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Recently, fractional differential equations have been used to model various physical and engineering problems. One may need a reliable and efficient numerical technique for the solution of these types of differential equations, as sometimes it is not easy to get the analytical solution. However, in general, in the existing investigations, involved parameters and variables are defined exactly, whereas in actual practice it may contain uncertainty because of error in observations, maintenance induced error, etc. Therefore, the purpose of this paper is to find the dynamic response of fractionally damped beam approximately under fuzzy and interval uncertainty.

Here, a semi analytical approach, variational iteration method (VIM), has been considered for the solution. A newly developed form of fuzzy numbers known as double parametric form has been applied to model the uncertainty involved in the system parameters and variables.

VIM has been successfully implemented along with double parametric form of fuzzy number to find the uncertain dynamic responses of the fractionally damped beam. The advantage of this approach is that the solution can be written in power series or compact form. Also, this method converges rapidly to have the accurate solution. The uncertain responses subject to impulse and step loads have also been computed and the behaviours of the responses are analysed. Applying the double parametric form, it reduces the computational cost without separating the fuzzy equation into coupled differential equations as done in traditional approaches.

Uncertain dynamic responses of fuzzy fractionally damped beam using the newly developed double parametric form of fuzzy numbers subject to unit step and impulse loads have been obtained. Gaussian fuzzy numbers are used to model the uncertainties. In the methodology using the alpha cut form, corresponding beam equation is first converted to an interval-based fuzzy equation. Next, it has been transformed to crisp form by applying double parametric form of fuzzy numbers. Finally, VIM has been applied to solve the same for the general fuzzy responses. Various numerical examples have been taken in to consideration.

In this paper, a mixture of exponential and Rayleigh distributions in the proportions α and 1 − α and all the parameters in the mixture distribution are estimated based on fuzzy data.

The methods such as maximum likelihood estimation (MLE) and method of moments (MOM) are applied for estimation. Fuzzy data of triangular fuzzy numbers and Gaussian fuzzy numbers for different sample sizes are considered to illustrate the resulting estimation and to compare these methods. In addition to this, the obtained results are compared with existing results for crisp data in the literature.

The application of fuzziness in the data will be very useful to obtain precise results in the presence of vagueness in data. Mean square errors (MSEs) of the resulting estimators are computed using crisp data and fuzzy data. On comparison, in terms of MSEs, it is observed that maximum likelihood estimators perform better than moment estimators.

Classical methods of obtaining estimators of unknown parameters fail to give realistic estimators since these methods assume the data collected to be crisp or exact. Normally, such case of precise data is not always feasible and realistic in practice. Most of them will be incomplete and sometimes expressed in linguistic variables. Such data can be handled by generalizing the classical inference methods using fuzzy set theory.

Fuzzy numbers are often used to represent non-probabilistic uncertainty in engineering, decision-making and control system applications. In these applications, fuzzy arithmetic operations are frequently used for solving mathematical equations that contain fuzzy numbers. There are two approaches proposed in the literature for implementing fuzzy arithmetic operations: the α-cut approach and the extension principle approach using different t-norms. Computational methods for the implementation of fuzzy arithmetic operations in different applications are also proposed in the literature; these methods are usually developed for specific types of fuzzy numbers. This chapter discusses existing methods for implementing fuzzy arithmetic on triangular fuzzy numbers using both the α-cut approach and the extension principle approach using the min and drastic product t-norms. This chapter also presents novel computational methods for the implementation of fuzzy arithmetic on triangular fuzzy numbers using algebraic product and bounded difference t-norms. The applicability of the α-cut approach is limited because it tends to overestimate uncertainty, and the extension principle approach using the drastic product t-norm produces fuzzy numbers that are highly sensitive to changes in the input fuzzy numbers. The novel computational methods proposed in this chapter for implementing fuzzy arithmetic using algebraic product and bounded difference t-norms contribute to a more effective use of fuzzy arithmetic in construction applications. This chapter also presents an example of the application of fuzzy arithmetic operations to a construction problem. In addition, it discusses the effects of using different approaches for implementing fuzzy arithmetic operations in solving practical construction problems.

The purpose of this paper is to investigate the influence of decision-makers’ (DM) risk bearing attitudes and the effect of the decision-making environment on estimating the overall degree of agility of an organization. The present study explores an extended agility model in a specific organization's hierarchy and reflects how decision-making attitudes alter an organizational agility scenario.

The concept of fuzzy logic has been explored in this paper. Based on DMs’ linguistic judgments, a fuzzy appropriateness rating as well as fuzzy priority weights have been determined for different levels of agile system hierarchy. Using a multi-grade fuzzy approach the overall agility index has been determined. The concept of fuzzy numbers ranking has been explored to show the effect of decision-making attitudes on agility estimations.

Decision-making attributes, e.g. the category of DM (neutral, risk-averse and risk-taking), affect the quantitative evaluation of the overall agility degree, which is correlated with a predefined agility measurement scale.

This study explores a triangular fuzzy membership function to express DMs’ linguistic judgments as fuzzy representations. Apart from triangular fuzzy numbers, trapezoidal and Gaussian fuzzy numbers may also be used for agility evaluation. The model may be used in other agile industries for benchmarking and selection of the best approach.

Selecting the right decision-making group to compute and analyze the agility level for a particular organization is an important managerial decision. In the case of benchmarking of various agile enterprises the decision-making group bearing the same attitude should be utilized.

Agile system modeling and development of agility appraisement platforms have been attempted by previous researchers while the influence of DMs’ risk bearing attitudes, and the effect of the decision-making environment on estimating the overall degree of agility, have rarely been studied. In this context, the authors explore an exhaustive agility model for implementing in a case study and reveal how decision-making attitudes alter organizational agility scenarios.

Smart grid is an integration between traditional electricity grid and communication systems and networks. Providing reliable services and functions is a critical challenge for the success and diffusion of smart grids that needs to be addressed. The purpose of this study is to determine the critical criteria that affect smart grid reliability from the perspective of users and investigate the role big data plays in smart grid reliability.

This study presents a model to investigate and identify criteria that influence smart grid reliability from the perspective of users. The model consists of 12 sub-criteria covering big data management, communication system and system characteristics aspects. Multi-criteria decision-making approach is applied to analyze data and prioritize the criteria using the fuzzy analytic hierarchy process based on the triangular fuzzy numbers. Data was collected from 16 experts in the fields of smart grid and Internet of things.

The results show that the “Big Data Management” criterion has a significant impact on smart grid reliability followed by the “System Characteristics” criterion. The “Data Analytics” and the “Data Visualization” were ranked as the most influential sub-criteria on smart grid reliability. Moreover, sensitivity analysis has been applied to investigate the stability and robustness of results. The findings of this paper provide useful implications for academicians, engineers, policymakers and many other smart grid stakeholders.

The users are not expected to actively participate in smart grid and its services without understanding their perceptions on smart grid reliability. Very few works have studied smart grid reliability from the perspective of users. This study attempts to fill this considerable gap in literature by proposing a fuzzy model to prioritize smart grid reliability criteria.

Aiming at the problems of poor accuracy and limitation in strength assessment of spot welding vehicle body caused by uncertain factors, such as key component size and nugget diameter, the numerical models of strength uncertainty analysis of spot-welded joints were constructed based on evidence theory and fuzzy theory.

Evidence theory and fuzzy theory are used to deal with the uncertainty of design parameter, and differential evolution algorithms are used to calculate the propagation process of uncertainty in this model. Furthermore, efficient relationship between the strength of welded joints and each design parameter is constructed by using response surface proxy model, which effectively avoids the problem of repeated complex finite element analysis in uncertainty analysis.

The results show that the constructed uncertainty numerical model is effective for the multiple uncertainties and give interval results under different probabilities and affiliations, which can more effectively evaluate the strength of the welded body structure to avoid overly conservative estimates for deterministic design.

The evidence theory is improved and combined with differential evolution algorithm and response surface method to effectively improve the computational efficiency. Based on the improved evidence theory and fuzzy algorithm, the numerical models for the uncertainty analysis of solder joint strength of welded structures are constructed and their feasibility is verified.

This paper aims to overcome the defect that the traditional clustering method is excessively dependent on initial clustering radius and also provide new technical measures for detecting the component content of lubricating oil based on the fuzzy neural system model.

According to the layers model of the fuzzy neural system model for the given sample data pair, the new clustering method can be implemented, and through the fuzzy system model, the detection method for the selected oil samples is given. By applying this method, the composition contents of 30 kinds of oil samples in lubricating oil are checked, and the actual composition contents of oil samples are compared.

Through the detection of 21 mineral elements in 30 oil samples, it can be known that the four mineral elements such as Zn, P, Ca and Mg have largest contribution rate to the lubricating oil, and they can be regarded as the main factors for classification of lubricating oil. The results show that the fuzzy system to be established based on sample data clustering has better performance in detection lubricant component content.

In spite of lots of methods for detecting the component of lubricating oil at the present, there is still no detection of the component of lubricating oil through clustering method based on sample data pair. The new nearest clustering method is proposed in this paper, and it can be more effectively used to detect the content of lubricating oil.

The purpose of this paper is to develop a multi-attribute group decision-making (MAGDM) method under the q-rung orthopair trapezoidal fuzzy environment, which calculates the interaction between the criteria depending on the proposed q-rung orthopair trapezoidal fuzzy aggregation Choquet integral (q-ROTrFACI) and employ TODIM (an acronym in Portuguese of Interactive and Multi-criteria Decision Making) to consider the risk psychology of decision-makers, to determine the optimal ranking of alternatives.

In MAGDM, q-rung orthopair trapezoidal fuzzy numbers (q-ROTrFNs) are efficient to indicate the quantitative vagueness of decision-makers. The q-ROTrFACI operator is defined and some properties are proved. Then, a novel similarity measure is developed by fusing the area and coordinates of the q-rung orthopair trapezoidal fuzzy function. Based on the above, a Choquet integral-based TODIM (CI-TODIM) method to consider the risk psychology of decision-makers is proposed and two cases are provided to prove superiority of the method.

The paper investigates q-ROTrFACI operator to productively solve problems with interdependent criteria. Then, an approach is proposed to determine the center point of q--ROTrFNs and a q-rung orthopair trapezoidal fuzzy similarity is constructed. Furthermore, CI-TODIM method is devised based on the proposed q-ROTrFACI operator and similarity in q-rung orthopair trapezoidal fuzzy context. The illustration example of business models' solutions and hypertension health management are given to demonstrate the effectiveness and superiority of proposed method.

The paper develops a novel CI-TODIM method that effectively solves the MAGDM problems under the premise of fully considering the priority of criteria and the risk preference of decision-makers, which provides guiding advantages for practical decision-making and enriches the application of decision-making theory.

The purpose of this study is to design a DSS for construction sectors, which can determine the status of the related supplier alternatives, accompanying G-T, SC measures and their interrelated metrics. In today’s era, a supplier is observed as significant among entire agents of green supply chain (SC) management. Presently, it is determined that appraising worth of the supplier under green-traditional (G-T), SCs concerns still require the support of novel algorithmic/decision support systems (DSSs), which could embrace potential decision-making.

The authors have proposed a DSS (consisting of the implementation of multi-level multi-criterion decision-making [ML-MCDM], reference point approach [RPA] and multi-objective optimization on the basis of simple ratio analysis [MOOSRA] methods on constructed MCDM supplier evaluation appraisement module) for measuring the performance score of clay-brick suppliers coming under G-T SCs corresponding to fuzzy and non-fuzzy information. A comparative analysis is conducted among the performance scores against alternatives, obtained by the three methods, i.e. ML-MCDM, RPA and MOOSRA, for robustly making a potential decision.

The presented research offers a DSS toward managers of construction sectors for benchmarking the performance scores against supplier alternatives under G-T SC measures and their interrelated metrics, modeled by fuzzy cum non-fuzzy information.

Presented research work exhibited a DSS that can be used by construction sectors for benchmarking the supplier alternatives in accordance with their performance scores under G-T SCs. The MCDM G-T supplier evaluation appraisement module is constructed pertaining to small-scale clay-brick production units, located in the northern part of India to check the effectiveness of the proposed DSS.

The lack of suitable indicators tailored to manufacturing industries’ needs, particularly to small and medium enterprises (SMEs), has been the major challenge to measure and manage industrial sustainability performance. This paper aims to empirically analyze and select the useful and applicable indicators to measure sustainability performance in the context of SMEs.

A systematic review was carried out to identify potential sustainability indicators from the literature. A questionnaire was designed based on the identified indicators and then pretested with the selected industrial experts, scholars, and researchers to further refine the indicators before data collection from the Italian footwear SMEs. Fuzzy Delphi method with consistency aggregation method was applied to analyze and select the final indicators.

The study’s findings show that the selected indicators emphasized measuring progress toward achieving industrial sustainability goals in terms of increasing financial benefits, reducing costs, improving market competitiveness, improving the effectiveness of resources utilization, and promoting the well-being of employees, customers and the community. In doing so, Italian footwear SMEs can contribute to achieving the Sustainable Development Goals (SDGs) by promoting health and well-being, promoting sustainable economic growth, providing productive employment and decent work, and ensuring responsible consumption and production.

The results of this study have significant social implications in terms of promoting the well-being of employees, customers, and the community.

By providing empirically supported indicators tailored to measure and manage sustainability performance in the context of SMEs, this paper contributes to the existing knowledge in the field of industrial sustainability performance measurement. Furthermore, it links the selected indicators to their respective SDGs to provide policy implications.