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Time modeling is a crucial feature in many application domains. However, temporal information often is not crisp, but is subjective and fuzzy. The purpose of this paper is to address the issue related to the modeling and handling of imperfection inherent to both temporal relations and intervals.

On the one hand, fuzzy extensions of Allen temporal relations are investigated and, on the other hand, extended temporal relations to define the positions of two fuzzy time intervals are introduced. Then, a database system, called Fuzzy Temporal Information Management and Exploitation (Fuzz-TIME), is developed for the purpose of processing fuzzy temporal queries.

To evaluate the proposal, the authors have implemented a Fuzz-TIME system and created a fuzzy historical database for the querying purpose. Some demonstrative scenarios from history domain are proposed and discussed.

The authors have conducted some experiments on archaeological data to show the effectiveness of the Fuzz-TIME system. However, thorough experiments on large-scale databases are highly desirable to show the behavior of the tool with respect to the performance and time execution criteria.

The tool developed (Fuzz-TIME) can have many practical applications where time information has to be dealt with. In particular, in several real-world applications like history, medicine, criminal and financial domains, where time is often perceived or expressed in an imprecise/fuzzy manner.

The social implications of this work can be expected, more particularly, in two domains: in the museum to manage, exploit and analysis the piece of information related to archives and historic data; and in the hospitals/medical organizations to deal with time information inherent to data about patients and diseases.

This paper presents the design and characterization of a novel and intelligent database system to process and manage the imperfection inherent to both temporal relations and intervals.

Many studies have proposed variant fuzzy time series models for uncertain and vague data. The purpose of this paper is to adapt a fuzzy time series combined with genetic algorithm (GA) to forecast tourist arrivals in Taiwan.

Different cases are studied to understand the effect of variation of fuzzy time series order, number of intervals and population size on the fitness function which decreases with increase in fuzzy time series order and number of fuzzy intervals, but do not have marginal effect due to change in population size.

Results based on an example of forecasting Taiwan’s tourism demand was used to verify the efficacy of proposed model and confirmed its superiority to existing models providing solutions for different orders of fuzzy time series, number of intervals and population size with a smaller forecasting error as measured by root mean square error.

This study provides a viable forecasting methodology, adapting a fuzzy time series combined with an evolutionary GA. The proposed hybridized framework of fuzzy time series and GA, where GA is used to calibrate fuzzy interval length, is flexible and replicable to many industrial situations.

The purpose of this paper is to provide a better method for quality management to maintain an essential level of quality in different fields like product quality, service quality, air quality, etc.

In this paper, a hybrid adaptive time-variant fuzzy time series (FTS) model with genetic algorithm (GA) has been applied to predict the air pollution index. Fuzzification of data is optimized by GAs. Heuristic value selection algorithm is used for selecting the window size. Two algorithms are proposed for forecasting. First algorithm is used in training phase to compute forecasted values according to the heuristic value selection algorithm. Thus, obtained sequence of heuristics is used for second algorithm in which forecasted values are selected with the help of defined rules.

The proposed model is able to predict AQI more accurately when an appropriate heuristic value is chosen for the FTS model. It is tested and evaluated on real time air pollution data of two popular tourism cities of India. In the experimental results, it is observed that the proposed model performs better than the existing models.

The management and prediction of air quality have become essential in our day-to-day life because air quality affects not only the health of human beings but also the health of monuments. This research predicts the air quality index (AQI) of a place.

The proposed method is an improved version of the adaptive time-variant FTS model. Further, a nature-inspired algorithm has been integrated for the selection and optimization of fuzzy intervals.

Investigation of the smoking model is important as it has a direct effect on human health. This paper focuses on the numerical analysis of the fractional order giving up smoking model. Nonetheless, due to observational or experimental errors, or any other circumstance, it may contain some incomplete information. Fuzzy sets can be used to deal with uncertainty. Yet, there may be some inconsistency in the membership as well. As a result, the primary goal of this proposed work is to numerically solve the model in a type-2 fuzzy environment.

Triangular perfect quasi type-2 fuzzy numbers (TPQT2FNs) are used to deal with the uncertainty in the model. In this work, concepts of r2-cut at r1-plane are used to model the problem's uncertain parameter. The Legendre wavelet method (LWM) is then utilised to solve the giving up smoking model in a type-2 fuzzy environment.

LWM has been effectively employed in conjunction with the r2-cut at r1-plane notion of type-2 fuzzy sets to solve the model. The LWM has the advantage of converting the non-linear fractional order model into a set of non-linear algebraic equations. LWM scheme solutions are found to be well agreed with RK4 scheme solutions. The existence and uniqueness of the model's solution have also been demonstrated.

To deal with the uncertainty, type-2 fuzzy numbers are used. The use of LWM in a type-2 fuzzy uncertain environment to achieve the model's required solutions is quite fascinating, and this is the key focus of this work.

In the initial stage of product design, product portfolio identification (PPI) aims to translate customer needs (CNs) into product specifications (PSs). This is an essential task, since understanding what customers really want is at the center of product design. However, design information is incomplete and design knowledge is minimal during this stage. Furthermore, PPI is often a confusing and frustrating task, especially when customer preferences are changing rapidly. To facilitate the task, the purpose of this paper is to capture the time-sensitive mapping relationship between CNs and PSs.

This paper proposes a design sequential pattern mining model to uncover implicit but valuable knowledge from chronological transaction records. First, CNs and PSs from these records are transformed and connected according to the transaction time. Second, procedures such as litemset generation, data transformation and pattern mining are conducted based on the AprioriAll algorithm. Third, the uncovered patterns are modified and applied by engineers.

Using the retrieved patterns, engineers can keep up with the dynamics of customer preferences with regard to different PSs.

Computational experiments on a case study of customization of desktop computers show that the proposed method is capable of extracting useful sequential patterns from a design database.

Considering the times tamps of the transactions, a sequential pattern mining-based method is proposed to extract valuable patterns. These patterns can help engineers identify market trends and the correlation among PSs.

Most projects are facing delays, and accelerating the pace of project progress is a necessity. Project managers are responsible for completing the project on time with minimum cost and with maximum quality. This study provides a trade-off between time, cost, and quality objectives to optimize project scheduling.

The current paper presents a new resource-constrained multi-mode time–cost–quality trade-off project scheduling model with lags under finish-to-start relations. To be more realistic, crashing and overlapping techniques are utilized. To handle uncertainty, which is a source of project complexity, interval-valued fuzzy sets are adopted on several parameters. In addition, a new hybrid solution approach is developed to cope with interval-valued fuzzy mathematical model that is based on different alpha-levels and compensatory methods. To find the compatible solution among conflicting objectives, an arithmetical average method is provided as a compensatory approach.

The interval-valued fuzzy sets approach proposed in this paper is denoted to be scalable, efficient, generalizable and practical in project environments. The results demonstrated that the crashing and overlapping techniques improve time–cost–quality trade-off project scheduling model. Also, interval-valued fuzzy sets can properly manage expressions of the uncertainty of projects which are realistic and practical. The proposed mathematical model is validated by solving a medium-sized dataset an adopted case study. In addition, with a sensitivity analysis approach, the solutions are compared and the model performance is confirmed.

This paper introduces a new continuous-based, resource-constrained, and multi-mode model with crashing and overlapping techniques simultaneously. In addition, a new hybrid compensatory solution approach is extended based on different alpha-levels to handle interval-valued fuzzy multi-objective mathematical model of project scheduling with influential uncertain parameters.

Train re-scheduling remains a longstanding challenge in railway operation. To design high-quality timetable in fuzzy environment, the purpose of this paper is to study train re-scheduling problem under the fuzzy environment, in which the fuzzy coefficients of the constraint resources have the fuzzy boundaries.

Based on the improved fuzzy linear programming, the train re-scheduling model is constructed. Aiming at dealing with the fuzzy characteristics of the constraint coefficients value range boundaries, the description method of this kind of objective function is proposed and the solving approach is presented. The model has more adaptability to model a common train re-scheduling problem, in which some resources of the constraints are uncertain and have the characteristics of fuzziness and the boundaries of the resources are fuzzy.

Two numerical examples are carried out and it shows that the model proposed in this paper can describe the train re-scheduling problem precisely, dealing with the fuzzy boundaries of the fuzzy coefficients of the constraint resources. And the algorithm present is suitable to solve the problem. The approach proposed in this paper can be a reference for developers of railway dispatching system.

It is the first time to study train re-scheduling problem under the fuzzy environment, in which the fuzzy coefficients of the constraint resources have the fuzzy boundaries.

The interval multi-objective optimization problems (IMOPs) are universal and vital uncertain optimization problems. In this study, an interval multi-objective grey wolf optimization algorithm (GWO) based on fuzzy system is proposed to solve IMOPs effectively.

First, the classical genetic operators are embedded into the interval multi-objective GWO as local search strategies, which effectively balanced the global search ability and local development ability. Second, by constructing a fuzzy system, an effective local search activation mechanism is proposed to save computing resources as much as possible while ensuring the performance of the algorithm. The fuzzy system takes hypervolume, imprecision and number of iterations as inputs and outputs the activation index, local population size and maximum number of iterations. Then, the fuzzy inference rules are defined. It uses the activation index to determine whether to activate the local search process and sets the population size and the maximum number of iterations in the process.

The experimental results show that the proposed algorithm achieves optimal hypervolume results on 9 of the 10 benchmark test problems. The imprecision achieved on 8 test problems is significantly better than other algorithms. This means that the proposed algorithm has better performance than the commonly used interval multi-objective evolutionary algorithms. Moreover, through experiments show that the local search activation mechanism based on fuzzy system proposed in this study can effectively ensure that the local search is activated reasonably in the whole algorithm process, and reasonably allocate computing resources by adaptively setting the population size and maximum number of iterations in the local search process.

This study proposes an Interval multi-objective GWO, which could effectively balance the global search ability and local development ability. Then an effective local search activation mechanism is developed by using fuzzy inference system. It closely combines global optimization with local search, which improves the performance of the algorithm and saves computing resources.

The purpose of this paper is to investigate the performance of a turbine structure of the oil and gas Egyptian company in terms of reliability, mean time to failure (MTTF), mean time to repair (MTTR) and mean time between failures (MTBF) under fuzzy environment and working criteria. This paper examines the impact of the failure of various components on the complete turbine structure of the oil and gas system.

To overcome the problem of uncertain behavior of available data for various components, the right triangular generalized fuzzy number (RTrGFN) is proposed to be taken into the account to express the uncertainty which attains some tolerance in data. Furthermore, reliability indices are calculated with the help of the Lambda Tau method and the arithmetic operations on right generalized triangular fuzzy numbers (RTrGFN).

This paper explores the reliability of a repairable 3 out of 4 structure of turbines and along with the other parameters namely MTTF, MTTR and MTBF; under a fuzzy environment. Failure rates and repair times are expected to be exponential. The ranking of components of the structure is being found to decide the priority for maintenance.

This paper investigates the performance of the system with different spread/tolerance like 15%, 25% and 50% of crisp data. It helps to predict realistic results in the range value. To enhance the system's performance, the most important item of the system requires greater attention. For this, the authors find the sensitive part by ranking. For ranking, an extended approach has been developed to find the sensitive unit of the system by using the right triangular generalized fuzzy number. This paper explores the most and least sensitive component of the system, which helps the maintenance department to plan the maintenance action.

The control charts are used in many production areas because they give an idea about the quality characteristic(s) of a product. The control limits are calculated and the data are examined whether the quality characteristic(s) is/are within these limits. At this point, it may be confusing to comment, especially if it is slightly below or above the limit values. In order to overcome this situation, it is suitable to use fuzzy numbers instead of crisp numbers. The purpose of this paper is to demonstrate how to create control limits of X ¯ -R control charts for a specified data set of interval type-2 fuzzy sets.

There are methods in the literature, such as defuzzification, distance, ranking and likelihood, which may be applicable for interval type-2 fuzzy set. This study is the first that these methods are adapted to the X ¯ -R control charts. This methodology enables interval type-2 fuzzy sets to be used in X ¯ -R control charts.

It is demonstrated that the methods – such as defuzzification, distance, ranking and likelihood for interval type-2 fuzzy sets – could be applied to the X ¯ -R control charts. The fuzzy control charts created using the methods provide similar results in terms of in/out control situations. On the other hand, the sample points depicted on charts show similar pattern, even though the calculations are different based on their own structures. Finally, the control charts obtained with interval type-2 fuzzy sets and the control charts obtained with crisp numbers are compared.

Based on the related literature, research works on interval type-2 fuzzy control charts seem to be very limited. This study shows the applicability of different interval type-2 fuzzy methods on X ¯ -R control charts. For the future study, different interval type-2 fuzzy methods may be considered for X ¯ -R control charts.

The unique contribution of this research to the relevant literature is that interval type-2 fuzzy numbers for quantitative control charts, such as X ¯ -R control charts, is used for the first time in this context. Since the research is the first adaptation of interval type-2 fuzzy sets on X ¯ -R control charts, the authors believe that this study will lead and encourage the people who work on this topic.