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The purpose of this research is to develop a new approach for analyzing the fuzzy reliability of a series and parallel system. Also to introduce definition of L‐R type interval valued triangular vague set and certain Tω‐based arithmetic operations between two L‐R type interval valued triangular vague sets.

In the proposed approach using a fault tree an interval valued vague fault tree is developed for the system in which the fuzzy reliability of each component of the system is represented by a L‐R type interval valued triangular vague set. Then with the help of a developed interval valued vague fault tree an algorithm is developed to analyze the fuzzy system reliability.

For numerical verification of the proposed approach the fuzzy reliability of the basement flooding has been analyzed using the existing approaches and the proposed approach. Comparing the results of existing approaches and the proposed approach, it has been shown that the uncertainty about the reliability is minimized using the proposed approach and the results are exact. While using the existing approaches the results are approximate due to approximate product of triangular vague sets and interval valued triangular vague sets.

The paper introduces a new approach for analyzing the fuzzy system reliability using Tω‐based arithmetic operations over L‐R type interval valued triangular vague sets.

The purpose of this paper is to present research methods in processing uncertain information.

Vague set and rough set are both‐wings‐mode for expressing uncertainty systems, and based on the both‐wings‐mode of expressing uncertainty systems, the connections of vague set and rough set are discussed.

This paper presents the relationships between vague set and rough set.

Based on these connections between vague set and rough set, theoretical and means of vague set can be used for rough set; also theoretical and means of rough set can be used for vague set.

The paper contributes to the discussion on the research of vague set and rough set. The conclusions are useful in information processing.

The concept of agile supply chain (ASC) has become increasingly important as means of achieving a competitive edge in turbulent business environments. An ASC is a dynamic alliance of member enterprises, the adaptation of which is likely to introduce velocity, responsiveness and flexibility into the manufacturing system. In ASC management, supplier/partner selection is a key strategic concern; influenced by various agility-related criteria/attributes. Therefore, evaluation and selection of potential supplier in an ASC has become an important multi-criteria decision-making problem. The purpose of this paper is to report, a supplier selection procedure (module) in the context of ASC.

During supplier selection, subjectivity of evaluation information (human judgment) often creates conflict and bears some kind of uncertainty. To overcome this, the present work attempts to explore vague set theory to deal with uncertainties in the supplier selection decision-making process. Since, vague sets can provide more accurate information as compared to fuzzy sets. It considers true membership function as well as false membership function which give more superior results for uncertain information. In this procedure, first, linguistic variables have been used to assess appropriateness rating (performance extent) as well as priority weights for individual quantitative or qualitative criterions. Second, the concept of degree of similarity and probability of vague sets has been used to determine appropriate ranking order of the potential supplier alternatives.

A case empirical example has been provided. It has been proved that the methodology would be fruitful in considering different evaluation criterion (indices); may be contradicting in nature like beneficial and cost criterions. The application of vague set theory has also been proved as a better option to work under uncertain (fuzzy) decision-making environment in comparison to fuzzy set theory.

The application of vague set theory in multi-criteria group decision making has been reported in literature to a limited extent. Application of vague set as a decision-making tool in agile supplier selection appears relative new and unexplored work area. The work has got remarkable managerial implications.

The purpose of this paper is to present a new methodology, named vague lambda‐tau, used for reliability analysis of a combustion system, which could be used for managerial decision making and future system maintenance strategy.

This paper involves the qualitative and quantitative analysis of a combustion system. In qualitative analysis, the Petri net model is obtained from its equivalent fault tree and in quantitative analysis, the reliability parameters are evaluated using vague lambda‐tau methodology. Further, a decision support system based on vague sets is developed to overcome the limitations of traditional risk analysis.

The reliability parameters (such as expected number of failures, mean time between failures, availability, and reliability) of the compressor system are evaluated. The proposed, vague sets‐based reliability analysis and risk analysis not only overcome the limitations associated with traditional approaches but also integrate the confidence level of domain experts and expert's experience, in a more flexible and realistic manner.

Instead of fuzzy sets, this paper used vague sets for reliability analysis with Petri net modelling because in real life problems, there may be hesitation regarding the belongingness of an object to a set or not. In fuzzy set theory, there is no means to incorporate such type of hesitation.

The purpose of this paper is to attempt supplier selection considering economic, environmental and social sustainability issues.

Subjective human judgment bears some kind of vagueness and ambiguity; fuzzy set theory has immense potential to overcome this. Owing to the advantage of intuitionistic fuzzy numbers set over classical fuzzy numbers set; three decision-making approaches have been applied here in intuitionistic fuzzy setting (namely, intuitionistic-TOPSIS, intuitionistic-MOORA and intuitionistic-GRA) to facilitate supplier selection in sustainable supply chain.

The stated objective of this research “to verify application potential of different decision support systems (in intuitionistic fuzzy setting) in the context of sustainable supplier selection” has been carried out successfully. A case empirical research has been conducted by applying three different decision-making approaches: intuitionistic fuzzy-TOPSIS, intuitionistic fuzzy-MOORA and intuitionistic fuzzy-GRA to an empirical data set of sustainable supplier selection problem. The ranking orders thus obtained through exploration of aforesaid three approaches have been explored and compared.

As compared to generalized fuzzy numbers, intuitionistic fuzzy numbers exhibit a membership degree, a non-membership degree and the extent of hesitation; a better way to capture inconsistency, incompleteness and imprecision of human judgment. Application potential of aforesaid three decision support approaches has been demonstrated in this reporting for a case sustainable supplier selection.

In recent years, the application of robots in different industrial sectors such as nuclear power generation, construction, automobile, firefighting and medicine, etc. is increasing day by day. In large industrial plants generally humans and robots work together to accomplish several tasks and lead to the problem of safety and reliability because any malfunction event of robots may cause human injury or even death. To access the reliability of a robot, sufficient amount of failure data is required which is sometimes very difficult to collect due to rare events of any robot failures. Also, different types of their failure pattern increase the difficulty which finally leads to the problem of uncertainty. To overcome these difficulties, this paper presents a case study by assessing fuzzy fault tree analysis (FFTA) to control robot-related accidents to provide safe working environment to human beings in any industrial plant.

Presented FFTA method uses different fuzzy membership functions to quantify different uncertainty factors and applies alpha-cut coupled weakest t-norm (Tω) based approximate fuzzy arithmetic operations to obtain fuzzy failure probability of robot-human interaction fault event which is the main contribution of the paper.

The result obtained from presented FFTA method is compared with other listing approaches. Critical basic events are also ranked using V-index for making suitable action plan to control robot-related accidents. Study indicates that the presented FFTA is a good alternative method to analyze fault in robot-human interaction for providing safe working environment in an industrial plant.

Existing fuzzy reliability assessment techniques designed for robots mainly use triangular fuzzy numbers (TFNs), triangle vague sets (TVS) or triangle intuitionistic fuzzy sets (IFS) to quantify data uncertainty. Present study overcomes this shortcoming and generalizes the idea of fuzzy reliability assessment for robots by adopting different IFS to control robot-related accidents to provide safe working environment to human. This is the main contribution of the paper.

This paper presents a comprehensive review of the available literature on applications of the rough set theory. Concepts of the rough set theory are discussed for approximation, dependence and reduction of attributes, decision tables and decision rules. The applications of rough sets are discussed in pattern recognition, information processing, business and finance, industry, environment engineering, medical diagnosis and medical data analysis, system fault diagnosis and monitoring and intelligent control systems. Development trends and future efforts are outlined. An extensive list of references is also provided to encourage interested readers to pursue further investigations.

In this way, the aim of this study is to expand and evelop the application of this technique in FMEA to rank failure modes of ESQ of academic libraries in an intuitionistic fuzzy environment. Assessment of electronic service quality (ESQ) of libraries is significantly important according to their major roles. It should be noted that the ESQ has a significant impact on customer satisfaction, which improves organizational performance. Accordingly, low ESQ means waste of organizational resources and poor user satisfaction. So, there is a dire need to reflect reasons inducing failure modes in academic library ESQ. Thus, investigation of failure modes affecting academic library ESQ is highly important. One solution in this area is utilization of the intuitionistic fuzzy (IF) failure mode and effects analysis (FMEA) as one of the widely used methods for prediction and identification of failure modes.

The present study in terms of objective is applied and in terms of the type of method is descriptive-analytical. The research sample included four experts of Yazd academic Libraries (Iran). To collect data, three types of questionnaires were distributed among experts. The purpose of the first questionnaire was to identify and reach an agreement on e-library failure modes. Type II questionnaire was used to determine the importance of identified risk factors and Type III questionnaire was used to prioritize the factors.

Results indicate that the difficulty of using websites, lack of provided information feedback to users and lack of links on the website to users' are the main priorities for improving ESQ in the studied academic libraries.

In this approach, the Intuitionistic fuzzy Elimination Et Choix Traduisant la REalité and technique for order of preference by similarity to ideal solution method were used to rank failure modes in academic library ESQ within the FMEA framework.]

The purpose of this study is to develop Markovian model to obtain the transient probabilities to determine mean-time-to-failure and reliability function and further steady state availability of the repairable system. As the system parameters are uncontrollable factors; thus the life times, repair times and recovery/reboot time are assumed to be as uncertain or fuzzified distributions.

The fuzzy approach is introduced to investigate the reliability measures of load sharing repairable system which consists of two operating units and one standby unit. On the failure of an operating component, it is instantly spotted, located and sent for recovery procedures with coverage probability. In case of imperfect recovery, reboot takes place.

On the basis of extension principle and mathematical programming approach, the authors establish membership functions for system characteristics with the help of α-cuts. To demonstrate the practical validity of the proposed fuzzified model, numerical illustrations are performed.

The model proposed for reliability analysis may cheer up the continuance of the work towards more applications in repairable systems. Therefore, the reader is provided with useful intuition into the nature of fuzzy computations and practical amendments while measuring ambiguous data.

Distribution problems deal with distribution from a number of sources to a number of destinations. Each source offers amounts of goods, while each destination demands quantities of these goods. The object is to find the cheapest transporting schedule that satisfies demand without violating supply restraints. In this paper we propose the use of fuzzy sets to represent the provisional information related to costs, demands and other variables. Moreover, we suggest including the problem of shortest route for the distribution vehicles. Finally, to solve this complex problem we propose using a genetic algorithm with a fuzzy fitness function.