Averaging Aggregation Operators Research Articles

Fermatean trapezoidal fuzziness average aggregation scheme for selection of infant clothing by group decision-making

The textile industry has gradually increased its use of various chemicals and the quantity of residues produced. Newborn baby apparel should be made of safe materials since it often comes into touch with them. Infant cloth selection is determined via group decision-making in Fermatean trapezoidal fuzzy number (FTFN). This study provides a new score and accuracy function and weighted, ordered, and hybrid averaging aggregation operators on FTFN. The properties of the proposed averaging aggregation operators on FTFN are presented. An algorithm for the multi-attribute group decision-making (MAGDM) approach will be proposed by applying the proposed averaging aggregation operators. The case studies concentrate on choosing newborn clothing with reduced chemical content within the textile sector. The presentation of the sensitivity analysis of the criterion weights is conducted to guarantee the durability and stability of the framework that has been implemented. Furthermore, a comprehensive analysis compares the novel framework with previous models, highlighting its superior performance.

An enhanced CRADIS decision model for optimizing radioactive waste reduction through transmutations based on Disc Spherical Fuzzy information

Radioactive waste reduction through transmutation techniques is significant for mitigating environmental risks and ensuring long-term safety. It offers a sustainable approach to minimizing the volume of radioactive waste, contributing to both environmental preservation and enhanced nuclear energy sustainability. This paper introduces an extension of aggregation operations to hybrid operators in Disc Spherical Fuzzy Sets (D-SFSs), including D-SFS algebraic hybrid weighted averaging and D-SFS hybrid geometric aggregation operators. These novel operators are tailored for D-SFSs and are supported by rigorous proofs, enhancing their theoretical robustness. Additionally, a Maximum Deviation Method (MDM) is developed in conjunction with a proposed distance measure to assess attribute weights in Multiple Attribute Decision-Making (MADM) problems with Disc Spherical Fuzzy (D-SF) information. The study proposes a new MADM method in the D-SF environment, leveraging the D-SF distance measure and the Compromise Ranking of Alternatives from Distance to Ideal Solution (CRADIS) method. Notably, the paper focuses on extending D-SFs to the CRADIS method, particularly when weight information is entirely unknown. A comprehensive case study on optimizing radioactive waste volume reduction through transmutation technologies is provided. A comparative analysis with existing decision-making methods validates the improved MADM method’s validity and practicality.

Selection of an Appropriate Global Partner for Companies Using the Innovative Extension of the TOPSIS Method with Intuitionistic Hesitant Fuzzy Rough Information

In this research, we introduce the intuitionistic hesitant fuzzy rough set by integrating the notions of an intuitionistic hesitant fuzzy set and rough set and present some intuitionistic hesitant fuzzy rough set theoretical operations. We compile a list of aggregation operators based on the intuitionistic hesitant fuzzy rough set, including the intuitionistic hesitant fuzzy rough Dombi weighted arithmetic averaging aggregation operator, the intuitionistic hesitant fuzzy rough Dombi ordered weighted arithmetic averaging aggregation operator, and the intuitionistic hesitant fuzzy rough Dombi hybrid weighted arithmetic averaging aggregation operator, and demonstrate several essential characteristics of the aforementioned aggregation operators. Furthermore, we provide a multi attribute decision-making approach and the technique of the suggested approach in the context of the intuitionistic hesitant fuzzy rough set. A real-world problem for selecting a suitable worldwide partner for companies is employed to demonstrate the effectiveness of the suggested approach. The sensitivity analysis of the decision-making results of the suggested aggregation operators are evaluated. The demonstrative analysis reveals that the outlined strategy has applicability and flexibility in aggregating intuitionistic hesitant fuzzy rough information and is feasible and insightful for dealing with multi attribute decision making issues based on the intuitionistic hesitant fuzzy rough set. In addition, we present a comparison study with the TOPSIS approach to illustrate the advantages and authenticity of the novel procedure. Furthermore, the characteristics and analytic comparison of the current technique to those outlined in the literature are addressed.

EDAS method for circular pythagorean fuzzy with improved Dombi power aggregation operators and their application in policy analysis and decision support systems

A circular Pythagorean fuzzy set is a very dominant and reliable technique for coping with uncertain and vague information in genuine life problems because it contains the membership function, non-membership function, and radius between both grades with a condition that is the sum of the pair will be contained in the unit interval. The objective of this article is to define some improved Dombi operational laws based on circular improved Pythagorean fuzzy values. Moreover, we discuss some drawbacks of the existing Dombi aggregation operators based on circular improved Pythagorean fuzzy numbers. We also defined some improved Dombi averaging and geometric aggregation operators and their properties. Later on, a technique of evaluation based on distance from the average solution is stated by using the proposed operators. Additionally, we resolve the problem of policy analysis and decision support systems based on multi-attribute decision-making problems for initiated techniques to enhance the worth of the derived theory. Finally, we illustrate some examples for showing the supremacy and validity of the proposed theory with the help of comparative analysis between proposed ranking values and some existing ranking values.

T-Spherical fuzzy TOPSIS method based on distance measures and Hamacher Heronian mean averaging aggregation operators and its application to waste management

T-Spherical fuzzy sets provide a robust framework for handling uncertainty in real-world decision-making. This paper addresses the construction of T-Spherical fuzzy Heronian mean averaging aggregation operators using novel Hamacher operations. The study mathematically verifies the properties of these operators and develops new distance measures such as Hamming, Euclidean and Jaccard for quantifying dissimilarity between T-Spherical fuzzy numbers. Furthermore, the TOPSIS method is implemented using the proposed operators and distance measures to solve a practical decision-making problem in selecting the best transportation firm for medical waste disposal. A sensitivity analysis is made to assesses the efficacy of the proposed operators, while a comparison study with existing methods is exhibited to establish their efficiency.

A novel multi-criteria group decision making algorithm for enhancing supply chain efficiency under high uncertainty during crisis based on q-rung orthopair fuzzy information

In recent years, q-rung orthopair fuzzy sets (q-ROFSs) have been becoming gradually more advantageous in handling information with high uncertainty. Several multi-criteria group decision-making (MCGDM) algorithms under q-ROFS information have been proposed in literature and used to solve various real-life problems. However, several shortcomings of some existing MCGDM algorithms under certain circumstances also emerged which limit their applicability. To overcome these challenges and deal with information under high uncertainty more accurately and reasonably, we propose a novel MCGDM algorithm under q-ROF information, i.e., (q-ROF-MCGDM), that retains the advantages of currently available methods, but extend its applicability by introducing a new q-rung orthopair fuzzy weighted averaging aggregation operator (q-ROFWAAO) along with a new entropy measure. The proposed q-ROF-MCGDM algorithm involves the steps: firstly, the input requirement in terms of alternatives, criteria and expert evaluations are required. Secondly, aggregating expert opinions using weights and normalizing decision matrices, and finally, calculating entropy weights and aggregating overall evaluations for final prioritization. Further, new operational laws have been developed and several necessary properties of the proposed q-ROFWAAO are also proved. Moreover, a sensitivity and comparative analysis has been carried out for validity and effectiveness of the proposed q-ROF-MCGDM algorithm. The proposed q-ROF-MCGDM algorithm has been implemented to enhance the efficiency of the United Arab Emirates (UAE) food industry under high uncertainty during the recent crisis. Finally, an evaluation of identifying and prioritizing the most severe food SC disruptions and appropriate mitigation strategies under crisis is provided to demonstrate applicability of the proposed q-ROF-MCGDM algorithm, and the obtained real case results confirm its usefulness. Findings of the study offer valuable insights to both food industry researchers and managers in developing effective recovery strategies, mitigating risks, and improving overall efficiency to ensure the survival of food businesses during the crisis.

Benchmarking of industrial wastewater treatment processes using a complex probabilistic hesitant fuzzy soft Schweizer–Sklar prioritized-based framework

The objective of this research work is to effectively handle the intricate and uncertain nature of decision-making in the context of industrial wastewater treatment. The prioritization of wastewater treatment is of utmost importance in order to save the environment, promote human health, ensure adherence to legal regulations, conserve resources, and foster overall sustainability. The demand for efficient and sustainable wastewater treatment processes is increasing globally, but selecting appropriate treatment technologies for industrial effluents is challenging due to its complex nature. Our study aims to provide a systematic framework for evaluating and selecting treatments based on efficacy, affordability, and environmental impact. Aggregation operators are one of the fundamental ideas in the framework of information fusion for addressing real-life problems. Numerous scholars have made significant contributions to the development of aggregation operators specifically designed for multi-parameter decision-making (MPDM) whenever circumstances are characterized by uncertainty. Regrettably, the current operators can only be employed within strict limits and constraints. Therefore, this research formulates novel prioritized aggregation operators that alleviate the restrictive constraints associated with the current operators. After this, we present a new methodology that combines the Schweizer–Sklar prioritized aggregation operators with a complex probabilistic hesitant fuzzy soft framework. For this purpose, we develop the averaging aggregation operators and geometric aggregation operators. Following that, we proceed to examine the theorems and properties associated with them by providing rigorous proofs. Then, we develop a novel decision-making technique with a numerical example based on the wastewater treatment process. Through this novel technique, the best process is the activated sludge process. We perform the validity tests to evaluate the feasibility and effectiveness of MPDM techniques.

A Bipolar Complex Fuzzy CRITIC-ELECTRE III Approach Using Einstein Averaging Aggregation Operators for Enhancing Decision Making in Renewable Energy Investments

A Bipolar Complex Fuzzy CRITIC-ELECTRE III Approach Using Einstein Averaging Aggregation Operators for Enhancing Decision Making in Renewable Energy Investments

A Pythagorean fuzzy [formula omitted]-number-based neutrality aggregation model for AI-enabled energy efficiency management

Artificial intelligence (AI)-enabled energy efficiency in buildings leverages AI to optimize energy consumption, enhancing sustainability and aiding decision-makers in selecting cost-effective and environmentally friendly solutions. Pythagorean fuzzy Z̃ number sets, capable of handling high uncertainty, play a crucial role in representing fuzzy information in decision-making. This research introduces novel operational laws and weighted aggregation operators, focusing on neutral addition and scalar multiplication. Comprehensive investigations into the properties of these laws lead to groundbreaking aggregation operators tailored for Pythagorean fuzzy Z̃ number information. These include weighted, ordered weighted, and hybrid neutral averaging aggregation operators, along with a novel approach for calculating attribute weights. Relationships and characteristics of these operators are explored, and an algorithm for solving multiple attribute group decision-making problems is provided. A practical example illustrates the approach’s superiority, supported by comparative results.

Utilizing sine trigonometric q-spherical fuzzy rough aggregation operators for group decision-making and their role in digital transformation

q-spherical fuzzy rough set (q-SFRS) is also one of the fundamental concepts for addressing more uncertainties in decision problems than the existing structures of fuzzy sets, and thus its implementation was more substantial. The well-known sine trigonometric function maintains the periodicity and symmetry of the origin in nature and thus satisfies the expectations of the experts over the multi-parameters. Taking this feature and the significance of the q-SFRSs into consideration, the main objective of the article is to describe some reliable sine trigonometric laws for SFSs. Associated with these laws, we develop new average and geometric aggregation operators to aggregate the q-spherical fuzzy rough numbers. Then, we presented a group decision-making strategy to address the multi-attribute group decision-making problem using the developed aggregation operators. To verify the value of the defined operators, a MAGDM strategy is provided along with applications for selecting a Cloud Service Provider and a Digital Transformation Vendor for digital transformation. Moreover, a comparative study is also performed to present the effectiveness of the developed approach.

Rough Neutrosophic Shapley Weighted Einstein Averaging Aggregation Operator and its Application in Multi-Criteria Decision-Making Problem

The study of aggregation operators has played a crucial role in various decision-making methods. The primary function of the aggregation operator is to combine multiple numbers into a single value. While Einstein operators offer a compact notation and can handle complex and large datasets, they do not consider the interaction involved in determining the criteria weights or account for imprecise and indeterminate data. To overcome this limitation, this paper introduces an improved aggregation operator, the rough neutrosophic Shapley weighted Einstein averaging aggregation operator. The rough neutrosophic sets offer a method for effectively managing the fuzziness and uncertainty that commonly occur in real-world scenarios and the Shapley fuzzy measure helps us understand the importance or value of different elements in each scenario. This operator combines the Shapley fuzzy measure with Einstein operators under rough neutrosophic sets, which are an effective tool for handling incomplete, indeterminate, and inconsistent information. The proposed operator satisfies essential algebraic properties such as idempotency, boundedness, and monotonicity. This paper also presents a decision-making methodology based on the proposed operator, with attribute values derived from the rough neutrosophic set. Finally, the applicability of the suggested aggregation operator is illustrated with a numerical example.

Lifetime Extension of Wireless Sensor Networks by Perceptive Selection of Cluster Head Using K-Means and Einstein Weighted Averaging Aggregation Operator under Uncertainty

Lifetime Extension of Wireless Sensor Networks by Perceptive Selection of Cluster Head Using K-Means and Einstein Weighted Averaging Aggregation Operator under Uncertainty

Multi-Attribute Group Decision-Making Problem Based On Q-Rung Orthopair Fuzzy Set Under Confidence Environment

Emergency decision-making for communities and countries is an important and critical tool. It improves the effectiveness and reliability to response emergencies which minimizes the rate of casualties, environmental damages and economic losses. In the event of emergency decision-making, the main issue is extreme imprecision, ambiguity, and fuzziness. This paper is devoted to the study of q‐rung orthopair fuzzy aggregation operators under the confidence levels and their applications to multiple-attribute group decision making (MAGDM) problems. The concept of q-rung orthopair fuzzy set (q-ROFS) is used as tool to describe undetermined information and is superior to the intuitionistic set (IFS) and Pythagorean fuzzy set (PFS). The distinguishing feature of the q-ROFS is that the sum of the q-th power of the membership degree and the q-th power of non-membership degree is bounded by 1. As a result, the range of uncertain information that it may describe is expanded. In this work, we focus on MAGDM problems under the fuzzy environment. First, based on aggregation operators some drawbacks of the already existing MAGDM methods are analyzed. Moreover, we present some modified operational laws and some of their properties to overcome these drawbacks. Next, related to q-ROFS fuzzy-weighted averaging (q-ICROFWA) and fuzzy-weighted power averaging (q-ICROFWPA) aggregation operator under confidence levels along with their properties are presented. By using these operators’ q-ICROFWA and q-ICROFWPA an advanced method is proposed to deal with MAGDM problems in fuzzy environment. At last, the validity and feasibility of this method is illustrated with some numerical examples.

The Characteristics of Circular Fermatean Fuzzy Sets and Multicriteria Decision-Making Based on the Fermatean Fuzzy t-Norm and t-Conorm

When diverse decision makers are involved in the decision-making process, taking average of decision values might not reflect an accurate point of view. To overcome such a scenario, the circular Fermatean fuzzy (CFF) set, an advancement of the Fermatean fuzzy (FF) set, and the interval-valued Fermatean fuzzy set (IVFFS) are introduced in this current study. The proposed CFF set is a circle with a centre as association value (AV) and nonassociation value (NAV) with a radius at most equal to 2. It is built in such a way that it covers all the decision makers’ opinion value through a circle. Due to its geometric structure, the CFF set resolves ambiguity and risk more accurately and effectively than FF and IVFF. FF t-norm and t-conorm are used to investigate the properties of CFF sets, subsequent to which the algebraic operations between them are defined. A couple of CFF distance measures between CFF numbers are introduced and used in the selection of an electric autorickshaw along with the CFF weighted averaging and geometric aggregation operators. The overview and comparison analysis of the generated reports exemplifies the viability and compatibility of the CFF set strategy for selecting the best choices.

A Multi-Criteria Decision Support Model for Restaurant Selection Based on Users' Demand Level: The Case of Dianping.com

The Internet, by offering a variety of information sources such as online reviews, aids people in selecting restaurants. However, it also prolongs their decision-making process due to the need to integrate information across multiple criteria. Existing decision support models for choosing satisfactory restaurants overlook users' varying demand levels for each aspect of the restaurant, making the process less efficient. This paper aims to develop a multi-criteria decision support model for users to efficiently and accurately rank and select restaurants based on their demand level for various restaurant aspects. The 2-tuple linguistic ordered weighted averaging (2LOWA) aggregation operator is applied for the first time to aggregate user ratings, generating linguistic ratings that mirror the diverse levels of user demand for restaurant service, food, and environment. The importance weights (IW) method is introduced to calculate linguistic weights, thereby obtaining customized 2T-SFE composite scores under various user demand scenarios. The proposed model's applicability is demonstrated using a dataset comprising over 3.7 million reviews sourced from Dianping.com. The results show multiple personalized restaurant rankings with more linguistically understandable composite scores, enabling users to efficiently choose a suitable restaurant based on their preferences and requirements. Moreover, a list of restaurants satisfying most users with different demand levels can be generated by assessing their frequency of appearance in the top 10 restaurants across over 340 scenarios established by the proposed model. This contributes to offering more reliable and comprehensive restaurant recommendations and rankings, ultimately increasing customer satisfaction in the selection process.

Group decision making based on a novel aggregation operator under linguistic interval-valued Atanassov intuitionistic fuzzy information

Efficient aggregation methods and order relationships are crucial in solving group decision making (GDM) problems with linguistic interval-valued Atanassov intuitionistic fuzzy information. Based on a novel score function, this paper first presents a new method to rank linguistic interval-valued Atanassov intuitionistic fuzzy numbers (LIVAIFNs). The proposed ranking method overcomes the limitations of existing methods. Then, a new linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging (NLIVAIFWA) aggregation operator (AO) is proposed. The NLIVAIFWA AO of LIVAIFNs presented in this paper can overcome the drawbacks of the linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging (LIVAIFWA) AO, the linguistic interval-valued Atanassov intuitionistic fuzzy weighted geometric (LIVAIFWG) AO, the linguistic interval-valued Atanassov intuitionistic fuzzy Hamacher weighted averaging (LIVAIFHWA) AO and the improved linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging (ILIVAIFWA) AO of LIVAIFNs. Furthermore, some primary properties of the NLIVAIFWA AO are discussed, and a novel GDM method based on the provided NLIVAIFWA AO of LIVAIFNs is constructed. Finally, the effectiveness of the proposed GDM method is demonstrated through numerical examples, highlighting its superiority, and advantages.

Multiattribute decision making based on q-rung orthopair fuzzy Yager prioritized weighted arithmetic aggregation operator of q-rung orthopair fuzzy numbers

This paper proposes a new approach for multiattribute decision making (MADM) using the proposed q-rung orthopair fuzzy Yager prioritized weighted arithmetic (q-ROFYPWA) aggregation operator (AO) of q-rung orthopair fuzzy numbers (q-ROFNs). Firstly, we propose the q-ROFYPWA AO of q-ROFNs based on Yager’s t-conorm and t-norm and the concept of prioritized average AO. The proposed q-ROFYPWA AO consider the prioritized relationship among aggregating q-ROFNs. Moreover, we present several properties of the proposed q-ROFYPWA AO. Then, we propose a new MADM approach based on the proposed q-ROFYPWA AO of q-ROFNs. The propsoed MADM approach considers the prioritization among the attributes to overcome the drawbacks of the existing MADM approaches, where they cannot distinguish the ranking orders of the alternatives in some situations. The proposed MADM approach is very useful for MADM in the environment of q-ROFNs.

Cubical fuzzy Einstein Bonferrori mean averaging aggregation operators and their applications to multiple criteria group decision making problems

Consolidating cubical fuzzy numbers (CFNs) is essential in an uncertain decision-making process. This study focuses on creating innovative cubical fuzzy aggregation operators based on the newly proposed Einstein operational laws, utilizing the Bonferroni mean function to capture the interrelationships among the aggregated CFNs. The first contribution of this paper is introducing a novel cubical fuzzy Einstein Bonferroni mean averaging operator. Building upon this operator, we extend our research to develop cubical fuzzy Einstein Bonferroni mean weighted, ordered weighted, and hybrid averaging operators, taking into account the weights of the aggregated CFNs. To ensure their effectiveness, we thoroughly investigate the desirable properties of these proposed operators. Furthermore, we leverage the introduced operators to establish a new approach known as the cubical fuzzy linear assignment method, which proves valuable in resolving multiple criteria group decision-making problems. As a practical demonstration of the method’s utility, we apply it to address a real-life challenge: identifying the optimal location for constructing a wind power plant under a cubical fuzzy environment. To validate the effectiveness of our approach, we compare its results with those obtained using existing methods from the literature. Additionally, we conduct a statistical analysis to visualize the correlative conjunction between the ranking outcomes obtained by different operators

Cubic Pythagorean Hesitant Fuzzy Linear Spaces and Its Relevance in Multi Criteria Decision Making

Pythagorean fuzzy sets and interval valued Pythagorean fuzzy sets have an important role in decision making techniques. Pythagorean hesitant fuzzy sets are time and again used in dealing with uncertain and vague data. The motive of this paper is to introduce the notion cubic Pythagorean hesitant fuzzy linear spaces. We also present the notion of P(R)-intersection, P(R)-union of cubic Pythagorean hesitant fuzzy linear spaces with examples. Secondly, a series of operators like cubic Pythagorean hesitant fuzzy weighted averaging aggregation operators, cubic Pythagorean hesitant fuzzy order weighted averaging aggregation operators and cubic Pythagorean hesitant fuzzy hybrid order weighted averaging aggregation operators are developed. Then, these aggregation operators are further extended to cubic Pythagorean hesitant fuzzy prioritized weighted averaging aggregation operators by assigning priorities to the criteria. A real life MCDM problem has been illustrated and the effectiveness of the results are compared with those solved using cubic picture hesitant fuzzy prioritized weighted averaging aggregation operators.

MCDM technique using single-valued neutrosophic trigonometric weighted aggregation operators

Motivated based on the trigonometric t-norm and t-conorm, the aims of this article are to present the trigonometric t-norm and t-conorm operational laws of SvNNs and then to propose the SvNN trigonometric weighted average and geometric aggregation operators for the modelling of a multiple criteria decision making (MCDM) technique in an inconsistent and indeterminate circumstance. To realize the aims, this paper first proposes the trigonometric t-norm and t-conorm operational laws of SvNNs, which contain the hybrid operations of the tangent and arctangent functions and the cotangent and inverse cotangent functions, and presents the SvNN trigonometric weighted average and geometric operators and their properties. Next, a MCDM technique is proposed in view of the presented two aggregation operators in the circumstance of SvNNs. In the end, an actual case of the choice issue of slope treatment schemes is provided to indicate the practicability and effectivity of the proposed MCDM technique.