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The purpose of this paper is to create a numerical technique to tackle the challenge of selecting software reliability growth models (SRGMs).

A real-time case study with five SRGMs tested against a set of four selection indexes were utilised to show the functionality of TOPSIS approach. As a result of the current research, rating of the different SRGMs is generated based on their comparative closeness.

An innovative approach has been developed to generate the current SRGMs selection under TOPSIS environment by blending the entropy technique and the distance-based approach.

In any multi-criteria decision-making process, ambiguity is a crucial issue. To deal with the uncertain environment of decision-making, various devices and methodologies have been explained. Pythagorean fuzzy sets (PFSs) are perhaps the most contemporary device for dealing with ambiguity. This article addresses novel tangent distance-entropy measures under PFSs. Additionally, numerical illustration is utilized to ascertain the strength and authenticity of the suggested measures.

This study aims to research the influence mechanism of microtextured geometric parameters of dry gas seal end face on the tribological behavior under dry frictional conditions.

The microtexture was processed using laser processing, while the diamond-like carbon (DLC) film was applied through magnetron sputtering; the experimental platform of friction vibration was established, the frictional and vibrational properties of different geometric parameters were tested; the data signals of vibrational acceleration and frictional torque were collected and processed using data acquisition instrument. The entropy characteristic parameters of 3D vibrational acceleration were extracted based on wavelet packet decomposition method. The end-face topography was measured with ST400 three-dimensional noncontact surface topography instrument.

The geometry of pits plays a key role in influencing friction performance; the permutation entropy and fuzzy entropy of the vibration acceleration signal changed with variations in microtextured parameters. A textured surface with appropriately size parameters can trap debris, enhance the dynamic pressure effect, reduce impact between the friction interfaces and improve the frictional vibrational performance. In this research, microtextured surface with Φ150 µm-10% and Φ200 µm-5% can effectively reduce friction and vibration between the end faces of a dry gas seal.

DLC film improves the hardness of seal ring end face, and microtexture improves the dynamic effect; the tribological behavior monitoring can be realized by analyzing the characteristics of vibration acceleration sensitive parameter with friction state. The findings will provide a basis for further research in the field of tribology and the microtexture optimization of dry gas seal ring end face.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-12-2023-0389/

Water pipes degrade over time for a variety of pipe-related, soil-related, operational, and environmental factors. Hence, municipalities are necessitated to implement effective maintenance and rehabilitation strategies for water pipes based on reliable deterioration models and cost-effective inspection programs. In the light of foregoing, the paramount objective of this research study is to develop condition assessment and deterioration prediction models for saltwater pipes in Hong Kong.

As a perquisite to the development of condition assessment models, spherical fuzzy analytic hierarchy process (SFAHP) is harnessed to analyze the relative importance weights of deterioration factors. Afterward, the relative importance weights of deterioration factors coupled with their effective values are leveraged using the measurement of alternatives and ranking according to the compromise solution (MARCOS) algorithm to analyze the performance condition of water pipes. A condition rating system is then designed counting on the generalized entropy-based probabilistic fuzzy C means (GEPFCM) algorithm. A set of fourth order multiple regression functions are constructed to capture the degradation trends in condition of pipelines overtime covering their disparate characteristics.

Analytical results demonstrated that the top five influential deterioration factors comprise age, material, traffic, soil corrosivity and material. In addition, it was derived that developed deterioration models accomplished correlation coefficient, mean absolute error and root mean squared error of 0.8, 1.33 and 1.39, respectively.

It can be argued that generated deterioration models can assist municipalities in formulating accurate and cost-effective maintenance, repair and rehabilitation programs.

The decision-making to outsource and select the most suitable global manufacturing outsourcing partner (MOP) is complex and uncertain due to multiple conflicting qualitative and quantitative criteria as well as multiple alternatives. Vagueness and variability exist in ratings of criteria and alternatives by group of decision-makers (DMs). The paper provides a novel Stochastic Fuzzy (SF) method for evaluation and selection of agile and sustainable global MOP in uncertain and volatile business environment.

Four main selection criteria for global MOP selection were identified such as economic, agile, environmental and social criteria. Total 16 sub-criteria were selected. To consider the vagueness and variability in ratings by group of DMs, SF method using t-distribution or z-distribution was adopted. The criteria weights were determined using the Stochastic Fuzzy-CRiteria Importance Through Intercriteria Correlation (SF-CRITIC), while MOP selection was carried out using Stochastic Fuzzy-VIseKriterijumskaOptimizacija I KompromisnoResenje (SF-VIKOR) in the case study of footwear industry. Sensitivity analysis was performed to test the robustness of the proposed model. A comparative analysis of SF-VIKOR and VIKOR was made.

The worker’s wages and welfare, product price, product quality, green manufacturing process and collaboration with partners are the most important criteria for MOP selection. The MOP3 was found to be the best agile and sustainable global MOP for the footwear company. In sensitivity analysis, significance level is found to have important role in MOP ranking. Hence, the study concluded that integrated SF-CRITIC and SF-VIKOR is an improved method for MOP selection problem.

In a group decision-making, ambiguity, impreciseness and variability are found in relative ratings. Fuzzy variant Multi-Criteria Decision-Making methods cover impreciseness in ratings but not the variability. On the other hand, deterministic models do not cover either. Hence, the stochastic method based on the probability theory combining fuzzy theory is proposed to deal with decision-making problems in imprecise and uncertain environments. Most notably, the proposed model has novelty as it captures and reveals both the stochastic perspective and the fuzziness perspective in rating by group of DMs.

The proposed multi-criteria group decision-making model contributes to the sustainable and agile footwear supply chain management and will help the policymakers in selecting the best global MOP.

To the best of the authors’ knowledge, SF method has not been used to select MOP in the existing literature. For the first time, integrated SF-CRITIC and SF-VIKOR method were applied to select the best agile and sustainable MOP under uncertainty. Unlike other studies, this study considered agile criteria along with triple bottom line sustainable criteria for MOP selection. The novel method of SF assessment contributes to the literature and put forward the managerial implication for improving agility and sustainability of global manufacturing outsourcing in footwear industry.

The purpose of this article is to present the idea of a T-spherical hesitant fuzzy set associated with probability and to develop an extended multi-attributive border approximation area comparison (MABAC) method under probabilistic T-spherical hesitant fuzzy (Pt-SHF) settings.

The authors define some basic operational laws for Pt-SHF sets (Pt-SHFSs) and a comparison method of two probabilistic T-spherical hesitant fuzzy numbers (Pt-SHFNs) is proposed. Moreover, some Pt-SHF aggregation operators and the multi-attributive border approximation area comparison (MABAC) method are established under Pt-SHF scenario to solve group decision making problems.

The developed Pt-SHF MABAC method for multi-attribute group decision making (MAGDM) can overcome the drawbacks of conventional MABAC method and limitations for decision makers, which they face while providing their assessment concerning any object.

Clearly, this paper is devoted to MABAC method, MAGDM and probabilistic T-spherical hesitant fuzzy set theory.

The approach established can be used in a variety of scenarios, including decision making, engineering, and economics. An explanatory example is illustrated which shows the superiority and effectiveness of our proposed technique.

If a T-spherical fuzzy MAGDM problem under the probabilistic scenario needs to be evaluated, the involvement of probabilities in fuzzy system will be lost because of no information. This work fills a gap in literature by establishing the notion of probabilistic t-spherical hesitant fuzzy set to deal with the ambiguity, uncertainty in decision making problems.

Sustainability trends have changed the modus operandi in businesses even as the market environment becomes more socially conscious. However, relatively little research has been conducted on integrating social sustainability aspects with a focus on corporate social responsibility (CSR) into the selection of suppliers in the service sector, particularly the banking industry. In this paper, this study aims to propose a CSR decision support methodology to evaluate and prioritize socially responsible suppliers.

A novel integrated decision support methodology composed of Shannon Entropy and TOmada de Decisão Interativa e Multicritério (TODIM) methods is introduced. The Shannon-Entropy approach is used to estimate CSR factor weights, and TODIM is used to rank the suppliers, with the process completed in a group decision setting.

A Nigerian bank was used as a case study to test and show the usefulness of the CSR-based decision framework in evaluating and selecting socially responsible suppliers. The results show the topmost ranked suppliers that are recommended for future negotiations by the case (bank). The study will enable banks to select socially responsible suppliers, which could accelerate the attainment of sustainability objectives, protect their reputations and improve competitiveness.

This study pioneers the application of a novel decision methodology based on Shannon Entropy and TODIM in selecting socially sustainable suppliers in the Banking sector of an African emerging economy-Nigeria.

Platform-based enterprises, as micro-entities in the platform economy, have the potential to effectively promote the low-carbon development of both supply and demand sides in the supply chain. Therefore, this paper aims to provide a multi-criteria decision-making method in a probabilistic hesitant fuzzy environment to assist platform-type companies in selecting cooperative suppliers for carbon reduction in green supply chains.

This paper combines the advantages of probabilistic hesitant fuzzy sets (PHFS) to address uncertainty issues and proposes an improved multi-criteria decision-making method called PHFS-DNMEREC-MABAC for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Within this decision-making method, we enhance the standardization process of both the DNMEREC and MABAC methods by directly standardizing probabilistic hesitant fuzzy elements. Additionally, a probability splitting algorithm is introduced to handle probabilistic hesitant fuzzy elements of varying lengths, mitigating information bias that traditional approaches tend to introduce when adding values based on risk preferences.

In this paper, we apply the proposed method to a case study involving the selection of carbon emission reduction collaboration suppliers for Tmall Mart and compare it with the latest existing decision-making methods. The results demonstrate the applicability of the proposed method and the effectiveness of the introduced probability splitting algorithm in avoiding information bias.

Firstly, this paper proposes a new multi-criteria decision making method for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Secondly, in this method, we provided a new standard method to process probability hesitant fuzzy decision making information. Finally, the probability splitting algorithm was introduced to avoid information bias in the process of dealing with inconsistent lengths of probabilistic hesitant fuzzy elements.

Social media is widely used to capture citizens' opinions and topics deemed important. The importance or interest social media users attribute to a topic is traditionally measured by tweet frequency. This approach is practical but overlooks other user engagement tools such as retweets, likes, quotes, and replies. As a result, it may lead to a misinterpretation of social media signals. This paper aims to propose a method that considers all user engagement indicators and ranks the topics based on the interest attributed by social media users.

A multi-criteria decision-making framework was proposed, which calculates the relative importance of user engagement tools using objective (information entropy) and subjective (Bayesian Best-Worst Method) methods. The results of the two methods are aggregated with a combinative method. Then, topics are ranked based on their user engagement levels using Multi-Objective Optimization by Ratio Analysis.

The proposed approach was used to determine citizens' priorities in transport policy, and the findings are compared with those obtained solely based on tweet frequency. The results revealed that the proposed multi-criteria decision-making framework generated more comprehensive and robust results.

The proposed method provides a systematic way to interpret social media signals and guide institutions in making better policies, hence ensuring that the demands of users/society are properly addressed.

This study presents a systematic method to prioritize user preferences in social media. It is the first in the literature to discuss the necessity of considering all user engagement indicators and proposes a reliable method that calculates their relative importance.

This study aims to develop a cause-effect relationship between criteria that contribute to water security using the Intuitionistic Fuzzy-Decision-Making Trial and Evaluation Laboratory (IF-DEMATEL) method. Differently from the typical DEMATEL which utilizes crisp numbers, this modification introduces intuitionistic fuzzy numbers (IFNs) to enhance judgments in a group decision-making environment. In particular, the linguistic variables used in IF-DEMATEL are defined using the concept of three-tuple of IFNs.

Data with the linguistic variable “influence” were collected from a group of experts in water security via personal unstructured interviews. Seven water security criteria are considered in this study. Computational software was employed to execute the computational procedures of the IF-DEMATEL method. It is anticipated that by taking into account the hesitation degree of IFNs will reflect the scenario in real life, which could lead to precise decision-making.

The results show that “Over-Abstraction”, “Saltwater Intrusion” and “Limited Infrastructures” are the cause criteria that contribute to water security. In addition, the relationship map of influence shows that “Water Pollution” and “Rapid Urbanization” are the most vulnerable criteria as these two criteria are most easily affected by other criteria in a unidirectional relation.

It is anticipated that these findings will serve as useful references for water security management and policymakers.

The present study makes a noteworthy contribution to the modification of DEMATEL where three-tuple of intuitionistic fuzzy numbers are considered in the computations. The present study also provides additional evidence with respect to factors that contribute to water security.

This study aims to focus on sustainable supplier selection in a construction company considering a new multi-criteria decision-making (MCDM) method based on dominance-based rough set analysis. The inclusion of sustainability concept in industrial supply chains has started gaining momentum due to increased environmental protection awareness and social obligations. The selection of sustainable suppliers marks the first step toward accomplishing this objective. The problem of selecting the right suppliers fulfilling the sustainable requirements is a major MCDM problem since various conflicting factors are underplay in the selection process. The decision-makers are often confronted with inconsistent situations forcing them to make imprecise and vague decisions.

This paper presents a new method based on dominance-based rough sets for the selection of right suppliers based on sustainable performance criteria relying on the triple bottom line approach. The method applied has its distinct advantages by providing more transparency in dealing with the preference information provided by the decision-makers and is thus found to be more intuitive and appealing as a performance measurement tool.

The technique is easy to apply using “jrank” software package and devises results in the form of decision rules and ranking that further assist the decision-makers in making an informed decision that increases credibility in the decision-making process.

The novelty of this study of its kind is that uses the dominance-based rough set approach for a sustainable supplier selection process.