-world group decision-making situation, that is, ranking effectiveness of tests in spread analysis of COVID-19. Finally, a comparative analysis of the developed model with some existing mathematical tools such as fuzzy soft expert sets and fuzzy bipolar soft sets is provided to show the cogency and reliability of the initiated model.