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Book part

## Fuzzy Arithmetic Operations: Theory and Applications in Construction Engineering and Management

Fuzzy numbers are often used to represent non-probabilistic uncertainty in engineering, decision-making and control system applications. In these applications, fuzzy

### Abstract

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.

### Details

Fuzzy Hybrid Computing in Construction Engineering and Management
Type: Book
ISBN: 978-1-78743-868-2

Article

## PROCESSING OF FUZZY NUMBERS BY FUZZY RELATION EQUATIONS

In this paper we deal with fuzzy numbers that modelize uncertain quantities present in many fields of applications, such as man‐machine systems. Main attention is paid to…

### Abstract

In this paper we deal with fuzzy numbers that modelize uncertain quantities present in many fields of applications, such as man‐machine systems. Main attention is paid to inverse operations for fuzzy numbers which allow one to solve equations or systems of equations with fuzzy numbers. The relevance of the method proposed for the determination of parameters of fuzzy models is also stressed.

### Details

Kybernetes, vol. 15 no. 1
Type: Research Article
ISSN: 0368-492X

Article

## Ranking of customer requirements using the fuzzy centroid‐based method

The aim of this paper is to present a fuzzy centroid‐based method to ranking customer requirements with competition consideration. The proposed method not only focuses on…

### Abstract

#### Purpose

The aim of this paper is to present a fuzzy centroid‐based method to ranking customer requirements with competition consideration. The proposed method not only focuses on normal fuzzy numbers, but also considers non‐normal fuzzy numbers to capture the true customer requirements.

#### Design/methodology/approach

This paper proposes a new customer requirements ranking method using QFD that not only focuses on the voice of the customer, but also considers the competitive environment. The method uses fuzzy mathematics instead of crisp numbers; this is known as the fuzzy centroid‐based method.

#### Findings

A numerical example demonstrates that if the fuzzy numbers are non‐normal, previous ranking methods were shown to be incorrect and to have led to some misapplications. To avoid possible further misapplications or spread in the future, the correct centroid formula used for fuzzy numbers is derived and their simplified expressions for non‐normal fuzzy numbers are given.

#### Originality/value

Various methods have been developed to rate and rank customer needs; however, few methods consider the competitive environment. In addition, in real applications, fuzzy mathematics are usually more appropriate than crisp models. Many previous methods are misleading and have led to some misapplications if the fuzzy numbers are non‐normal. The paper contributes to theory and practice by explaining the reasons for using the fuzzy centroid‐based method.

### Details

International Journal of Quality & Reliability Management, vol. 27 no. 2
Type: Research Article
ISSN: 0265-671X

Article

## A decision support system for road freight transportation route selection with new fuzzy numbers

This study aims to propose a framework for designing appropriate triangular fuzzy numbers in a fuzzy analytic hierarchy process (FAHP) for selecting a road freight…

### Abstract

#### Purpose

This study aims to propose a framework for designing appropriate triangular fuzzy numbers in a fuzzy analytic hierarchy process (FAHP) for selecting a road freight transport route and investigate the appropriate fuzzy numbers determined from a reliable consensus among participating experts based on the Delphi method.

#### Design/methodology/approach

The fundamental nine-point scale was investigated and separated into nonfuzzy intervals for importance assessment. A total of 17 individual experts participated in this study, and their consensus was that appropriate fuzzy numbers could be obtained using a three-round Delphi process. Moreover, the appropriate fuzzy numbers were used instead of the primary fuzzy numbers to calculate the relative weights of the decision criteria for road freight route selection.

#### Findings

The results confirmed that the Delphi method can be easily and rigorously applied to define appropriate fuzzy numbers. Further, this framework can serve as a guideline for a situation wherein the input of other fuzzy multiple criteria decision-making tools must be provided.

#### Originality/value

The FAHP has been widely used to address the imprecise assessments of decision-makers. However, most existing studies on the incorporation of such techniques have not defined fuzzy numbers, which are relevant to the problem of interest. This study contributes by incorporating the Delphi method that can design an appropriate fuzzy number for road freight route selection.

### Details

foresight, vol. 22 no. 4
Type: Research Article
ISSN: 1463-6689

Article

## Assessing the efficiency of environmental regulations of large-scale enterprises based on extended fuzzy data envelopment analysis

As the functions of environmental regulations cannot be quantified while assessing their environmental efficiency, there has been no comprehensive evaluation of…

### Abstract

#### Purpose

As the functions of environmental regulations cannot be quantified while assessing their environmental efficiency, there has been no comprehensive evaluation of environmental efficiency. The purpose of this paper is to evaluate environmental regulations based on triangular and trapezoidal fuzzy numbers.

#### Design/methodology/approach

This paper uses L-R fuzzy numbers to transform the evaluation language into triangular fuzzy numbers, and adopts an α-level flexible slacks-based measurement model to evaluate the performance of these regulations. Trapezoidal fuzzy numbers are combined with a data envelopment analysis model, and an α-slack-based measurement (SBM) model is used to evaluate the environmental efficiency. The α-SBM model is confirmed to be stable and sustainable.

#### Findings

Relevant index data from 16,375 enterprises were collected to test the proposed model, and models corresponding to triangular fuzzy numbers and trapezoidal fuzzy numbers were used to evaluate their environmental efficiency. Comparative results showed that the proposed model is feasible and stable.

#### Originality/value

The main contributions of this study are twofold. First, this paper provides a valuable evaluation method for environmental regulation. Second, our research improves the practical performance of trapezoidal fuzzy data envelopment analysis and enhances its feasibility and stability.

### Details

Industrial Management & Data Systems, vol. 118 no. 2
Type: Research Article
ISSN: 0263-5577

Article

## One modification of fuzzy TOPSIS method

The purpose of this paper is to present one modification of the fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and to develop a…

### Abstract

#### Purpose

The purpose of this paper is to present one modification of the fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and to develop a corresponding computer program which could be used for the multicriteria decision making for problems in practice.

#### Design/methodology/approach

This method is based on the uncertainties and probabilities of input data for ratings of alternatives with respect to criteria and weights of criteria that are presented by triangular fuzzy numbers as probabilistic fuzzy values. These input data are transformed in the procedure into output data that are relevant for the ranking of alternatives and decision making.

#### Findings

The proposed method is based on the generalized mean and spread of fuzzy numbers that are calculated according to probability of fuzzy events due to Zadeh. Ranking of alternatives for relevant criteria performs according to relative expected closeness, coefficient of variation and relative standard deviation of distance of alternatives to the ideal solutions. The most acceptable rule is related to the minimal value of the expected relative distance to positive ideal solution, especially when the coefficient of variation of distance to this solution is small. The attached example, related to a real project, confirms these findings.

#### Originality/value

This paper proposes three novel contributions in this area. Unlike the methods proposed by other authors, the weighted fuzzy decision matrix is expressed by the matrix of generalized expected values and matrix of generalized variances. To compute elements of these two matrices, exact formulae are derived and then the modified fuzzy TOPSIS procedure is carried out.

### Details

Journal of Modelling in Management, vol. 8 no. 1
Type: Research Article
ISSN: 1746-5664

Article

## Fuzzy Matrix Games Considering the Criteria of the Players

A new method to solve zero‐sum two‐person games with imprecise values in their matrices of pay‐offs is suggested. The natural lack of precision generated by the use of…

### Abstract

A new method to solve zero‐sum two‐person games with imprecise values in their matrices of pay‐offs is suggested. The natural lack of precision generated by the use of fuzzy numbers in a fuzzy game requires the use of subjective criteria by the players in the resolution model. We apply a ranking function, the Average Value, which allows the decision makers to take into account their subjectivity. The use of this function raises again the solution of the fuzzy game when two criteria, one for each player, are used.

### Details

Kybernetes, vol. 20 no. 1
Type: Research Article
ISSN: 0368-492X

Article

## Systematic combination of fuzzy and grey numbers for supplier selection problem

Supplier selection is a complex multiple criteria decision (MCDM) problem which directly depends on decision makers’ choice. Some decisions are getting involved with…

### Abstract

#### Purpose

Supplier selection is a complex multiple criteria decision (MCDM) problem which directly depends on decision makers’ choice. Some decisions are getting involved with linguistic variables and they are not mathematically operable. To solve a typical decision problem through MCDM techniques, a number or a numerical interval should be defined. The purpose of this paper is to focus on that numerical interval and in a case of supplier selection, the aim is to close the decisions to the real number that the decision maker mentions and this number is in a numerical interval.

#### Design/methodology/approach

The proposed method deals with grey relational analysis (GRA) and develops it by applying triangular fuzzy numbers. The grey numbers have two defined bounds; the proposed method defines two fuzzy bounds for each grey attribute. In the proposed method, the fuzzy membership function has been employed for each bounds of grey attribute to make them to fuzzy bounds with two undefined bounds. Also to make comparison, with employing of TOPSIS technique, both of the grey fuzzy combination decision matrix and the original grey decision matrix are obtained.

#### Findings

The results indicate that, except to the ideal solutions, the grey relation coefficient for each alternative is too close to each other. Indeed, they are too close to zero. Applying the proposed method in problem of supplier selection shows the difference between two selected supplier in proposed method and the original grey method.

#### Originality/value

As mentioned heretofore this paper aims to make decision makers’s decision more accurate and actually there is no other researches which used this combination method.

### Details

Grey Systems: Theory and Application, vol. 5 no. 3
Type: Research Article
ISSN: 2043-9377

Article

## Assessment of quality services through linguistic variables

Improvements in quality have a very important role to play in services because such improvements add greater flexibility and give clients greater confidence in the…

### Abstract

#### Purpose

Improvements in quality have a very important role to play in services because such improvements add greater flexibility and give clients greater confidence in the services provided. Therefore, this paper aims to describe a framework for measuring quality in the provision of the service by using a SERVQUAL scale and fuzzy operators.

#### Design/methodology/approach

In this approach, a framework to assess quality in service provision is put forward which applies the SERVQUAL scale as an instrument of data collection. Fuzzy set theory is proposed and applied within this framework as a technique to make a quantitative assessment of the quality of the provision of services. A case study is used to illustrate how to apply this framework for this purpose. The data were processed and transformed into a fuzzy environment, and fuzzy numbers and operators were applied to the analysis of customers' assessment with regard to the dimensions of quality in the service provided.

#### Findings

The study demonstrated the differences between evaluations of the dimensions of quality assessed, and differences of the same customer in relation to these dimensions. The main points raised were the importance given by customers to the dimensions, and the gaps between customers' perceptions and expectations, when fuzzy numbers were used to assess levels of service quality, and to evaluating the prioritization of service quality.

#### Originality/value

This paper proposes the use of fuzzy theory within a framework by making a linguistic analysis when dealing with data collected in a SERVQUAL scale so as to assess service quality. The data were measured by examining the gap between customers' perceptions and expectations. The framework describes the phases of this assessment, and uses fuzzy operators.

### Details

Benchmarking: An International Journal, vol. 21 no. 1
Type: Research Article
ISSN: 1463-5771

Article

## A novel FMEA model based on fuzzy multiple-criteria decision-making methods for risk assessment

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…

### Abstract

#### Purpose

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.

#### Design/methodology/approach

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.

#### Findings

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.

#### Originality/value

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.

### Details

Journal of Enterprise Information Management, vol. 33 no. 5
Type: Research Article
ISSN: 1741-0398

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