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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 authors discuss the value of portfolio and Black–Scholes (B–S)-option pricing model in fuzzy environment.

The B–S option pricing model (OPM) is an important role of an OPM in finance. Here, every decision is taken under uncertainty. Due to randomness or vagueness, these uncertainties may be random or fuzzy or both. As the drift µ, the degree of volatility s, interest rate r, strike price k and other parameters of the value of the portfolio V(t), market price S_0 (t) and call option C(t) are not known exactly, so they are treated as positive fuzzy number. Partial expectation of fuzzy log normal distribution is derived. Also the value of portfolio at any time t and the B–S OPM in fuzzy environment are derived. A numerical example of B–S OPM is illustrated.

First, the authors are studying some various paper and some stochastic books.

This is a new technique.

Risk assessment is a very important step toward managing risks in various organizations and industries. One of the most extensively applied risk assessment techniques is failure mode and effects analysis (FMEA). In this paper, a novel fuzzy multiple-criteria decision-making (MCDM)-based FMEA model is proposed for assessing the risks of different failure modes more accurately.

In this model, the weight of each failure mode is considered instead of risk priority number (RPN). Additionally, three criteria of time, cost and profit are added to the three previous risk factors of occurrence (O), severity (S) and detection (D). Furthermore, the weights of the mentioned criteria and the priority weights of the decision-makers calculated by modified fuzzy AHP and fuzzy weighted MULTIMOORA methods, respectively, are considered in the proposed model. A new ranking method of fuzzy numbers is also utilized in both proposed fuzzy MCDM methods.

To show the capability and usefulness of the suggested fuzzy MCDM-based FMEA model, Kerman Steel Industries Factory is considered as a case study. Moreover, a sensitivity analysis is conducted for validating the achieved results. Findings indicate that the proposed model is a beneficial and applicable tool for risk assessment.

To the best of authors’ knowledge, no research has considered the weights of failure modes, the weights of risk factors and the priority weights of decision-makers simultaneously in the FMEA method.

Robot selection is basically a task of choosing appropriate robot among available alternatives with respect to some evaluation criteria. The task becomes much more complicated since apart from objective criteria a number of subjective criteria need to be evaluated simultaneously. Plenty of decision support systems have been well documented in existing literature which considers either objective or subjective data set; however, decision support module with simultaneous consideration of objective as well as subjective data has rarely been attempted before. The paper aims to discuss these issues.

Motivated by this, present work exhibits application potential of preference ranking organization method for enrichment evaluations (extended to operate under fuzzy environment) to solve decision-making problems which encounter both objective as well as subjective evaluation data.

An empirical case study has been demonstrated in the context of robot selection problem. Finally, a sensitivity analysis has been performed to make the robot selection process more robust. A trade-off between objective criteria measure and subjective criteria measure has been shown using sensitivity analysis.

Robot selection has long been viewed as an important decision-making scenario in the industrial context. Appropriate robot selection helps in enhancing value of the product and thereby, results in increased profitability for the manufacturing industries. The proposed decision support system considering simultaneous exploration of subjective as well as objective database is rarely attempted before.

The aim of this study is to show in detail the theoretical and practical foundations of a new feasibility technique for cash flow forecasting (CFF) based on triangular fuzzy numbers.

One of the most complicated problems business people face is determining if they have enough cash to be able to meet all future payments of a specific period. The uncertainty of forecasting the data to solve the problem suggests that a model based on fuzzy logic tools may provide a good way to obtain new techniques to ensure the feasibility of cash flow management.

This study shows how a specific company can obtain a quantitative idea of the risk of not being able to meet payments in a specific period. This idea can be put into practice with the usual computer tools.

This work presents a technique to predict the feasibility of CFF using triangular fuzzy numbers. There are other fuzzy numbers with which we can model the study problem and that offer certain advantages over to triangular ones.

A qualitative procedure is currently used to calculate the feasibility of a CFF. This work represents a step forward since it shows how to model quantitative feasibility.

The originality and value of this contribution consists of providing a complete model for a feasibility technique of CFF, as well as several proposals to mechanize the calculations and make the results more intuitive by means of spreadsheet graphs.

The recent global market trend is seemed enforcing existing manufacturing organizations (as well as service sectors) to improve existing supply chain systems or to take up/adapt advanced manufacturing strategies for being competitive. The concept of the agile supply chain (ASC) has become increasingly important as a means of achieving a competitive edge in highly turbulent business environments. An ASC is a dynamic alliance of member enterprises, the formation 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. Apart from traditional supplier/partner selection criteria; different agility-related criteria/attributes need to be taken under consideration while selecting an appropriate supplier in an ASC. The paper aims to discuss these issues.

Therefore, evaluation and selection of potential supplier in an ASC have become an important multi-criteria decision making problem. Most of the evaluation criteria being subjective in nature; traditional decision-making approaches (mostly dealing with objective data) fail to solve this problem. However, fuzzy set theory appears an important mean to tackle with vague and imprecise data given by the experts. In this work, application potential of the fuzzy multi-level multi-criteria decision making (FMLMCDM) approach proposed by Chu and Velásquez (2009) and Chu and Varma (2012) has been examined and compared to that of Fuzzy-techniques for order preference by similarity to ideal solution (TOPSIS) and Fuzzy-MOORA in the context of supplier selection in ASC.

It has been observed that similar ranking order appears in FMLMCDM as well as Fuzzy-TOPSIS. In Fuzzy-MOORA, the best alternative appears same as in case of FMLMCDM as well as Fuzzy-TOPSIS; but for other alternatives ranking order differs. A comparative analysis has also been made in view of working principles of FMLMCDM, Fuzzy-TOPSIS as well as Fuzzy-MOORA.

Application feasibility of FMLMCDM approach has been verified in comparison with Fuzzy-TOPSIS and Fuzzy-MOORA in the context of agile supplier selection.

The purpose of this paper is to consider the following problem; if the manager of the parallel network systems wants to add new sub-decision making units (sub-DMUs) to each parallel network system, he/she wants to know how much new fuzzy inputs allocate to new sub-DMUs and how much outputs these new sub-DMUs produce such that the efficiency of each parallel network system improve or preserve.

Resource allocation and target setting is a famous topic in management science, therefore many managers attention to this field. Data envelopment analysis is one approach to apply the resource. Resource allocation and target setting is a famous topic in management science, therefore many managers attention to this field. Data envelopment analysis is one approach to apply the resource allocation and target setting. In real application the structure of many DMUs are network and the data of them are imprecise. In this work first the authors calculate the fuzzy efficiency of parallel systems by common set of weights method, after that the authors propose an approach to find how much fuzzy inputs allocate to new sub-DMUs, and how much new fuzzy outputs produce, where the efficiency of each parallel network system improve or preserve.

It is found the value of inputs and outputs of new sub-DMUs, where the efficiency of each system not worse than before.

The method can be used in many organizations such as banks, chain stores, car factory, etc.

For the first time the authors allocate new sub-DMUs to each system, and the data of paper are fuzzy numbers.

One of the most important issues in supply chain (SC) management is the identification and management of the risk involved in it. The purpose of this paper is to propose a comprehensive model of supply chain risk management (SCRM) in the product life cycle (PLC) and the operational process cycle (OPC). To decrease the risks in a fuzzy environment, the model considers the organizational performance factors (OPF) and the risk operational practices (ROP).

Fuzzy analytic hierarchy process is used to determine the weights of the relationships between the PLC, OPC and OPF in the hierarchical structure of the decision problem. In addition, the fuzzy technique for order preference by similarity to ideal solution is employed to recognize the priority of ROPs in dealing with the performance factors. The integrated framework is evaluated using the case study of an automotive company in Iran.

The results demonstrated that the proposed model can be used to formulate an appropriate method for prioritizing defined alternatives to decrease risk and improve the organizational performance in SCRM under fuzzy conditions.

A major limitation of the study is that a few of the selected criteria for risk assessment are focused only on economic factors. Another limitation of the current study is related to the PLC, OPC and OPF being based on the work of Xia and Chen (2011).

The current study identified the more important stage in the PLC. More significant process in each stage of the PLC and weightier risk factors in each process of the OPC were determined. Some strategies for reducing risk in each stage of the PLC were presented. The best alternatives for reducing risks in SC were indicated.

It is worth mentioning that previous studies have not applied multiple criteria and alternatives to decrease the risks involved in the PLC and OPC parts of the SC under fuzzy conditions. However, it should be stated that some academics have used these techniques separately, in other specialized areas of the SC.

In today’s ever-changing global business environment, successful survival of manufacturing firms/production units depends on the extent of fulfillment of dynamic customers’ demands. Appropriate supply chain strategy is of vital concern in this context. Lean principles correspond to zero inventory level; whereas, agile concepts motivate safety inventory to face and withstand in turbulent market conditions. The leagile paradigm is gaining prime importance in the contemporary scenario which includes salient features of both leanness and agility. While lean strategy affords markets with predictable demand, low variety and long product life cycle; agility performs best in a volatile environment with high variety, mass-customization and short product life cycle. Successful implementation of leagile concept requires evaluation of the total performance metric and development of a route map for integrating lean production and agile supply in the total supply chain. To this end, the purpose of this paper is to propose a leagility evaluation framework using fuzzy logic.

A structured framework consisting of leagile capabilities/attributes as well as criterions has been explored to assess an overall leagility index, for a case enterprise and the data, obtained thereof, has been analyzed. Future opportunities toward improving leagility degree have been identified as well. This paper proposes a Fuzzy Overall Performance Index to assess the combined agility and leanness measure (leagility) of the organizational supply chain.

The proposed method has been found fruitful from managerial implication viewpoint.

This paper aimed to present an integrated fuzzy-based performance appraisement module in an organizational leagile supply chain. This evaluation module helps to assess existing organizational leagility degree; it can be considered as a ready reference to compare performance of different leagile organization (running under similar supply chain architecture) and to benchmark candidate leagile enterprises; so that best practices can be transmitted to the less-performing organizations. Moreover, there is scope to identify ill-performing areas (barriers of leagility) which require special managerial attention for future improvement.

In the rapidly changing business environment, companies must align with suppliers to streamline operations, as well as working together to achieve a level of agility beyond individual companies (Lin et al., 2006). Today’s more dynamic business environment increases the need for greater agility in supply chains, which increases both the importance and frequency of supplier/partner evaluation and benchmarking decision making. The purpose of this paper is to develop a multiple criterion appraisement index (model/module) for supplier/partner alternative firm benchmarking perspective under similar agile supply chain architecture.

In this reporting, evaluation information against subjectivity (uncertain environment) indices has been transformed mathematical dimensionless numbers by fuzzy-based computation module. A new interval-valued fuzzy number set conjunction with modified “technique for order preference by similarity to ideal solution” methodology has been explored from benchmarking (ranking order of firm under similar criterion) point of view of supplier firms.

In this context, a novel “fuzzy mathematical equation” has been developed in perceptive to compute the priority weights and appropriateness ratings of first-level measures which reduced the acquisition of supplementary priority weights and appropriateness ratings assessment in linguistic terms from group decision makers (DMs) for first-level indices. An empirical case study has been carried to ranking order the candidate partner/supplier alternative via collective index (CI) value. Lower value of “CI” reflected higher degree of performance extent. The authors found out the effectiveness and validity of proposed methodology for constructed appraisement module.

This research work shall be valuable for that organization which volunteer to obtain the ranking order of partner/supplier alternative (benchmark) under similar agile supply chain architecture in accordance to group DMs’ comprehensive information for select best one supplier for own firm. In this reporting, a novel fuzzy mathematical equation has been developed in order to compute the important weights as well as priority rating of first-level indices/measure which reduced the supplementary important weights and priority rating assessment from group DMs in linguistic terms in order to obtain the measures rating and weights.