Multi-attribute Decision-making Techniques Research Articles

Fuzzy analytic hierarchy process based generation management for interconnected power system

Decision makers consistently face the challenge of simultaneously assessing numerous attributes, determining their respective importance, and selecting an appropriate method for calculating their weights. This article addresses the problem of automatic generation control (AGC) in a two area power system (2-APS) by proposing fuzzy analytic hierarchy process (FAHP), an multi-attribute decision-making (MADM) technique, to determine weights for sub-objective functions. The integral-time-absolute-errors (ITAE) of tie-line power fluctuation, frequency deviations and area control errors, are defined as the sub-objectives. Each of these is given a weight by the FAHP method, which then combines them into an single final objective function. This objective function is then used to design a PID controller. To improve the optimization of the objective function, the Jaya optimization algorithm (JOA) is used in conjunction with other optimization techniques such as sine cosine algorithm (SCA), Luus–Jaakola algorithm (LJA), Nelder–Mead simplex algorithm (NMSA), symbiotic organism search algorithm (SOSA) and elephant herding optimization algorithm (EHOA). Six distinct experimental cases are conducted to evaluate the controller’s performance under various load conditions, with data plotted to show responses corresponding to fluctuations in frequency and tie-line exchange. Furthermore, statistical analysis is performed to gain a better understanding of the effectiveness of the JOA-based PID controller. For non-parametric evaluation, Friedman rank test is also used to validate the performance of the proposed JOA-based controller.

Selection of safety equipment with choquet integral operators and q-rung orthopair fuzzy information

The q-rung orthopair fuzzy set (q-ROFS) is a moderate mathematical model, that has diverse capabilities to handle uncertain and ambiguous information of human opinion during the decision analysis process. The Aczel Alsina operations are more flexible and valuable aggregating tools with parameter values ϻ ⩾ 1, reflecting smooth and accurate information by aggregating awkward and redundant information. The theory of the Choquet integral operator is also used to express the interaction between preferences or criteria by incorporating certain values of preferences. The primary features of this article are to derive some dominant mathematical approaches by combining two different theories like Choquet integral operators and operations of Aczel Alsina tools namely “q-rung orthopair fuzzy Choquet integral Aczel Alsina average” (q-ROFCIAAA), and “q-rung orthopair fuzzy Choquet integral Aczel Alsina geometric” (q-ROFCIAAG) operators. Some special cases and notable characteristics are also demonstrated to show the feasibility of derived approaches. Based on our derived aggregation approaches, a multi-attribute decision-making (MADM) technique aggregates redundant and unpredictable information. In light of developed approaches, a numerical example study to evaluate suitable safety equipment in the construction sector. To reveal the intensity and applicability of derived approaches by contrasting the results of prevailing approaches with currently developed AOs.

Analysis of Digital Green Innovation Based on Schweizer–Sklar Prioritized Aggregation Operators for Interval-Valued Picture Fuzzy Supply Chain Management

Digital green innovation economics and management for Industry 5.0 was not widely recognized, and the commonly referenced industry paradigm was Industry 4.0. Furthermore, digital green innovation is part of the above information referring to the integration of digital technologies with environmentally sustainable practices to develop innovative solutions that evaluate ecological challenges. In this manuscript, we evaluate the Schweizer–Sklar operational laws based on interval-valued picture fuzzy (IVPF) values. Further, we investigate prioritized aggregation operators based on Schweizer–Sklar operational laws for IVPF information, called IVPF Schweizer–Sklar prioritized averaging operator, IVPF Schweizer–Sklar prioritized geometric operator, IVPF Schweizer–Sklar prioritized weighted averaging operator, and IVPF Schweizer–Sklar prioritized weighted geometric operator. Some properties for the above-initiated operators are also derived. Additionally, we analyze the digital green innovation with the help of multi-attribute decision-making technique for initiated operators to show the reliability and supremacy of the proposed theory. Finally, we demonstrate examples for addressing the comparison among the initiated theory and existing ideas to improve the worth of the derived theory.

Implementation of Learning Management Systems (LMS) in higher education systems through bipolar complex hesitant fuzzy Aczel-Alsina power aggregation operators: A case review for China.

A learning management system (LMS) is a web-based application or software platform computed to facilitate the development, tracking, management, reporting, and delivery of education and training programs. Many valuable and dominant factors are working behind the Learning Management System (LMS), but no one can find which factor is most important and valuable for LMS during COVID-19 among the following five alternatives, called Improved Accessibility, Blended Learning, Collaboration and Communications, Assessment and Evaluation, and Administrative Efficiency. For this, first, we derive the techniques of bipolar complex hesitant fuzzy (BCHF) sets, and then we evaluate some flexible operational laws, called Algebraic operational laws and Aczel-Alsina operational laws. Secondly, using the above techniques, we elaborate the technique of BCHF Aczel-Alsina power averaging (BCHFAAPA), BCHF Aczel-Alsina power weighted averaging (BCHFAAPWA), BCHF Aczel-Alsina power geometric (BCHFAAPG), and BCHF Aczel-Alsina power weighted geometric (BCHFAAPWG) operators. Some basic properties are also investigated for each proposed operator. Further, to evaluate the problem concerning LMS, we compute the multi-attribute decision-making (MADM) techniques for invented operators. Finally, we select some prevailing operators and try to compare their ranking results with our proposed results to enhance the worth and capability of the invented theory.

Decision Support System for Single-Valued Neutrosophic Aczel–Alsina Aggregation Operators Based on Known Weights

Multiattribute decision making (MADM) approach is a well-known decision-making process utilized in a variety of fields such as solid waste management, renewable energy resources, air quality assurance, hotel location decision, sustainable supplier selection, partner recognition, green supplier enterprises, game theory, construction development authority, and weapon group target estimation. The aggregation operators (AOs) are essential components of the decision-making process and have a great capability to deal with ambiguous and unpredictable information in the different fields of fuzzy environments. In this article, we expressed the theory concepts of single-valued neutrosophic (SVN) sets (SVNS) and also characterized their basic operations. The power aggregation tools are allowed to input arguments to support each other among different arguments. Recently, Aczel–Alisna aggregation tools conquered great attention from several research scholars. We also exposed some reliable operations of Aczel–Alsina aggregation models under the consideration of SVN information. We established a series of new approaches, including the “single-valued neutrosophic Aczel–Alsina power weighted average” (SVNAAPWA) operator and “single-valued neutrosophic Aczel–Alsina power weighted geometric” (SVNAAPWG) operators. To show the effectiveness and compatibility of derived approaches, some prominent characteristics are also established. We constructed a MADM technique to solve an application of engineering and construction materials under consideration of our derived methodologies. An experimental case study is also presented to determine a suitable optimal option from a group of options. To find the flexibility of our proposed work, we provided a comparative study that compares the results of existing AOs with our proposed work. A comprehensive overview is also presented here.

MADM-based network selection and handover management in heterogeneous network: A comprehensive comparative analysis

As radio access technologies, processing speeds, and multimode interfaces of low-powered portable devices continue to advance, the future of wireless communication is envisioned to offer pervasive network coverage, high data rates, and a wide spectrum of services while maintaining high mobility. High data rates, wide range of services, huge connectivity, capacity, and good geographic coverage are being provided by the ultra-dense deployment of small base stations (BSs) in heterogeneous wireless networks (HWN). But dense deployment of small BSs, high mobility, network heterogeneity, imbalanced traffic, and dynamic user preferences lead to frequent handover. Network overhead, excessive energy consumption, and a decrease in service quality and user satisfaction can be due to frequent handover. So, handover management is one of the crucial challenges in the implementation of 5G and beyond in HWNs for ensuring seamless connectivity, energy efficiency, and the required quality of services and experiences. The effectiveness of handover decisions in HWNs relies on the implementation of a suitable network selection mechanism. Multi-attribute decision-making (MADM) is being used to model and analyze appropriate network selection complexities by considering a broad spectrum of intricate and conflicting decision criteria for efficient handover decisions in HWN. This article extensively explores, compares, and analyzes vital MADM techniques utilized for modeling appropriate network selection strategies in terms of algorithmic strategies, cardinality, types and significance of decision attributes, and network utilities. This article also examines, analyzes, and recognizes the recent mobility management challenges and trends in utilizing MADM strategies to tackle network selection issues in high-speed HWNs.

On Circular q-Rung Orthopair Fuzzy Sets with Dombi Aggregation Operators and Application to Symmetry Analysis in Artificial Intelligence

Circular q-rung orthopair fuzzy sets (FSs) were recently considered as an extension of q-rung orthopair FSs (q-ROFSs), circular intuitionistic FSs (Cir-IFSs), and circular Pythagorean FSs (Cir-PFSs). However, they are only considered for some simple algebraic properties. In this paper, we advance the work on circular q-ROFSs (Cirq-ROFSs) in Dombi aggregation operators (AOs) with more mathematical properties of algebraic laws. These include the circular q-rung orthopair fuzzy (Cirq-ROF) Dombi weighted averaging (Cirq-ROFDWA), Cirq-ROF Dombi ordered weighted averaging (Cirq-ROFDOWA), Cirq-ROF Dombi weighted geometric (Cirq-ROFDWG), and Cirq-ROF Dombi ordered weighted geometric (Cirq-ROFDOWG) operators. Additionally, we present the properties of idempotency, monotonicity, and boundedness for the proposed operators. In the context of artificial intelligence, symmetry analysis plays a significant and efficient role that can refer to several aspects. Thus, to compute the major aspect, we identify the multi-attribute decision-making (MADM) technique based on the proposed operators for Cirq-ROF numbers (Cirq-ROFNs) to enhance the worth of the evaluated operators. Finally, we use some existing techniques for comparison to our results to show the validity and supremacy of the proposed method.

A roommate problem and room allocation in dormitories using mathematical modeling and multi-attribute decision-making techniques

Purpose In recent decades, the student population in dormitories has increased notably, primarily attributed to the growing number of international students. Dormitories serve as pivotal environments for student development. The coordination and compatibility among students can significantly influence their overall success. This study aims to introduce an innovative method for roommate selection and room allocation within dormitory settings. Design/methodology/approach In this study, initially, using multi-attribute decision-making methods including the Bayesian best-worst method and weighted aggregated sum product assessment, the incompatibility rate among pairs of students is calculated. Subsequently, using a linear mathematical model, roommates are selected and allocated to dormitory rooms pursuing the twin objectives of minimizing the total incompatibility rate and costs. Finally, the grasshopper optimization algorithm is applied to solve large-sized instances. Findings The results demonstrate the effectiveness of the proposed method in comparison to two common alternatives, i.e. random allocation and preference-based allocation. Moreover, the proposed method’s applicability extends beyond its current context, making it suitable for addressing various matching problems, including crew pairing and classmate pairing. Originality/value This novel method for roommate selection and room allocation enhances decision-making for optimal dormitory arrangements. Inspired by a real-world problem faced by the authors, this study strives to offer a robust solution to this problem.

3D seismic analysis of mine planning using Aczel–Alsina aggregation operators based on T-spherical fuzzy information

3D seismic attributes analysis can help geologists and mine developers associate subsurface geological features, structures, faults, and ore bodies more precisely and accurately. The major influence of this application is to evaluate the usage of the 3D seismic attributes analysis in gold mine planning. For this, we evaluate the novel theory of complex T-spherical hesitant fuzzy (CTSHF) sets and their operational laws. Furthermore, we derive the CTSHF Aczel–Alsina weighted power averaging (CTSHFAAWPA) operator, CTSHF Aczel–Alsina ordered weighted power averaging (CTSHFAAOWPA) operator, CTSHF Aczel–Alsina weighted power geometric (CTSHFAAWPG) operator, and CTSHF Aczel–Alsina ordered.com weighted power geometric (CTSHFAAOWPG) operator. Some properties are also investigated for the above operators. Additionally, we evaluate the problems of 3D seismic attributes analysis to mine planning under the consideration of the proposed operators, for this, we illustrate the problem of the multi-attribute decision-making (MADM) technique for the above operators. Finally, we demonstrate some examples for making the comparison between prevailing and proposed information to improve the worth of the derived operators.

Archimedean Heronian mean operators based on complex intuitionistic fuzzy sets and their applications in decision-making problems

In this article, we derive the Archimedean aggregation operators for complex intuitionistic fuzzy sets, for this, first, we evaluate some Archimedean operational laws based on complex intuitionistic fuzzy values and then we discuss their special cases because the Archimedean norms are the general form of all existing norms, for instance, algebraic, Einstein, Hamacher, and Frank operational laws. Furthermore, we present the complex intuitionistic fuzzy Archimedean Heronian aggregation operator and complex intuitionistic fuzzy weighted Archimedean Heronian aggregation operator. Several special cases and the basic properties of the above-proposed operators are also diagnosed, because proposing the Heronian mean operators based on Archimedean norms are very challenging and complicated tasks, because of their features and structure. Additionally, a decision-making process is developed under the identified operators by using complex intuitionistic fuzzy information. Finally, we illustrate several examples to show the multi-attribute decision-making technique is more flexible than the prevailing works with the help of sensitive analysis between explored and certain prevailing works.

Quality of service attributes based hybrid decision-making framework for ranking cloud service providers under Fermatean fuzzy environment

Cloud Computing has gained substantial popularity due to its ability to offer diverse and dependable computing services suited to clients demands. Given the rapid expansion of this technology, an increasing number of IT service providers are competing to deliver cloud services that are both of excellent quality and cost-efficient, in order to best meet the requirements of their clients. With the extensive range of options available, selecting the best Cloud Service Provider (CSP) has become a challenging dilemma for the majority of cloud clients. When evaluating services offered by many CSPs, it is important to consider multiple attributes. Efficiently addressing the selection of the best CSP involves tackling a challenging Multi-Attribute Decision Making (MADM) problem. Several MADM techniques have been proposed in academic literature for evaluating CSPs. However, the persisting problems of inconsistency, uncertainty, and rank reversal remain unresolved. In this paper the authors present a hybrid MADM framework to rank eight CSPs using nine Quality of Service (QoS) attributes. In order to achieve this objective, Fermatean fuzzy sets-full consistency method (FFS-FUCOM) is combined with Grey-Relational-Analysis and the Technique-for-Order-Preference-by-Similarity-to-Ideal-Solution (Grey-TOPSIS) technique. The framework successfully resolved the aforementioned problems. Sensitivity analysis is conducted to assess the stability and robustness of the results produced by the proposed framework. The sensitivity analysis results indicate that the proposed framework offers an accurate and robust solution. A systematic ranking test is undertaken to ensure that the results are ranked in a systematic manner. Additionally, a comparative analysis is carried out with the most relevant study.

Dynamic Power Consumption in Base Transceiver Station in Urban and Rural Setting in Awka, Nigeria using Multi-Attribute Decision-Making Technique

The goal of this paper was to lower base transceiver station (BTS) dynamic power consumption. A multi-attribute decision-making technique was implemented that reflects the stochastic nature of cellular networks and guarantees cost-effective traffic generation and improved BTS power consumption performance. Every related candidate or attribute that is taken into consideration to help reduce power consumption is given a utility function, and the candidate with the highest utility value is chosen to meet the target. The Utility function that the Technique selects is the weighted sum of the normalized attributes. In contrast to the works of other authors, which lowered consumption by 20%, the developed dynamic power consumption model cut consumption to 25.14 percent. The two BTS of interest were measured, and the results showed that Mgbakwu BTS has two Peak (Busy) Hour periods: in the morning, 9.55Erlangs from 7.30am to 8.30am, and in the evening, 10.7Erlangs from 8.30pm to 9.30pm. The BTS is located in a rural/residential area. The BTS measurement and analysis for the UNIZIK temporary site revealed that it is located in a commercial/business setting with a morning peak (busy) hour period of 19.1 Erlangs between 10 and 11 a.m. 14.6 Erlangs is the afternoon peak hour, which runs from 3.30 to 4.30 p.m. The traffic generated in the BTS under various load situations is reflected in the relevant Power Consumption for both BTS.

Heuristic Path Search and Multi-Attribute Decision-Making-Based Routing Method for Vehicular Safety Messages

Efficient routing in urban vehicular networks is essential for timely and reliable safety message transmission, and the selection of paths and relays greatly affects the quality of routing. However, existing routing methods usually face difficulty in finding the globally optimal transmission path due to their greedy search strategies or the lack of effective ways to accurately evaluate relay performance in intricate traffic scenarios. Therefore, we present a vehicular safety message routing method based on heuristic path search and multi-attribute decision-making (HMDR). Initially, HMDR utilizes a heuristic path search, focusing on road section connectivity, to pinpoint the most favorable routing path. Subsequently, it employs a multi-attribute decision-making (MADM) technique to evaluate candidate relay performance. The subjective and objective weights of the candidate relays are determined using ordinal relationship analysis and the Criteria Importance Through Intercriteria Correlation (CRITIC) weighting methods, respectively. Finally, the comprehensive utility values of the candidate relays are calculated in combination with the link time and the optimal relay is selected. In summary, the proposed HMDR method is capable of selecting the globally optimal transmission path, and it comprehensively considers multiple metrics and their relationships when evaluating relays, which is conducive to finding the optimal relay. The experimental results show that even if the path length is long, the proposed HMDR method gives preference to the path with better connectivity, resulting in a shorter total transmission delay for safety messages; in addition, HMDR demonstrates faster propagation speed than the other evaluated methods while ensuring better one-hop distance and one-hop delay. Therefore, it helps to improve the performance of vehicular safety message transmission in intricate traffic scenarios, thus providing timely data support for secure driving.

Automotive brake friction composite materials using natural Grewia Optiva fibers

There have been growing concerns over using non-renewable resources while manufacturing goods and related environmental laws worldwide. As part of efforts to reduce dependence on non-renewable resources, the uses of natural resources in brake friction materials are gaining prominence. Therefore, a natural fiber from the Himalayan region, Grewia Optiva, was used in the present study to develop a sustainable material for automotive braking applications. Brake friction composite materials were manufactured with various amounts (0, 2.5, 5, 7.5, and 10 wt%) of Grewia Optiva fiber. The composites were evaluated for physicochemical and mechanical characterization, tribological properties, and noise propensity. The friction performance remains comparable for all composites between 0.41 and 0.44, while a 9–13% reduction in the specific wear rate was obtained for the ≥7.5 wt% Grewia Optiva fiber added to the composites. Fade-recovery performance improved significantly with increasing fiber amount, while friction fluctuations remained the lowest for the composite with 7.5 wt% Grewia Optiva fiber content. At the same time, the minimal stick-slip power was associated with the composite having no Grewia Optiva fiber content. Therefore, a multiattribute decision-making technique was employed to evaluate the overall performance of all the composites suggesting 7.5 wt% Grewia Optiva fiber as the optimal content.

Identification and classification of digital green innovation based on interaction Maclaurin symmetric mean operators by using T-spherical fuzzy information

The digital green concept refers to the devotion to digital technology, i.e., techniques of procedures in the area of ecological or sustainable conservation. It contains leveraging digital techniques, procedures, and new tools to evaluate environmental problems and promote sustainable development. The major influence of this article is to evaluate the selection of the best digital green technology. For this, we aim to propose the idea of Maclaurin symmetric mean (MSM) operators based on interaction operational laws for T-spherical fuzzy (TSF) information, such as TSF interaction weighted averaging (TSFIWA), generalized TSF interaction weighted averaging (GTSFIWA), TSF interaction weighted geometric averaging (TSFIWGA), TSF interaction MSM (TSFIMSM), TSF interaction Bonferroni mean (TSFIBM), and TSF interaction weighted Maclaurin symmetric mean (TSFIWMSM) operators. Some dominant and reliable properties are also invented for evaluation. Moreover, to address the best digital green innovation (DGI) among the top five DGIs, we illustrate the procedure of the multi-attribute decision-making (MADM) technique under the presence of the derived operators. Finally, we demonstrate a numerical example for evaluating the comparative study between the proposed and existing or prevailing operators to enhance the worth of the derived theory.

Novel intuitionistic fuzzy Aczel Alsina Hamy mean operators and their applications in the assessment of construction material

Aggregation operators (AOs) are utilized to overcome the effects of attributes under some specific degree of weight in the decision-making (DM) process. The AOs have a large capacity to deal with uncertain and unpredictable information in multi-attribute decision-making (MADM) problems. The Hamy mean (HM) aggregation tools are well-known aggregation models, which are utilized to define correlation among different input arguments adequately. The intuitionistic fuzzy (IF) sets (IFS) can express unpredictable and vague information. The Aczel Alsina aggregation expressions are extensions of triangular norms. Recently, Aczel Alsina aggregation tools attained a lot of attentions from numerous research scholars. By inspiring the robustness and reliability of Aczel Alsina aggregation tools, we expose some appropriate operations of Aczel Alsina expressions under consideration of IF information. In this manuscript, we developed an intuitionistic fuzzy Aczel Alsina HM (IFAAHM) and an intuitionistic fuzzy Aczel Alsina weighted HM (IFAAWHM) operator. We also expressed the theory of Dual HM (DHM) tools and established a series of new approaches including intuitionistic fuzzy Aczel Alsina Dual HM (IFAADHM) and intuitionistic fuzzy Aczel Alsina weighted Dual HM (IFAAWDHM) operators. Some reliable characteristics and special cases of our derived approaches are also presented. The authors solved an application of a MADM technique under consideration of our derived approaches. To check the reliability and dependency of our derived mythologies, we gave an experimental case study to evaluate a desirable construction material based on some specific criteria of different Alternatives. To see the advantages and compatibility of our derived approaches, by comparing the results of existing approaches with the results of currently discussed AOs.

Identification and Classification of Multi-Attribute Decision-Making Based on Complex Intuitionistic Fuzzy Frank Aggregation Operators

Invented by Frank in 1979, Frank’s t-norm and t-conorm operations possess improved modifications and can be applied more generally than the existing algebraic t-norm and t-conorm. The major objective of this article is to determine Frank’s operational laws based on complex intuitionistic fuzzy (CIF) information. Moreover, we examine the Frank aggregation operators (averaging and geometric) based on CIF set theory and Frank operational laws, such as the CIF Frank weighted averaging (CIFFWA) operator, CIF Frank ordered weighted averaging (CIFFOWA) operator, CIF Frank hybrid averaging (CIFFHA) operator, CIF Frank weighted geometric (CIFFWG) operator, CIF Frank ordered weighted geometric (CIFFOWG) operator and CIF Frank hybrid geometric (CIFFHG) operator. Some dominant and feasible properties of the invented techniques are also stated. Additionally, to evaluate the problem of osteoporosis in human bodies based on their causes and risk factors, we illustrate an application of the multi-attribute decision-making (MADM) technique with consideration of the invented methods to show the supremacy and validity of the derived techniques. Finally, we aim to compare the proposed scenarios with some valid existing or prevailing techniques to increase the value of the presented approaches.

Novel Fermatean Fuzzy Aczel–Alsina Model for Investment Strategy Selection

For choosing the optimal option for multiple issues, the multiattribute decision-making (MADM) technique within a Fermatean fuzzy environment is a well-known and significant method. This paper presents a novel superiority inferiority ranking (SIR) approach for Fermatean fuzzy sets in group decision-making using multicriteria to reduce investment risk. This approach aims to evaluate the strategies for selecting the optimal investment company. The SIR method is depicted, and its effectiveness in decision-making is explored. In this manuscript, we develop new types of Aczel–Alsina operations on the Fermatean fuzzy environment and Fermatean Fuzzy Aczel–Alsina (FF-AA) average aggregation operators, including their properties such as idempotency, monotonicity, and boundedness. Further, we introduce a Fermatean fuzzy Aczel–Alsina weighted average closeness coefficient (FF-AA-WA-CC) aggregation operator (AO) based on the closeness coefficient for MAGDM issues. By utilizing the proposed technique, we solve a numerical example of an MAGDM problem. The results show that this approach is accurate and practical, and consistent with a realistic investment circumstance. A demonstration was created to emphasize the significance and credibility of this approach and assess its validity by comparing its outcomes with the established methods.

A hybrid multi-attribute decision-making and data envelopment analysis model with heterogeneous attributes: The case of sustainable development goals

This study presents an integrated multi-attribute decision-making (MADM) and data envelopment analysis (DEA) framework for solving problems with heterogeneous attributes. We classify the heterogeneous attributes into desirable and undesirable classes and provide a model for aggregating the attributes’ weights and the alternatives’ scores. The proposed model is initially designed as a Multiple Objective Decision Making (MODM) problem with a Data Envelopment Analysis (DEA) policy and then reformulated as a linear programming model tackled through a goal programming approach. We apply the proposed model to a set of European countries based on their fulfillment of the 17 Sustainable Development Goals (SDGs) defined by the United Nations. We show the proposed approach minimizes computational efforts and complexities and maximizes the participation and satisfaction of decision-makers. We compare the rankings derived from our model with those obtained from standard MADM techniques such as Euclid and TOPSIS. We illustrate how the different normalization methods are applied to condition the discrimination power of the models and analyze the reversals triggered by TOPSIS relative to the other techniques. We conclude by noting that our model does not rely on the weights defined by the experts to determine the ranking, which constitutes a significant advantage over the standard MADM techniques in strategic evaluation environments.

Generalized Heronian Mean Operators Based on Archimedean T-Norms of the Complex Picture Fuzzy Information and Their Application to Decision-Making

Complex picture fuzzy set is a special picture fuzzy set where the truth, abstinence, and falsity grades are shown by a complex number and can effortlessly illustrate the problem and inconsistency in the genuine world. T-norm and t-conorm play an essential and beneficial role in the environment of fuzzy set theory; similarly, Archimedean t-norm and t-conorm have massive flexibility and dominancy in the information fusion procedure. The major contribution of this analysis is to explore the algebraic, Einstein, Hamacher, and Frank operational laws under the complex picture fuzzy set. Moreover, the principle of complex picture fuzzy Archimedean Heronian aggregation operator and complex picture fuzzy weighted Archimedean Heronian aggregation operator are also elaborated by using Archimedean t-norm and t-conorm. Additionally, by using the elaborated operators, a multiattribute decision-making technique is presented to elaborate the consistency and reliability of the explored works. Finally, many examples are illustrated for discussing the advantages and sensitive analysis and graphical representation of the investigated works.