Search Results (23)

The complexity of large-scale group decision-making (LSGDM) in the digital society is becoming increasingly prominent. How to achieve efficient consensus through social networks (SNs) has become a core challenge in improving the decision quality. First, conventional clustering methods often rely on a single-distance metric, neglecting both numerical assessments and preference rankings. Second, ensuring the decision authenticity requires considering diverse behaviors, such as trust propagations, risk preferences, and minority opinion expressions, for scientific decision-making in SNs. To address these challenges, a consensus-reaching process (CRP) method based on an enhanced K-means++ clustering is proposed. The above method not only focuses on minority opinion handling (MOH), but also incorporates decision indicator sets (DISs) to analyze the degree of opinion divergences within groups. First, the Hamacher aggregation operator with a decay factor completes trust matrices, improving the trust representation. Second, a personalized distance metric that combines cardinal distances with ordinal distances is incorporated into the enhanced K-means++ clustering, enabling more precise clustering. Third, weights for decision-makers (DMs) and subgroups are determined based on trust levels and degree centrality indices. Fourth, minority opinions are appropriately handled via considering the diverse backgrounds and expertise of DMs, leveraging a difference-oriented DIS to detect and adjust these opinions via weight modifications until a consensus is reached. Fifth, the alternative ranking is objectively generated via DIS scores derived from multigranulation rough approximations. Finally, the feasibility of the proposed method is validated via a case study on unmanned aerial vehicle (UAV) selection using online reviews, supported by a sensitivity analysis and comparative experiments demonstrating superior performances over existing methods. The result shows that the proposed model can enhance clustering accuracies with hybrid distances, objectively measure the consensus via DISs, handle minority opinions effectively, and improve LSGDM’s overall efficiencies. Full article

The symmetrical linear Diophantine fuzzy Hamacher aggregation operators play a fundamental role in many decision-making applications. The selection of a cyber security system is of paramount importance for maintaining digital assets. It necessitates a comprehensive review of threat landscapes, vulnerability assessments, and the specific needs of the organization in order to ensure the implementation of effective security measures. Smart grid (SG) technology uses modern communication and monitoring technologies to enhance the management and regulation of electricity production and transmission. However, greater dependence on technology and connection creates new vulnerabilities, exposing SG communication networks to large-scale attacks. Unlike previous surveys, which often give broad overviews of SG design, our research goes a step further, giving a full architectural layout that includes major SG components and communication linkages. This in-depth review improves comprehension of possible cyber threats and allows SGs to analyze cyber risks more systematically. To determine the best cybersecurity strategies, this study introduces a multi-criteria group decision-making (MCGDM) approach using the linear Diophantine fuzzy Hamacher prioritized aggregation operator (LDFHPAO). In real-world applications, aggregation operators (AOs) are essential for information fusion. This research presents innovative prioritized AOs designed to address MCGDM problems in uncertain environments. We developed the LDF Hamacher prioritized weighted average (LDFHPWA) and LDF Hamacher prioritized weighted geometric (LDFHPWG) operators, which address the shortcomings of traditional operators and provide a more robust modeling approach for MCGDM challenges. This study also outlines key characteristics of these new prioritized AOs. An MCGDM approach incorporating these operators is proposed and demonstrated to be effective through an example that compares and selects the optimal cybersecurity. Full article

In this paper, based on the advantages of q-rung orthopair fuzzy sets (q-ROFSs), complex fuzzy sets (CFSs) and cubic sets (CSs), the concept of complex cubic q-rung orthopair fuzzy sets (CCuq-ROFSs) is introduced and their operation rules and properties are discussed. The objective of this paper was to develop some novel Maclaurin symmetric mean (MSM) operators for any complex cubic q-rung orthopair fuzzy numbers (CCuq-ROFNs) using Hamacher t-norm and t-conorm inspired arithmetic operations. The advantage of employing Hamacher t-norm and t-conorm based arithmetic operations with the MSM operator lies in their ability to take into account not only the interrelationships among multiple attributes but also to provide flexibility in the aggregation process due to the involvement of additional parameters. Also, the prominent characteristic of the MSM is that it can capture the interrelationship among the multi-input arguments and can provide more flexible and robust information fusion. Thus, based on the CCuq-ROF environment, we develop some new Hamacher operations for CCuq-ROFSs, such as the complex cubic q-rung orthopair fuzzy Hamacher average (CCuq-ROFHA) operator, the weighted complex cubic q-rung orthopair fuzzy Hamacher average (WCCuq-ROFHA) operator, the complex cubic q-rung orthopair fuzzy Hamacher Maclaurin symmetric mean (CCuq-ROFHMSM) operator and the weighted complex cubic q-rung orthopair fuzzy Hamacher Maclaurin symmetric mean (WCCuq-ROFHMSM) operator. Further, we develop a novel multi-attribute group decision-making (MAGDM) approach based on the proposed operators in a complex cubic q-rung orthopair fuzzy environment. Finally, a numerical example is provided to demonstrate the effectiveness and superiority of the proposed method through a detailed comparison with existing methods. Full article

It is difficult to describe the hesitation and uncertainty of experts by single-valued information, and the differences in the importance of attributes are often ignored during the decision-making process. This paper introduces the probability and interval values into Fermatean hesitant fuzzy set (FHFS) and creatively proposes the probabilistic interval-valued Fermatean hesitant fuzzy set (PIVFHFS) to deal with information loss. This new fuzzy set allows decision makers to use interval-valued information with probability to express their quantitative evaluation, which broadens the range of information expression, effectively reflects the important degree of different membership degrees, and can describe uncertain information more completely and accurately. Under the probabilistic interval-valued Fermatean hesitant fuzzy environment, several new aggregation operators based on Hamacher operation are proposed, including the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher weighted averaging (PIVFHFHWA) operator and geometric (PIVFHFHWG) operator, and their basic properties and particular forms are studied. Then, considering the general correlation between different attributes, this paper defines the probabilistic interval-valued Fermatean hesitant fuzzy Hamacher Choquet integral averaging (PIVFHFHCIA) operator and geometric (PIVFHFHCIG) operator and discusses related properties. Finally, a multi-attribute decision-making (MADM) method is presented and applied to the decision-making problem of reducing carbon emissions of manufacturers in the supply chain. The stability and feasibility of this method are demonstrated by sensitivity analysis and comparative analysis. The proposed new operators can not only consider the correlation between various factors but also express the preference information of decision makers more effectively by using probability, thus avoiding information loss in decision-making progress to some extent. Full article

The q-rung orthopair fuzzy (q-ROF) set is an efficient tool for dealing with uncertain and inaccurate data in real-world multi-attribute decision-making (MADM). In MADM, aggregation operators play a significant role. The majority of well-known aggregation operators are formed using algebraic, Einstein, Hamacher, Frank, and Yager t-conorms and t-norms. These existing t-conorms and t-norms are some special cases of Archimedean t-conorms (ATCNs) and Archimedean t-norms (ATNs). Therefore, this article aims to extend the ATCN and ATN operations under the q-ROF environment. In this paper, firstly, we present some new operations for q-ROF sets based on ATCN and ATN. After that, we explore a few desirable characteristics of the suggested operational laws. Then, using these operational laws, we develop q-ROF Archimedean weighted averaging (geometric) operators, q-ROF Archimedean order weighted averaging (geometric) operators, and q-ROF Archimedean hybrid averaging (geometric) operators. Next, we develop a model based on the proposed aggregation operators to handle MADM issues. Finally, we elaborate on a numerical problem about site selection for software operating units to highlight the adaptability and dependability of the developed model. Full article

The collection of Hamacher t-norms was created by Hamacher in 1970, which played a critical and significant role in computing aggregation operators. All aggregation operators that are derived based on Hamacher norms are very powerful and are beneficial because of the parameter $0\le \zeta \le +\infty$. Choquet first posited the theory of the Choquet integral (CI) in 1953, which is used for evaluating awkward and unreliable information to address real-life problems. In this manuscript, we analyze several aggregation operators based on CI, aggregation operators, the Hamacher t-norm and t-conorm, and Atanassov intuitionistic fuzzy (A-IF) information. These are called A-IF Hamacher CI averaging (A-IFHCIA), A-IF Hamacher CI ordered averaging (A-IFHCIOA), A-IF Hamacher CI geometric (A-IFHCIG), and A-IF Hamacher CI ordered geometric (A-IFHCIOG) operators; herein, we identify their most beneficial and valuable results according to their main properties. Working continuously, we developed a multi-attribute decision-making (MADM) procedure for evaluating awkward and unreliable information, with the help of the TOPSIS technique for order performance by similarity to the ideal solution, and derive operators to enhance the worth and value of the present information. Finally, by comparing the pioneering information with some of the existing operators, we illustrate some examples for evaluating the real-life problems related to enterprises, wherein the owner of a company appointed four senior board members of the enterprise to decide what was the best Asian company in which to invest money, to show the supremacy and superiority of the invented approaches. Full article

Intercity railway is an important system for the development of urban agglomeration, and the site selection of the Line Management Department of Intercity Railway (LMDIR) is a significant task for the railway department when constructing intercity railways. Owing to the complexity and uncertainty during the selection process, we constructed a multiple expert multi-criteria decision making (MEMCDM) method to provide a rational decision support model for a railway management department in the Fermatean cubic fuzzy set context. In this regard, an innovative extension called Fermatean cubic fuzzy sets (FCFSs) that integrates Fermatean fuzzy sets (FFSs) and cubic sets; several basic theories of FCFSs, including the score and accuracy functions; and distance measures are also given. Then, a series of Fermatean cubic fuzzy Hamacher operators are put forward to flexibly fuse Fermatean cubic fuzzy information, and the corresponding valuable characteristics of these operators are also investigated. Thirdly, the Fermatean cubic fuzzy logarithmic percentage-change-driven objective weighting (LOPCOW) approach is recommended based on the score function to recognize the importance of criteria, and the similarity-based method is deployed to identify the expert weight information. Fourthly, a hybrid MEMCDM methodology integrating the proposed Fermatean cubic fuzzy Hamacher operators, the LOPCOW method, whose evaluation is based on distance from average solution (EDAS) method based on regret theory, is designed to ascertain the prioritization of the schemes. Consequently, an empirical test concerning the site selection of LMDIR is shown to validate the feasibility and usefulness of the designed MEMCDM approach. The analysis involving the sensibility test and comparison study with prior methods is displayed to emphasize the effectuality and advantages of the propounded method. The outcomes demonstrate that the hybrid method recommended in this research possesses superior robustness and feasibility to cope with complicated decision issues. The findings of this research show that the presented method can recommend more credible site selection of LMDIR when encountering uncertainties and abundant impact factors. Full article

We introduce the notion of the interval-valued linear Diophantine fuzzy set, which is a generalized fuzzy model for providing more accurate information, particularly in emergency decision-making, with the help of intervals of membership grades and non-membership grades, as well as reference parameters that provide freedom to the decision makers to analyze multiple objects and alternatives in the universe. The accuracy of interval-valued linear Diophantine fuzzy numbers is analyzed using Frank operations. We first extend the Frank t-conorm and t-norm (FT${}_c$T${}_n$) to interval-valued linear Diophantine fuzzy information and then offer new operations such as the Frank product, Frank sum, Frank exponentiation, and Frank scalar multiplication. Based on these operations, we develop novel interval-valued linear Diophantine fuzzy aggregation operators (AOs), including the “interval-valued linear Diophantine fuzzy Frank weighted averaging operator and the interval-valued linear Diophantine fuzzy Frank weighted geometric operator”. We also demonstrate various features of these AOs and examine the interactions between the proposed AOs. FT${}_c$T${}_n$s offer two significant advantages. Firstly, they function in the same way as algebraic, Einstein, and Hamacher t-conorms and t-norms. Secondly, they have an additional parameter that results in a more dynamic and reliable aggregation process, making them more effective than other general t-conorm and t-norm approaches. Furthermore, we use these operators to design a method for dealing with multi-criteria decision-making with IVLDFNs. Finally, a numerical case study of the novel carnivorous issue is shown as an application for emergency decision-making based on the proposed AOs. The purpose of this numerical example is to demonstrate the practicality and viability of the provided AOs. Full article

On the basis of Hamacher operations, in this manuscript, we interpret bipolar complex fuzzy Hamacher weighted average (BCFHWA) operator, bipolar complex fuzzy Hamacher ordered weighted average (BCFHOWA) operator, bipolar complex fuzzy Hamacher hybrid average (BCFHHA) operator, bipolar complex fuzzy Hamacher weighted geometric (BCFHWG) operator, bipolar complex fuzzy Hamacher ordered weighted geometric (BCFHOWG) operator, and bipolar complex fuzzy Hamacher hybrid geometric (BCFHHG) operator. We present the features and particular cases of the above-mentioned operators. Subsequently, we use these operators for methods that can resolve bipolar complex fuzzy multiple attribute decision making (MADM) issues. We provide a numerical example to authenticate the interpreted methods. In the end, we compare our approach with existing methods in order to show its effectiveness and practicality. Full article

Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. In this analysis, we use the massive dominant and more consistent principle of power aggregation operators (PAOs) based on general t-norm and t-conorm, which manage awkward and inconsistent data in real-world dilemmas such as medical diagnosis, pattern recognition, cleaner production evaluation in gold mines, the analysis of the cancer risk factor, etc. The principle of averaging, geometric, Einstein, and Hamacher aggregation operators are specific cases of generalized PAOs. We combine the principle of complex intuitionistic fuzzy soft (CIFS) information with PAOs to initiate CIFS power averaging (CIFSPA), CIFS weighted power averaging (CIFSWPA), CIFS ordered weighted power averaging (CIFSOWPA), CIFS power geometric (CIFSPG), CIFS weighted power geometric (CIFSWPG), and CIFS ordered weighted power geometric (CIFSOWPG), and their flexible laws are elaborated. Certain specific cases (such as averaging, Einstein, and Hamacher operators) of the explored operators are also illustrated with the help of different t-norm and t-conorm operators. A MADM process is presented under the developed operators based on the CIFS environment. Finally, to investigate the supremacy of the demonstrated works, we employed a sensitivity analysis and geometrical expressions of the initiated operators with numerous prevailing works to verify the efficiency of the proposed works. This manuscript shows how to make decisions when there is asymmetric information about enterprises. Full article

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of $\left[0, 1\right]$ that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from $\left[0, 1\right]$ intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work. Full article

In the age of the information-based economy and the rapid advancements of data schemes, business management has been faced with extraordinary difficulties and has entered into a reasonable period where the board’s conventional enterprise execution assessment centers around the interests of investors. Speculators accept money-related information as their basis and focus on the investigation of material fascination, and in the event of the off chance that they do not, they cannot confirm the next economy period. In this way, enterprise execution reflects the interests of investors and business strategists for the needs of partners, which is significant for the forthcoming rivalry. Given that, the collection of data is a significant research tool that has lately been considered by researchers for data examination. In this paper, we have established multi-criteria decision-making methods for the assessment of business execution with spherical fuzzy information. We have applied Hamacher aggregation operators such as the spherical cubic fuzzy Hamacher weighted averaging (SCFHWA) operator, the spherical cubic fuzzy Hamacher ordered weighted averaging (SCFHOWA) operator, the spherical cubic fuzzy Hamacher hybrid averaging (SCFHHA) operator, the spherical cubic fuzzy Hamacher weighted geometric (SCFHWG) operator, the spherical cubic fuzzy Hamacher ordered weighted geometric (SCFHOWG) operator, and the spherical cubic fuzzy Hamacher hybrid geometric (SCFHHG) operator for the appraisal of the best choice of enterprise. We ultimately defend the proposed approach with the existing strategies for possibility and adequacy. Full article

Linguistic interval-valued intuitionistic fuzzy sets, as an extension of interval-valued intuitionistic fuzzy sets, have strong practical value in the management of complex uncertainty system with qualitative evaluation information. This study focuses on the development of several linguistic interval-valued intuitionistic fuzzy Hamacher (LIVIFH) aggregation operators based on the extended Hamacher t-norm and s-norm. First, the extended Hamacher t-norm and s-norm, which are applicable to linguistic information environment, are applied to define the linguistic interval-valued intuitionistic fuzzy Hamacher operational laws. Second, based on the proposed operational laws, this study defines the linguistic interval-valued intuitionistic fuzzy Hamacher weighted average (LIVIFHWA) operator and the linguistic interval-valued intuitionistic fuzzy Hamacher weighted geometric (LIVIFHWG) operator, and then investigates their properties. Furthermore, the degeneracy and monotonicity of the proposed operators with respect to the adjustable parameter are explored. Finally, a multiple attribute group decision-making (MAGDM) approach is developed based on the proposed LIVIFH aggregation operators, and then this approach is applied to a supplier selection problem. Parameter analysis indicates that the adjustable parameter in the proposed LIVIFH aggregation operators could reflect the attitudes of decision makers. The LIVIFHWA operator would be more appropriate to optimistic decision makers, and the LIVIFHWG operator to pessimistic decision makers. In addition, as the adjustable parameter increasing, both attitudes tend to be neutral. The proposed method is also compared with two other approaches to show its feasibility and efficiency. Full article

The social capital selection of a public–private-partnership (PPP) project could be regarded as a classical multiple attribute group decision-making (MAGDM) issue. In this paper, based on the traditional gained and lost dominance score (GLDS) method, the q-rung orthopair fuzzy entropy-based GLDS method was used to solve MAGDM problems. First, some basic theories related to the q-rung orthopair fuzzy sets (q-ROFSs) are briefly reviewed. Then, to fuse the q-rung orthopair fuzzy information effectively, the q-rung orthopair fuzzy Hamacher weighting average (q-ROFHWA) operator and q-rung orthopair fuzzy Hamacher weighting geometric (q-ROFHWG) operator based on the Hamacher operation laws are proposed. Moreover, to determine the attribute weights, the q-rung orthopair fuzzy entropy (q-ROFE) is proposed and some significant merits of it are discussed. Next, based on the q-ROFHWA operator, q-ROFE, and the traditional GLDS method, a MAGDM model with q-rung orthopair fuzzy information is built. In the end, a numerical example for social capital selection of PPP projects is provided to testify the proposed method and deliver a comparative analysis. Full article

In this paper, we introduce certain aggregation operators, namely, the m-polar fuzzy (mF) Hamacher weighted average operator, mF Hamacher ordered weighted average (mFHOWA) operator, mF Hamacher hybrid average (mFHHA) operator, mF Hamacher weighted geometric (mFHWG) operator, mF Hamacher weighted ordered geometric operator, and mF Hamacher hybrid geometric (mFHHG) operator. We discuss some properties of these operators, inclusive of their ability to implement both symmetric and asymmetric treatments of the items. We develop an algorithmic model to solve multi-attribute decision-making (MADM) problems in mF environment using mF Hamacher weighted average operator (mFHWA) and mFHWG operators. They can compensate for the possible asymmetric roles of the attributes that describe the problem. In the end, to prove the validity and feasibility of the proposed work, we give applications for selecting the most affected country regarding human trafficking, selecting health care waste treatment methods and selecting the best company for investment. We also solve practical MADM problems by using ELECTRE-I method, and give a comparative analysis. Full article