Determine Weights Of Criteria Research Articles

Bilateral Data Asset Matching in Digital Innovation Ecosystems: A Regret Theory Approach

This study addresses the bilateral matching of data assets with expected levels in digital innovation ecosystems, incorporating regret-avoidance behavior. First, given the potential hesitation between two parties throughout the matching process, expressing preference information using probability hesitant fuzzy sets is reasonable. Second, the Lance scoring function best captures the gap in expectation and satisfaction between the matching parties. Based on regret theory, we develop a matching strategy that considers both parties’ utilities and satisfaction levels. We construct an optimization model to determine criteria weights using a novel Lance distance metric. Subsequently, a multi-objective optimization model is formulated to maximize satisfaction while ensuring stability in the supply–demand matching process. A numerical example underscores the suggested method's effectiveness and shows its practical applicability in data asset matching scenarios. This study advances the field by integrating psychological factors and sophisticated fuzzy set theory into the decision-making process for allocating data assets in digital ecosystems.

Supporting multi-criteria decision-making processes with unknown criteria weights

Decision support systems are crucial in today’s tech-driven world, assisting decision-makers with complex choices. Determining criteria weights is a paramount aspect, significantly influencing outcomes. Traditionally, criteria weights are derived from objective measures, subjective expert knowledge, or a combination of both, each with its own strengths and limitations. This paper presents a novel approach for addressing unknown criteria relevance by systematically generating weight vectors, thus exploring a broader decision problem space. The proposed methodology is adaptable to various multi-criteria methods, enhancing its applicability across different scenarios. Its effectiveness is empirically validated through two practical examples: Glomerular Filtration Rate (GFR) evaluation and bridge construction method selection, demonstrating its broad applicability. Comparative analysis with existing objective weighting techniques reveals the limitations of current approaches and highlights the improved decision-making capabilities enabled by the proposed method. This research addresses a critical gap in the reliability and robustness of existing methods, particularly in situations with unknown criteria weights. Key contributions include a new decision-making methodology and an innovative ranking formulation using fuzzy sets, with empirical verification strengthening the utility of the approach. This paper offers a promising solution for advancing multi-criteria decision analysis, especially in complex scenarios with uncertain criteria relevance.

Fuzzy RANCOM: A novel approach for modeling uncertainty in decision-making processes

Multi-Criteria Decision Analysis (MCDA) methods are essential for addressing real-world challenges in the dynamic field of decision support technology. As technology advances, the expanding variety of multi-criteria evaluation methods highlights the critical importance of method selection for reliable results. These methods can be applied to scenarios involving both precise data and uncertainties. Expert knowledge is relevant in navigating real-world decision problems, particularly in uncertain environments where judgment inaccuracies can create challenges. Determining criteria weights is a pivotal step, as it significantly influences final outcomes and provides a nuanced understanding of each factor's impact on the evaluation.This paper addresses the pressing need for methods that account for uncertainty and effectively reduce the impact of inaccuracies in expert judgment. To this end, we introduce the Fuzzy RANking COMparison (RANCOM) method, a novel fuzzy subjective weighting approach that extends the advantages of the original RANCOM method to manage uncertainty. Using Triangular Fuzzy Numbers (TFNs), the proposed extension maintains simplicity, rapid execution, and flexibility in establishing criteria relationships. Key contributions of this paper include the development of the Fuzzy RANCOM method and a comparative analysis with the Fuzzy Analytical Hierarchy Process (AHP) method. Through multiple simulations, the study examines the operational dynamics of these methods, offering a valuable tool for decision-makers, especially in contexts where expert judgments may be prone to inaccuracies. The development of the Fuzzy RANCOM method provides a robust solution, equipping decision-makers with an effective tool to determine criteria weights while minimizing the impact of potential judgment errors.

Analyzing New Quality Productive Forces in New Energy Vehicle Companies Based on a New Multi-Criteria Decision Analysis Model

Assessing the new quality productive forces (NQPF) of new energy vehicle (NEV) companies is crucial for promoting the sustainable development of the NEV industry. This paper systematically evaluated and analyzed the NQPF of Chinese listed NEV companies from 2018 to 2022 using a novel multi-criteria decision analysis (MCDA) model. To address limitations in traditional MCDA models, such as unbalanced weight distribution, insufficient ranking differentiation, and incomplete identification of key influencing factors, this study introduced a new model, IDOCRIW-PROBID (integrated determination of objective criteria weights—preference ranking on the basis of ideal-average distance). First, an evaluation index system tailored to NEV companies’ NQPF was developed. Then, the IDOCRIW method was used to objectively assign weights to the indicators, enhancing the scientific rigor of the weight distribution. The PROBID method was employed to rank companies based on their NQPF, identifying differences between them. Additionally, an obstacle degree model was introduced to analyze key influencing factors, compensating for the traditional MCDA model’s limitations in this regard. The results showed, first, that the proposed IDOCRIW-PROBID model has a high degree of consistency with the classical Entropy-TOPSIS (technique for order of preference by similarity to ideal solution) model in terms of ranking the results (correlation coefficient = 0.91), and that IDOCRIW-PROBID offers higher differentiation compared to other MCDA models, validating its reliability and superiority. Second, during the study period, the development levels of NQPF in Chinese listed NEV companies varied significantly, with most companies at a low level of development and showing a downward trend, indicating that companies face considerable challenges in improving their NQPF. Third, the obstacle degree analysis revealed that R&D lease fees, R&D depreciation and amortization, and direct R&D investment were the primary factors hindering NQPF growth. This research provides theoretical support and decision-making insights for strategic optimization in NEV companies and informs government policy formulation.

Decision Analysis Algorithm Using Frank Aggregation in the SWARA Framework with p,qRung Orthopair Fuzzy Information

The present study introduces an innovative approach to multi-criteria decision making (MCDM) aimed at handling decision analysis involving p,qrung orthopair fuzzy (p,qROF) data, where the criteria weights are completely unknown. To achieve this objective, we formulate generalized operational rules referred to as Frank operational rules, tailored for p,qROF numbers (p,qROFNs) utilizing the Frank t-norm and t-conorm. With these newly devised operations as a foundation, we create a variety of p,qROF aggregation operators (AOs) to effectively aggregate p,qROF information. Furthermore, we examine specific instances of these operators and rigorously establish their desirable properties, including idempotency, monotonicity, boundedness, and symmetry. Subsequently, we adapt the SWARA technique to the realm of p,qROF fuzzy data and this adapted technique becomes instrumental in determining criteria weights within the proposed MCDM framework centered around proposed AOs. We furnish a descriptive example to exemplify the practicality of the developed approach. Lastly, the effectiveness and soundness of our approach are underscored through both parameter analysis and a comparative evaluation.

Hydrogen energy storage technology selection through a cutting-edge probabilistic linguistic decision framework

As a viable alternative to traditional energy forms, hydrogen energy proves effective owing to its feasible cost and reduced pollution. The storage of such a renewable energy source is essential for ensuring energy security and promoting sustainability. However, earlier studies on energy storage technology (EST) selection cannot handle complex linguistic expressions and hesitation during the decision process. Motivated by the issue, a probabilistic linguistic decision approach is developed in the present study to model linguistic expressions in daily conversations effectively. Besides, a new integrated approach is introduced by considering the regret factor for expert weight determination, weighted Cronbach’s approach for criteria weight determination, and a novel ranking procedure with a weighted approximation for prioritizing ESTs. A case example is exemplified by considering nine criteria and six ESTs to clarify the usefulness and practicality of the proposed framework. The main novelty/benefits of the study are: (i) handle uncertainty better; (ii) capture interrelationship among criteria; (iii) reduce bias by methodically determining the importance of experts; and (iv) provide a personalized ranking of ESTs. Findings depict that total cost is the foremost driver for hydrogen EST selection, while pressure cylinder storage is the most viable technology. Finally, the benefits and usefulness of the study are realized through sensitivity and comparison analyses. This study can guide and assist energy officials, academicians, governments, and other stakeholders facing hydrogen EST selection issues.

A Novel Group Decision Making Model to Compare Online Shopping Platforms

Over the years, E-commerce industry has been witnessing a phenomenal growth, thanks to rapid technological advancement in Industry 4.0. There has been a standout surge in the use of various online shopping platforms (OSP) for daily use. The recent pandemic has accelerated the growth trajectory and made a transformational change in the digital commerce landscape. As a result, there has been a proliferation of OSPs in the competitive domain. It is therefore pertinent to address the questions: How do the customers select their favorite OSP? To what extent the OSPs differ based on consumers’ preferences? The present work addresses these questions by proposing a novel group decision making framework. The ongoing study provides several innovative extensions of multi criteria decision making models like Borda count, criteria importance assessment (CIMAS), modified preference selection index (MPSI), and root assessment method (RAM). In this paper, the researchers provide a novel use of the Borda count method, integrated with CIMAS for determining criteria weights utilizing ranking of the criteria. Further, a novel extension of MPSI and RAM has been made with multiple normalizations. In this paper, the authors demonstrate a rare combination of vector and non-linear normalization using the Heron mean. The present paper derives the final criteria weights by combining Borda count, CIMAS and multi-normalization based MPSI (MNMPSI) using Bayesian logic. The criteria are selected based on Uses and Gratification theory (UGT). The findings reveal that interactive app interface and features (C16), user-friendly interface and search (C13), convenience in shopping (C14), product availability and variety (C12) and discounts and offers (C8) exert significant influence in selecting the OSP. Further, it is observed that Flipkart (A2) and Amazon (A1) are the top performers in the eyes of the users. The stability and reliability of the proposed methodology are examined by conducting a sensitivity analysis and comparing with several other models. The robustness of the proposed methodology and practical relevance of the findings of the present work shall provide notable impetus to the analysts and strategic decision-makers.

Sustainable supplier selection in the apparel industry: an integrated AHP-TOPSIS model for multi-criteria decision analysis

PurposeIn the apparel industry, suppliers play a significant role, directly affecting customer service levels and business profits. Integrating sustainable requirements into supplier selection not only aligns with global environmental goals but also enhances business performance, social responsibility and overall industry well-being. This study aims to design a multi-criteria model to evaluate and select the most sustainable suppliers in the fashion industry, trying to balance the conflicts in the set of sustainable development criteria.Design/methodology/approachThe integration of analytic hierarchy process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) offers advantages in sustainable supplier selection within the apparel industry. The AHP plays a crucial role in engaging multiple decision-makers with conflicting criteria to reach a consensus during the decision-making process. Conversely, the TOPSIS is used to compute alternative ratings. By simultaneously determining criteria weights and incorporating stakeholder preferences, hybrid models enhance decision-making strength and overcome limitations observed in classical multi-criteria decision-making techniques.FindingsThis research identified and classified 16 critical criteria impacting the selection of apparel industry suppliers, focusing on sustainable development. The criteria were weighted, providing a robust statistical foundation for the selection model. The results indicated that the most influential criteria were staff training, production capability, flexibility and practice of recycling. The proposed sustainable supplier selection model explains to decision-makers how criteria influence supplier ranking results compared to traditional models, supporting managers in making informed and sustainable supply chain decisions through continuous updates and enhancements.Originality/valueThis research provides new insight into the weighted impact of factors related to sustainable supplier selection in the apparel industry. The combination of a precise process and scientific knowledge will improve the quality of sustainable supplier selection.

MEREC-MABAC method based on cumulative prospect theory for picture fuzzy sets: Applications to wearable health technology devices

Since there is a causal connection between the performance of the alternative with criteria removed and the assessment of the criteria weights, Method based on the Removal Effects of Criteria (MEREC) can reflect the objectivity of statistical data from this new perspective. Multi-Attributive Border Approximation area Comparison (MABAC) approach considers the subjective psychological characteristics of decision makers (DMs), particularly personal preferences and cognitive limitations, through expert scoring. Cumulative prospect theory (CPT) takes into account both potential gains and losses. We propose applying the MEREC method to picture fuzzy sets (PFS) for the first time to determine criteria weights. We suggest an alternate ranking approach for the CPT-MABAC algorithm based on the Hamming distance of the picture rejection membership degree that corresponds to four behavioral states: acceptance, opposition, abstention, and rejection. We develop the PFS-MEREC-CPT-MABAC evaluation framework to tackle the multiple attribute decision-making (MADM) problems while evaluating the performance of wearable health technology devices (WHTDs). The model achieves a compromise between objectivity and subjectivity as well as capturing the psychological behavior of the experts. Finally, in order to determine the soundness and effectiveness of this integrated research approach, sensitivity and comparison analysis are done to compare the results of its operation with those of existing models.

A novel BWM-entropy-COPRAS group decision framework with spherical fuzzy information for digital supply chain partner selection

The transformation and upgrading of traditional supply chain models through digital technology receive widespread attention from the fields of circular economy, manufacturing, and sustainable development. Enterprises need to choose a digital supply chain partner (DSCP) during the process of digital transformation in uncertain and sustainable environments. Thus, the research constructs an innovative decision methodology for selecting the optimal DSCP to achieve digital transformation. The proposed methodology is propounded based upon the entropy measure, generalized Dombi operators, integrated weight-determination model, and complex proportional assessment (COPRAS) method under spherical fuzzy circumstances. Specifically, a novel entropy measure is proposed for measuring the fuzziness of spherical fuzzy (SF) sets, while generalized Dombi operators are presented for fusing SF information. The related worthwhile properties of these operators are discussed. Further, an integrated criteria weight-determination model is presented by incorporating objective weights obtained from the SF entropy-based method and subjective weights from the SF best worst method. Afterward, an improvement of the COPRAS method is proposed based on the presented generalized Dombi operators with SF information. Lastly, the practicability and validity of the proposed methodology are verified by an empirical study that selects an appropriate DSCP for a new energy vehicle enterprise to finish the goal of digital transformation. The sensitivity and comparative analysis are carried out to illustrate the stability, reliability, and superiority of the propounded methodology from multiple perspectives. The results and conclusions indicate that the propounded method affords a synthetic and systematic uncertain decision-making framework for identifying the optimal DSCP with incomplete weight information.

A CRITIC-CODAS Approach for Ranking WirelessCommunication Technologies in Precision Agriculture: Application to Irrigation System

This study evaluates and ranks wireless communication technologies for agricultural irrigation systems using the CRITIC-CODAS multi-criteria decision-making method. Technologies including WSN, LPWAN, LoRa, 5G, IoT, and NB-IoT are compared based on range, power consumption, data rate, coverage, latency, battery life, and device density. The CRITIC method is used to objectively determine criteria weights, with data rate, latency, and battery life emerging as the most important factors. 5G ranks highest with its superior data rate and device density, but its high-power needs may limit suitability for remote agriculture. IoT offers a balanced option across multiple criteria, while WSN excels in power efficiency and battery life. LPWAN, LoRa, and NB-IoT provide excellent range and battery life for wide-area, low-power applications despite lower data rates. The analysis provides a framework for stakeholders to select appropriate technologies based on specific agricultural requirements. Matching wireless technologies to irrigation needs can enhance agricultural sustainability and productivity. Further research could explore technology combinations, cost factors, and real-world testing. This systematic evaluation approach can be extended to other smart agriculture applications to optimize technology adoption.

Last Word in Last-Mile Logistics: A Novel Hybrid Multi-Criteria Decision-Making Model for Ranking Industry 4.0 Technologies

The complexity, increasing flow number and volumes, and challenges of last-mile logistics (LML) motivate or compel companies, authorities, and the entire community to think about ways to increase efficiency, reliability, and profits, reduce costs, reduce negative environmental impacts, etc. These objectives can be met by applying Industry 4.0 (I4.0) technologies, but the key question is which one. To solve this task, this paper used an innovative method that combines the fuzzy analytic network process (fuzzy ANP) and the fuzzy axial-distance-based aggregated measurement (fuzzy ADAM) method. The first was used for determining criteria weights and the second for selecting the best variant. The best solution is e/m-marketplaces, followed by cloud-computing-supported management and control systems and blockchain. These results indicate that widely adopted and implemented technologies are suitable for last-mile logistics. Newer technologies already producing significant results have serious potential for further development in this area. The main novelties and contributions of this paper are the definition of a new methodology based on multi-criteria decision-making (MCDM) methods, as well as its application for ranking I4.0 technologies for LML.

Evaluation and selection of E-learning websites using intuitionistic fuzzy confidence level based Dombi aggregation operators with unknown weight information

In recent years, the surge in online learning has eclipsed traditional classroom teaching, elevating the prominence of e-learning platforms. However, the quest for a reliable methodology to evaluate these platforms has remained pressing. While several studies have explored this domain, none have integrated decision experts’ confidence levels. This study bridges this gap by seamlessly incorporating confidence levels into Dombi aggregation operators within an intuitionistic fuzzy framework. The study introduces two innovative operators: the confidence-level intuitionistic fuzzy Dombi weighted averaging operator (CIFDWA) and the confidence-level intuitionistic fuzzy Dombi weighted geometric operator (CIFDWG). These operators are employed to form a novel multi-attribute group decision-making (MAGDM) approach, which is demonstrated by applying them to select the optimal e-learning website in a real-world scenario. The “Stepwise Weight Assessment Ratio Analysis (SWARA)” method is utilized to determine criteria weights. The findings highlight the critical importance of sub-criteria such as topic diversity, pricing, content credibility, data security, and user interface simplicity. The analysis reveals Unacademy as the leading platform, closely followed by Byju’s. Through meticulous comparative analysis and sensitivity evaluations, we underscore the stability and coherence of the proposed model. The study’s novelty lies in its innovative approach to integrating confidence levels in multi-attribute group decision-making scenarios, promising broader applications across various real-world contexts. Educational advisers and management can leverage this methodology to empower students with informed choices.

A new integrated rough multi-criteria decision-making model for enterprise resource planning software selection.

Enterprise resource planning (ERP) is widely used to boost the total market power of businesses. The wrong selection is one of the key reasons why ERP installations fail. Due to the complexity of the business environment and the range of ERP systems, choosing an ERP system is a complex and time-consuming procedure. ERP alternatives may be assessed using several criteria, so the ERP selection process may be considered a multi-criteria decision-making (MCDM) problem. In this study, the rough best worst method (BWM) was used to determine criteria weights, while the newly developed rough integrated simple weighted sum product (WISP) was used to rank ERP alternatives. Results suggest that the SFT-4 coded software is regarded as the best option, followed by SFT-5, SFT-6, SFT-2, SFT-3, and SFT-1. Results of the newly developed rough WISP method are compared to those of existing rough techniques in the sensitivity analysis. The differences between them have been found to be negligible. The outcomes show how effectively developed rough BWM and WISP integrated method performs in terms of ERP selection with usability, accuracy, ease of use, and consistency. This study will help decision-makers in a context where ERP is implemented choose the best ERP software for different sectors.

An integrated cost based approach for warehouse performance evaluation: A new multiphase model

Warehouses represent key links in domestic and international commodity flows. The increasing shortage of workers and increasing costs on the one hand, and the increasing number and stricter demands of users on the other hand lead warehouse managers to realize their operations as efficiently as possible. A proposed model has an objective of enabling companies to monitor warehouse performance in an authoritative, reliable, and simple way and define appropriate corrective measures accordingly. The proposed empirical research consists of three stages, where in the first stage a combination of Principal Component Analysis-Data Envelopment Analysis methods was applied in order to determine efficient warehouses based on 90 decision making units. In the second phase, a completely new method called Interval Fuzzy Rough Pivot Pair-wise Relative Criteria Importance Assessment method used for determining criteria weights was developed and applied, which is one of the most important novelties of this study. In the last phase, the Interval Fuzzy Rough Measurement of Alternatives and Ranking according to the Compromise Solution method was applied to rank the alternatives. Twelve criteria were observed to evaluate 21 alternatives. Based on the results, it was concluded that salary stood out as the most important criterion, while amortization stood out as the least significant criterion. On the other hand, alternatives A9 and A10 stood out as the best-ranked alternatives while A1, A2, and A3 stood out as the least efficient ones. The paper provides clear scientific contributions that are reflected in the reduction of the gap that was observed after reviewing the literature where there is a lack of papers dealing with this task. Also, the combination of methods applied in the paper has not been used so far, so it can be said that this paper represents an excellent basis for further research. The model has practical contributions as it allows decision-makers to make quality decisions regarding the operation of their warehouses in different time periods or observation periods, as well as it represents a decision support tool that can be used for better warehouse management.

Three-way decision TOPSIS for food business location under a benefit-opportunity-cost-risk platform

This work holistically evaluates the factors that can aid decision makers in finding the optimal location for food businesses in developing economies. It integrates the analytic hierarchy process (AHP) in determining criteria weights (i.e. benefit, opportunity, cost, risk) and the newly introduced three-way decision – Technique for Order Preference by Similarity to Ideal Solution (3WD-TOPSIS) method in identifying the priority factors. Applying the AHP yields the assignment of more priorities to benefits and opportunities rather than costs and risks, reflecting the benefit – or opportunity-oriented attitudes of food businesses. Meanwhile, the implementation of 3WD-TOPSIS results in the identification of government regulations and restrictions, proximity to consumers, parking capacity, supply chain strategy, and socio-economic status as the most crucial location decision factors. Findings from the comparative analyses show a high agreement between the results and those of other comparable methods. Managerial insights from these findings are outlined in this work.

A Novel Hybrid Gray MCDM Model for Resilient Supplier Selection Problem

The current business climate has generated considerable uncertainty and disrupted supply chain processes. Suppliers have frequently been identified as the primary source of hazards responsible for supply chain disruptions. Using a strategic approach to supplier selection that prioritizes providers with resilience features, mitigating the risk exposure inherent in supply chains is possible. This study proposes a comprehensive gray multiple-criteria decision making (MCDM) method incorporating resilience attributes to supplier selection. To determine criteria weights, the gray PSI and gray BWM methodologies were used, and to evaluate and prioritize resilient providers, the gray MCRAT and gray COBRA methodologies were applied. According to the results obtained by the suggested methodology, the supplier that demonstrated the greatest degree of resilience was determined to be the provider categorized as SPIR 4. The sequential sequence of the SPIR numbers is as follows: SPIR 5, SPIR 1, SPIR 3, SPIR 2, and SPIR 6. The data demonstrate that the developed approach produced accurate results.

Impact of Normalization on Entropy-Based Weights in Hellwig's Method: A Case Study on Evaluating Sustainable Development in the Education Area.

Determining criteria weights plays a crucial role in multi-criteria decision analyses. Entropy is a significant measure in information science, and several multi-criteria decision-making methods utilize the entropy weight method (EWM). In the literature, two approaches for determining the entropy weight method can be found. One involves normalization before calculating the entropy values, while the second does not. This paper investigates the normalization effect for entropy-based weights and Hellwig's method. To compare the influence of various normalization methods in both the EWM and Hellwig's method, a study evaluating the sustainable development of EU countries in the education area in the year 2021 was analyzed. The study used data from Eurostat related to European countries' realization of the SDG 4 goal. It is observed that vector normalization and sum normalization did not change the entropy-based weights. In the case study, the max-min normalization influenced EWM weights. At the same time, these weights had only a very weak impact on the final rankings of countries with respect to achieving the SDG 4 goal, as determined by Hellwig's method. The results are compared with the outcome obtained by Hellwig's method with equal weights. The simulation study was conducted by modifying Eurostat data to investigate how the different normalization relationships discovered among the criteria affect entropy-based weights and Hellwig's method results.

Testing the suitability of vector normalization procedure in topsis method: application to wheel loader selection

The object of the research consists of testing the suitability of the vector normalization procedure (NP) in the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) method. One of the most problematic steps of the Multi-Criteria Decision Making (MCDM) process is related to the application of NPs by default to transform different measurement units of criteria into a comparable unit. This is because of the absence of a universal agreement that defines which NP is the most suitable for a given MCDM method. In the literature, there are thirty-one available NPs, each one of them has its strengths and weaknesses and, accordingly, can efficiently be applied to an MCDM method and even worst to another. Let’s note that many NPs (e. g., NPs of sum, max-min, vector, and max) have been used by default (i. e., without suitability study) in the TOPSIS method. Consequently, outcomes of multi-criteria evaluation and rankings of alternatives considered in the decision problems could have led to inconsistent solutions, and, therefore, decision-makers could have made irrational or inappropriate decisions. That’s why suitability studies of NPs become indispensable. Moreover, a description of the methodology, proposed in this research, is outlined as follows: 1) method of weighting based on an ordinal ranking of criteria and Lagrange multiplier (for determining criteria weights); 2) TOPSIS method (for ranking considered alternatives); 3) a statistical approach with 3-estimate (for comparing effects generated by the used NPs). In the research, twelve different NPs are compared to each other in the TOPSIS method via a numerical example, which deals with the wheel loader selection problem. The results of the comparison indicate that, amongst the twelve different NPs analyzed in this suitability study, vector NP has the lesser effect on the considered alternatives’ evaluation outcomes, when used with the TOPSIS method. The vector NP-TOPSIS approach can therefore be applied to solve multi-criteria decision problems. Its application further allows the decision-makers and users to better select efficient solutions and, consequently, to make conclusive decisions.

Interval-valued T-spherical fuzzy extended power aggregation operators and their application in multi-criteria decision-making

Abstract As an effective tool to show the fuzziness of qualitative information, the interval-valued T-spherical fuzzy set can utilize three kinds of information, namely, membership, abstinence, and non-membership, to show the opinions of decision-maker. Given this advantage, many interval-valued T-spherical fuzzy multi-criteria decision-making (IVTSF-MCDM) methods have been designed. However, most of the existing IVTSF-MCDM methods have a common limitation that the inability to effectively show the impacts of extreme data. To address this limitation, this study develops a novel MCDM method based on interval-valued T-spherical fuzzy extended power aggregation operator. First, interval-valued T-spherical fuzzy cross-entropy (CE) and interval-valued T-spherical fuzzy symmetrical CE are defined to measure the difference between two interval-valued T-spherical fuzzy numbers, which are used to determine criteria weights in MCDM. Second, interval-valued T-spherical fuzzy extended power average operator and interval-valued T-spherical fuzzy extended power geometric operator are proposed, and their properties are investigated. Moreover, in view of that criteria may be assigned to different weights, this study defines interval-valued T-spherical fuzzy extended power weighted average operator and interval-valued T-spherical fuzzy extended power weighted geometric operator to derive the order of alternatives. Finally, the applicability of the proposed method is validated by the case about investment country selection, while the sensitivity and comparison analyses are also conducted to further prove its advantages and effectiveness.