scholarly journals A Piecewise Linear FGM Approach for Efficient and Accurate FAHP Analysis: Smart Backpack Design as an Example

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1319 ◽  
Author(s):  
Hsin-Chieh Wu ◽  
Toly Chen ◽  
Chin-Hau Huang
Keyword(s):  
Fuzzy Numbers ◽  
Fuzzy Ahp ◽  
Piecewise Linear ◽  
Geometric Mean ◽  
Experimental Results ◽  
Membership Functions ◽  
Triangular Fuzzy Numbers ◽  
The Real ◽  
Straight Lines ◽  
Fuzzy Geometric Mean

Most existing fuzzy AHP (FAHP) methods use triangular fuzzy numbers to approximate the fuzzy priorities of criteria, which is inaccurate. To obtain accurate fuzzy priorities, time-consuming alpha-cut operations are usually required. In order to improve the accuracy and efficiency of estimating the fuzzy priorities of criteria, the piecewise linear fuzzy geometric mean (PLFGM) approach is proposed in this study. The PLFGM method estimates the α cuts of fuzzy priorities and then connects these α cuts with straight lines. As a result, the estimated fuzzy priorities will have piecewise linear membership functions that resemble the real shapes. The PLFGM approach has been applied to the identification of critical features for a smart backpack design. According to the experimental results, the PLFGM approach improved the accuracy and efficiency of estimating the fuzzy priorities of these critical features by 33% and 80%, respectively.

scholarly journals Refractured Well Selection for Multicriteria Group Decision Making by Integrating Fuzzy AHP with Fuzzy TOPSIS Based on Interval-Typed Fuzzy Numbers

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Tiejun Li ◽  
Jianhua Jin ◽  
Chunquan Li
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Fuzzy Ahp ◽  
Fuzzy Topsis ◽  
Selection Problem ◽  
Triangular Fuzzy Numbers ◽  
Analytic Hierarchy ◽  
Multicriteria Group Decision Making

Multicriteria group decision making (MCGDM) research has rapidly been developed and become a hot topic for solving complex decision problems. Because of incomplete or non-obtainable information, the refractured well-selection problem often exists in complex and vague conditions that the relative importance of the criteria and the impacts of the alternatives on these criteria are difficult to determine precisely. This paper presents a new model for MCGDM by integrating fuzzy analytic hierarchy process (AHP) with fuzzy TOPSIS based on interval-typed fuzzy numbers, to help group decision makers for well-selection during refracturing treatment. The fuzzy AHP is used to analyze the structure of the selection problem and to determine weights of the criteria with triangular fuzzy numbers, and fuzzy TOPSIS with interval-typed triangular fuzzy numbers is proposed to determine final ranking for all the alternatives. Furthermore, the algorithm allows finding the best alternatives. The feasibility of the proposed methodology is also demonstrated by the application of refractured well-selection problem and the method will provide a more effective decision-making tool for MCGDM problems.

scholarly journals A FUZZY AHP MULTI-CRITERIA DECISION-MAKING APPROACH APPLIED TO COMBINED COOLING, HEATING, AND POWER PRODUCTION SYSTEMS

2011 ◽  
Vol 10 (03) ◽  
pp. 497-517 ◽  
Author(s):  
ANA NIETO-MOROTE ◽  
FRANCISCO RUZ-VILA
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Production Systems ◽  
Fuzzy Ahp ◽  
Geometric Mean ◽  
Power Production ◽  
Linguistic Terms ◽  
Minimization Method ◽  
Local Weight ◽  
Combined Cooling

Most of the real-world multicriteria decision-making (MCDM) problems contain a mixture of quantitative and qualitative criteria; therefore quantitative MCDM methods are inadequate for handling this type of decision problems. In this paper, a MCDM method based on the Fuzzy Sets Theory and on the Analytic Hierarchy Process (AHP) is proposed. This method incorporates a number of perspectives on how to approach the fuzzy MCDM problem, as follows: (1) combining quantitative and qualitative criteria; (2) expressing criteria pair-wise comparison in linguistic terms and performance of the alternative on each criterion in linguistic terms or exact values when criterion is qualitative or quantitative, respectively; (3) converting all the assessments into trapezoidal fuzzy numbers; (4) using the difference minimization method to calculate the local weight of criteria, employing the algebraic operations of fuzzy numbers based on the concept of α-cuts; (5) calculating the global weight of criteria and the global performance of each alternative using geometric mean and the weighted sum, respectively; (6) using the centroid method to rank the alternatives. Finally, an illustrative example on evaluation of several combined cooling, heat, and power production systems is used to demonstrate the effectiveness of the proposed methodology.

scholarly journals New Aggregation Operator for Triangular Fuzzy Numbers based on the Geometric Means of the Slopes of the L- and R- Membership Functions

2012 ◽  
Vol 2 (2) ◽  
pp. 74-76
Author(s):  
Manju Pandey ◽  
Dr. Nilay Khare
Keyword(s):  
Recent Work ◽  
Membership Function ◽  
Fuzzy Numbers ◽  
Arithmetic Mean ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Membership Functions ◽  
Triangular Fuzzy Numbers ◽  
Geometric Means ◽  
The Individual

In recent work authors have proposed four new aggregation operators for triangular and trapezoidal fuzzy numbers based on means of apex angles [1][2][3][4]. Subsequently authors have proposed [5] a new aggregation operator for TFNs based on the arithmetic mean of slopes of the L- and R- membership lines. In this paper the work is extended and a new aggregation operator for TFNs is proposed in which the L- and R- membership function lines of the aggregate TFN have slopes which are the geometric means of the corresponding L- and R- slopes of the individual TFNs. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TFN aggregates have also been computed.

scholarly journals PERFORMANCE EVALUATION MODEL OF ROMANIAN MANUFACTURING LISTED COMPANIES BY FUZZY AHP AND TOPSIS

2020 ◽  
Vol 26 (4) ◽  
pp. 808-836 ◽  
Author(s):  
Adrian Ioan Ban ◽  
Olimpia Iuliana Ban ◽  
Victoria Bogdan ◽  
Diana Claudia Sabau Popa ◽  
Delia Tuse
Keyword(s):  
Manufacturing Industry ◽  
Fuzzy Numbers ◽  
Stock Exchange ◽  
Fuzzy Ahp ◽  
Evaluation Model ◽  
Listed Companies ◽  
Annual Reports ◽  
Financial Indicators ◽  
Linguistic Variables ◽  
Triangular Fuzzy Numbers

We are interested in the hierarchy of the main Romanian companies in the manufacturing industry by considering eight financial and seven non-financial indicators. Thirty three listed companies, that are non-financial institutions, were selected for the study and in order to control the reliability of the data we used the Bucharest Stock Exchange database, official data published by the Romanian Ministry of Public Finance, and the annual reports released by the companies on their websites, collecting information for the years 2011–2015. Because the human thinking is subjective and ambiguous we prefer linguistic variables, converted afterwards in triangular fuzzy numbers, to represent the importance of indicators. Our method involves the calculation of the weights of individual or categories of indicators based on Fuzzy Analytic Hierarchy Process. Then, the level of performance for each company, separately for financial, non-financial and all indicators is obtained by TOPSIS method. We deduce an objective hierarchy of the companies on a rigorous basis, which is however dependent from the choice of indicators and the conversion scale of linguistic variables into triangular fuzzy numbers. Also, following the obtained results we concluded that the overall performance of companies for the analyzed period is significantly influenced by non-financial indicators.

scholarly journals Some Properties of Membership Functions Composed of Triangle Functions and Piecewise Linear FunctionsThis work has been partially supported in 2019-2020 by the domestic research grant of University of Marketing and Distribution Sciences in Kobe (Japan).

2021 ◽  
Vol 29 (2) ◽  
pp. 103-115
Author(s):  
Takashi Mitsuishi
Keyword(s):  
Fuzzy Sets ◽  
Linear Function ◽  
Piecewise Linear ◽  
Gaussian Function ◽  
Piecewise Linear Function ◽  
Approximate Reasoning ◽  
Evaluation Function ◽  
Membership Functions ◽  
Composite Function ◽  
Straight Lines

Summary. IF-THEN rules in fuzzy inference is composed of multiple fuzzy sets (membership functions). IF-THEN rules can therefore be considered as a pair of membership functions [7]. The evaluation function of fuzzy control is composite function with fuzzy approximate reasoning and is functional on the set of membership functions. We obtained continuity of the evaluation function and compactness of the set of membership functions [12]. Therefore, we proved the existence of pair of membership functions, which maximizes (minimizes) evaluation function and is considered IF-THEN rules, in the set of membership functions by using extreme value theorem. The set of membership functions (fuzzy sets) is defined in this article to verifier our proofs before by Mizar [9], [10], [4]. Membership functions composed of triangle function, piecewise linear function and Gaussian function used in practice are formalized using existing functions. On the other hand, not only curve membership functions mentioned above but also membership functions composed of straight lines (piecewise linear function) like triangular and trapezoidal functions are formalized. Moreover, different from the definition in [3] formalizations of triangular and trapezoidal function composed of two straight lines, minimum function and maximum functions are proposed. We prove, using the Mizar [2], [1] formalism, some properties of membership functions such as continuity and periodicity [13], [8].

A MULTI-ATTRIBUTE COMPARISON OF TURKISH QUALITY CONSULTANTS BY FUZZY AHP

2007 ◽  
Vol 06 (01) ◽  
pp. 191-207 ◽  
Author(s):  
UFUK CEBECI ◽  
DA RUAN
Keyword(s):  
Customer Satisfaction ◽  
Analytic Hierarchy Process ◽  
Fuzzy Numbers ◽  
Fuzzy Ahp ◽  
Iso 9000 ◽  
Analytical Tool ◽  
Triangular Fuzzy Numbers ◽  
Analytic Hierarchy ◽  
Hierarchy Process ◽  
Pair Wise Comparison

Quality consultants are used in ISO 9000 implementation projects especially by many small and medium-sized enterprises. Clients do not always appreciate differences between quality consultants. This paper aims to provide an analytical tool to select the best quality consultant providing the most customer satisfaction. The clients of three Turkish quality consultancy firms were interviewed and the most important criteria taken into account by the clients while they were selecting their consultancy firms were determined by a designed questionnaire. The fuzzy analytic hierarchy process was applied to compare these consultancy firms. The means of the triangular fuzzy numbers produced by the customers and experts for each comparison were successfully used in the pair wise comparison matrices.

scholarly journals A Systematic Approach to OptimizinghValue for Fuzzy Linear Regression with Symmetric Triangular Fuzzy Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xilong Liu ◽  
Yizeng Chen
Keyword(s):  
Linear Regression ◽  
Systematic Approach ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Numerical Study ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Linear Regression ◽  
The Real ◽  
Optimal Value ◽  
Sample Data

A systematic approach is proposed to optimizehvalue for fuzzy linear regression (FLR) analysis using minimum fuzziness criteria with symmetric triangular fuzzy numbers (TFNs). Firstly, a new concept of credibility is defined to evaluate the performance of FLR models with differenthvalues when a set of sample data pairs is given. Secondly, based on the defined concept of credibility, a programming model is formulated to optimize the value ofh. Finally, both the numerical study and the real application show that the approach proposed in this paper is effective and efficient; that is, optimal value forhcan be determined definitely with respect to a set of given sample data pairs.

New Aggregation Operator for Triangular Fuzzy Numbers based on the Geometric Means of the Slopes of the L- and R- Membership Functions

2018 ◽  
Vol 2 (2a) ◽  
pp. 74-76
Author(s):  
Manju Pandey ◽  
Dr. Nilay Khare
Keyword(s):  
Recent Work ◽  
Membership Function ◽  
Fuzzy Numbers ◽  
Arithmetic Mean ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Membership Functions ◽  
Triangular Fuzzy Numbers ◽  
Geometric Means ◽  
The Individual

In recent work authors have proposed four new aggregation operators for triangular and trapezoidal fuzzy numbers based on means of apex angles [1][2][3][4]. Subsequently authors have proposed [5] a new aggregation operator for TFNs based on the arithmetic mean of slopes of the L- and R- membership lines. In this paper the work is extended and a new aggregation operator for TFNs is proposed in which the L- and R- membership function lines of the aggregate TFN have slopes which are the geometric means of the corresponding L- and R- slopes of the individual TFNs. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TFN aggregates have also been computed.

scholarly journals Fuzzy AHP Method for Selection of a Suitable Seismic Retrofitting Alternative in Low-Rise Buildings

2018 ◽  
Vol 4 (5) ◽  
pp. 1074 ◽  
Author(s):  
Reza Pashaei ◽  
Abdolreza S. Moghadam
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Fuzzy Ahp ◽  
Seismic Retrofitting ◽  
Triangular Fuzzy Numbers ◽  
Analytic Hierarchy ◽  
Hierarchy Process ◽  
Pair Wise Comparison ◽  
Selection Of

Decision making for selecting an appropriate alternative among nominated alternatives is still a problem among retrofit designers. It is clear that selected alternative should comply the current codes in terms of structural criteria, but the other criteria may not be considered. The main goal of this study is to introduce a suitable method for making a decision in order to find the best alternative considering the effective criteria in retrofitting of low-rise buildings. Analytic Hierarchy Process (AHP), as a technique of Multi-Criteria Decision Making (MCDM), is compatible to solve the problem. Effective criteria have been categorized to structural, operational, economic and functional criteria and sixteen sub-criteria considered as a pattern that satisfies the entire involved group including structural and architectural engineers, contractor, client, and authorities in retrofitting of low-rise buildings. Since most of the involved criteria such as aesthetic, durability, and compatibility have fuzzy nature and cannot be compared numerically, fuzzy AHP can be a compatible method for comparison different retrofitting alternatives among both fuzzy and non-fuzzy criteria. A matrix of pair-wise comparison (MPC) is used for determining the weight of criteria and also for scoring the alternatives respect to each criterion. A Fuzzy Importance scale with Triangular Fuzzy Numbers (TFN) is applied for comparing the criteria. The method is examined by a case study and the results show the used method can help designers for selecting the appropriate alternative.

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