Fuzzy Weighted Average Research Articles

An Approach to Evaluating The Chinese Male College Student Basketball Players' Specialized Physical Constitution with Fuzzy Information

With the league development, the improvement of college students' man basketball player movement level is important. The men's basketball athlete's special physical quality is to influence basketball level, one of the important factors in college basketball player development stage of special physical quality is good or bad will directly affect the movement to raise the level of college students. According to the characteristics of b asketball players, as well as characteristics of the modem basketball movement, the present situation and trend, the establishment of college students in our country male basketball players special physical quality evaluation items and standards, in order to provide the reference for the future training. In this paper, we investigate the multiple attribute group decision making problems for evaluating the C hinese male college student basketball players ’ specialized physical constitution with f uzzy information . We utilize the f uzzy weighted average ( FWA ) operator to aggregate the f uzzy information corresponding to each alternative and get the overall value of alternatives, then rank the alternatives and select the most desirable one (s) by using the formula of the degree of possibility for the comparison between two fuzzy variables. Finally an illustrative example has been given to show the developed approach . Keywords: Multiple Attribute Group Decision Making (MAGDM), Fuzzy Information, Fuzzy Weighted Average (FWA) Operator, Chinese Male College Student, Specialized Physical Constitution

A QFD-based fuzzy MCDM approach for supplier selection

Supplier selection is a highly important multi-criteria group decision making problem, which requires a trade-off between multiple criteria exhibiting vagueness and imprecision with the involvement of a group of experts. In this paper, a fuzzy multi-criteria group decision making approach that makes use of the quality function deployment (QFD) concept is developed for supplier selection process. The proposed methodology initially identifies the features that the purchased product should possess in order to satisfy the company’s needs, and then it seeks to establish the relevant supplier assessment criteria. Moreover, the proposed algorithm enables to consider the impacts of inner dependence among supplier assessment criteria. The upper and the lower bounds of the weights of supplier assessment criteria and ratings of suppliers are computed by using the fuzzy weighted average (FWA) method. The FWA method allows for the fusion of imprecise and subjective information expressed as linguistic variables or fuzzy numbers. The method produces less imprecise and more realistic overall desirability levels, and thus it rectifies the problem of loss of information. A fuzzy number ranking method that is based on area measurement is used to obtain the final ranking of suppliers. The computational procedure of the proposed framework is illustrated through a supplier selection problem reported in an earlier study.

Methods for strategic decision-making problems with immediate probabilities in intuitionistic fuzzy setting

With respect to decision-making problems by using probabilities, immediate probabilities and information that can be represented with intuitionistic fuzzy information or interval-valued intuitionistic fuzzy information, some new decision analysis are proposed. Firstly, some operational laws, score function and accuracy function of intuitionistic fuzzy values or interval-valued intuitionistic fuzzy values are introduced. Then, we have developed some new probability aggregation operators with intuitionistic fuzzy information: Probability Intuitionistic Fuzzy Weighted Average (P-IFWA) operator, Immediate Probability Intuitionistic Fuzzy Ordered Weighted Average (IP-IFOWA) operator, Probability Intuitionistic Fuzzy Ordered Weighted Average (P-IFOWA) operator, Probability Intuitionistic Fuzzy Weighted Geometric (P-IFWG) operator, Immediate Probability Intuitionistic Fuzzy Ordered Weighted Geometric (IP-IFOWG) operator and Probability Intuitionistic Fuzzy Ordered Weighted Geometric (P-IFOWG) operator and applied these operators to decision-making problem about the selection of the optimal production strategy. Furthermore, we shall extend the developed models and procedures to solve probabilistic decision-making problems with interval-valued intuitionistic fuzzy information. Finally, we give an illustrative example about selection of strategies to verify the developed approach and to demonstrate its feasibility and practicality.

Fuzzy aggregation operators in decision making with Dempster–Shafer belief structure

We study the decision-making problem with Dempster–Shafer theory of evidence. We analyze how to deal with this model when the available information is uncertain and it can be represented with fuzzy numbers. We use different types of aggregation operators that aggregate fuzzy numbers such as the fuzzy weighted average (FWA), the fuzzy ordered weighted averaging (FOWA) operator and the fuzzy hybrid averaging (FHA) operator. As a result, we get the belief structure fuzzy weighted average (BS-FWA), the belief structure fuzzy ordered weighted averaging (BS-FOWA) operator and the belief structure fuzzy hybrid averaging (BS-FHA) operator. We further generalize this new approach by using generalized and quasi-arithmetic means. We also develop an illustrative example regarding the selection of investments where we can see the different results obtained by using different types of fuzzy aggregation operators.

Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision making

In this paper, we define various induced intuitionistic fuzzy aggregation operators, including induced intuitionistic fuzzy ordered weighted averaging (OWA) operator, induced intuitionistic fuzzy hybrid averaging (I-IFHA) operator, induced interval-valued intuitionistic fuzzy OWA operator, and induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator. We also establish various properties of these operators. And then, an approach based on I-IFHA operator and intuitionistic fuzzy weighted averaging (WA) operator is developed to solve multi-attribute group decision-making (MAGDM) problems. In such problems, attribute weights and the decision makers' (DMs') weights are real numbers and attribute values provided by the DMs are intuitionistic fuzzy numbers (IFNs), and an approach based on I-IIFHA operator and interval-valued intuitionistic fuzzy WA operator is developed to solve MAGDM problems where the attribute values provided by the DMs are interval-valued IFNs. Furthermore, induced intuitionistic fuzzy hybrid geometric operator and induced interval-valued intuitionistic fuzzy hybrid geometric operator are proposed. Finally, a numerical example is presented to illustrate the developed approaches.

Analytical solution methods for the fuzzy weighted average

For the fuzzy weighted average (FWA), despite various discrete solution algorithms and their improvements, attempts at analytical solutions are very rare. This paper provides an analytical solution method for the FWA based on the conclusions of the Karnik–Mendel (KM) algorithm. Compared with the two current popular kinds of α-cut based computational methods for the FWA (mathematical programming transformations and direct iterate computations), our method is precise, and, has a concise structure, efficient computation process, and sound theoretical proofs. We propose two algorithms for computing the analytical solution of the FWA. Two numerical examples illustrate our proposed approach.

Alpha-Level Aggregation: A Practical Approach to Type-1 OWA Operation for Aggregating Uncertain Information with Applications to Breast Cancer Treatments

Type-1 Ordered Weighted Averaging (OWA) operator provides us with a new technique for directly aggregating uncertain information with uncertain weights via OWA mechanism in soft decision making and data mining, in which uncertain objects are modeled by fuzzy sets. The Direct Approach to performing type-1 OWA operation involves high computational overhead. In this paper, we define a type-1 OWA operator based on the \alpha-cuts of fuzzy sets. Then, we prove a Representation Theorem of type-1 OWA operators, by which type-1 OWA operators can be decomposed into a series of \alpha-level type-1 OWA operators. Furthermore, we suggest a fast approach, called Alpha-Level Approach, to implementing the type-1 OWA operator. A practical application of type-1 OWA operators to breast cancer treatments is addressed. Experimental results and theoretical analyses show that: 1) the Alpha-Level Approach with linear order complexity can achieve much higher computing efficiency in performing type-1 OWA operation than the existing Direct Approach, 2) the type-1 OWA operators exhibit different aggregation behaviors from the existing fuzzy weighted averaging (FWA) operators, and 3) the type-1 OWA operators demonstrate the ability to efficiently aggregate uncertain information with uncertain weights in solving real-world soft decision-making problems.

A new approach to solving fuzzy weighted average model

This paper suggests a new approach to solving fuzzy weighted average (FWA) model, where t-distribution is used for normalization of quantitative data, ratings of alternatives versus qualitative criteria and the importance weights among criteria are assessed in linguistic values represented by fuzzy numbers. Membership functions of the final fuzzy evaluation values can be developed. A ranking method based on relative areas of a fuzzy number is applied to defuzzify these fuzzy numbers to order alternatives. Finally, a numerical example demonstrates the computational procedure of the proposed model.

A new fuzzy weighted average (FWA) method based on left and right scores: An application for determining a suitable location for a gas oil station

The selection of a facility location from alternative locations is a multiple criteria decision making (MCDM) problem including both quantitative and qualitative criteria. In many real-life cases, determining the exact values for MCDM problems, and especially for facility location selection problems, is difficult or impossible, so the values of alternatives with respect to the criteria or/and the values of criteria weights are considered as fuzzy values (fuzzy numbers) such that the conventional crisp approaches for solving facility location selection problems and other MCDM problems tend to be less effective for dealing with the imprecise or vagueness nature of the linguistic assessments. In such conditions, fuzzy MCDM methods are applied for facility location selection problem and other fuzzy MCDM problems. In this paper, we propose a new fuzzy weighted average (FWA) method based on left and right scores for fuzzy MCDM problems. Moreover, we apply the proposed method to a real application. As a result, we found that the proposed method is practical for facility location selection problems. Besides, it seems that the proposed FWA method is very accurate, flexible, simple, and easy to use when compared to other versions of the FWA method.

An efficient fuzzy weighted average algorithm for the military UAV selecting under group decision-making

The fuzzy weighted average (FWA), which is a function of fuzzy numbers and is useful as an aggregation method in engineering or management science based on fuzzy sets theory. It provides a discrete approximate solution by α-cuts level representation of fuzzy sets and interval analysis. Since the FWA method has an exponential complexity, thus several researches have focused on reducing this complexity. This paper also presents an enhanced fuzzy weighted average approach to achieve the objective of reducing the complexity. This proposed approach is through an improved initial solution for original FWA algorithm, and a two-phase concept by extending and applying both the algorithms of Chang et al. [4] and Guu [14]. Although the complexity of the proposed FWA algorithm is O( n) the same as Guu [14] which is the best level achieved to date. But from the experimental results appear that the proposed algorithm is more efficient, which only needs a few evaluated numbers and spend much less overall CPU time than Guu [14] and other FWA algorithms. In order to demonstrate the usefulness of this study, a practical example for unmanned aerial vehicle (UAV) selecting under military requirement has illustrated. Additionally, a computer-based interface, which helps the decision maker make decisions more efficiently, has been developed.

A fuzzy logic model for benchmarking the knowledge management performance of construction firms

Knowledge management is rapidly becoming a key organizational capability for creating competitive advantage in the construction industry. The emergence of knowledge management in this capacity poses enormous challenges to executives of construction firms. This paper proposes a model for benchmarking the knowledge management performance of construction firms that can guide and assist construction business executives in meeting these challenges. The proposed model incorporates benchmarking and knowledge management concepts with fuzzy set theory to adequately handle imprecision, vagueness, and uncertainty that prevail in this process. It uses the fuzzy-weighted average (FWA) algorithm to evaluate the knowledge management performance of construction firms. It is an internal reporting model that can provide powerful diagnostic information to executives of construction firms by evaluating their firm’s knowledge management performance, identifying their firm’s strengths and weaknesses with regard to each knowledge management practice, and setting priorities for managerial actions related to knowledge management practices that need improvement. A real-world case study is presented to illustrate the implementation and utility of the proposed model.

A new algorithm for computing the fuzzy weighted average

A new fuzzy weighted average computation algorithm (NFWA) based on the α-cuts representation of fuzzy numbers is presented in this paper. For each α-cuts, the endpoints of the fuzzy weighted average (FWA) can be calculated from two particular switch points. In the proposed algorithm, these two switch points are computed with an opposite direction searching process, although recursive, which is remarkably efficient. The calculation complexity of the new algorithm is O(n). Experimental result demonstrates that compared with some commonly used FWA algorithms, the new algorithm approach requires the least CPU time, and then may be the fastest available FWA algorithm to date.

Generalised fuzzy weighted mean and its applications

Fuzzy weighted arithmetic average or fuzzy weighted average (FWA) for short has been deeply studied. However, no attention has been paid to other fuzzy weighted means such as fuzzy weighted geometric mean (FWGM), fuzzy weighted harmonic mean (FWHM) and the like. This paper presents a very general fuzzy weighted mean, which we refer to as generalised fuzzy weighted mean (GFWM). It includes FWA, FWGM, FWHM, fuzzy weighted quadratic mean (FWQM) and fuzzy weighted root-power mean (FWRM) as its special cases. Linear programming models for solving GFWM and its special cases are developed and the order relationships among FWA, FWGM and FWHM are investigated. Numerical examples that illustrate the computational processes of FWA, FWGM and FWHM are provided and their order relationships are numerically examined.

A decision support system for engineering design based on an enhanced fuzzy MCDM approach

Design concept is an important wealth-creating activity in companies and infrastructure. However, the process of designing is very complex. Besides, the information required during the conceptual stage is incomplete, imprecise, and fuzzy. Hence, fuzzy set theory should be used to handle linguistic problem at this stage. This paper presents a fuzzy integrated approach to assess the performance of design concepts. And those criteria rating, relative weights and performance levels are captured by fuzzy numbers, and the overall performance of each alternative is calculated through an enhanced fuzzy weighted average (FWA) approach. A practical numerical example is provided to demonstrate the usefulness of this study. In addition, this paper, in order to make computing and ranking results easier to increase the recruiting productivity, develops a computer-based decision support system to help make decisions more efficiently.

Aggregation Using the Fuzzy Weighted Average as Computed by the Karnik–Mendel Algorithms

By connecting work from two different problems-the fuzzy weighted average (FWA) and the generalized centroid of an interval type-2 fuzzy set-a new alpha-cut algorithm for solving the FWA problem has been obtained, one that is monotonically and superexponentially convergent. This new algorithm uses the Karnik-Mendel (KM) algorithms to compute the FWA -cut end-points. It appears that the KM -cut algorithms approach for computing the FWA requires the fewest iterations to date, and may therefore be the fastest available FWA algorithm to date.

Aggregation Using the Linguistic Weighted Average and Interval Type-2 Fuzzy Sets

The focus of this paper is the linguistic weighted average (LWA), where the weights are always words modeled as interval type-2 fuzzy sets (IT2 FSs), and the attributes may also (but do not have to) be words modeled as IT2 FSs; consequently, the output of the LWA is an IT2 FS. The LWA can be viewed as a generalization of the fuzzy weighted average (FWA) where the type-1 fuzzy inputs are replaced by IT2 FSs. This paper presents the theory, algorithms, and an application of the LWA. It is shown that finding the LWA can be decomposed into finding two FWAs. Since the LWA can model more uncertainties, it should have wide applications in distributed and hierarchical decision-making.

A Comparison of Discrete Algorithms for Fuzzy Weighted Average

Fuzzy weighted average (FWA), which can be applied to various fields such as engineering design, decision analysis, etc., and as function of fuzzy numbers, is suitable for the problem of multiple occurrences of fuzzy parameters. Additional fuzziness may be introduced in the alpha-cut arithmetic. This paper reviews and compares discrete algorithms for the FWAs in both theoretical comparison and numerical comparisons, as opposed to the linear programming algorithms that may be efficient but require the help of linear programming software. An alternative efficient algorithm is also proposed. The algorithm introduces an all-candidate (criteria ratings) weights-replaced benchmark adjusting procedure other than a binary (dichotomy) search in the existing methods. The theoretical worst-case comparison shows that the algorithms of Guu and Guh and our alternative algorithm require the same order of calculation complexity O(n), where n is the number of FWA terms. Yet, the Guh algorithm always requires 2(n-1) calculations to be performed. The algorithm of Guu requires the elemental comparison complexity O(n), and is superior to the other algorithms, in the worst case. On the other hand, our alternative algorithm and Lee and Park algorithm have the same comparison complexity O(n log n). Yet, our alternative algorithm requires O(n) calculation complexity which is better than O(n log n) of the Lee and Park algorithm. The numerical experiments show that the algorithm of Guu and our alternative algorithm generally perform and converge faster by requiring fewer calculations than that of Lee and Park's algorithm. The alternative algorithm requires a slightly smaller number of calculations than that of the Guu algorithm, due to the use of the convergent benchmark adjustment procedure rather than a somewhat fixed binary search. Conversely, in the number of element comparisons, Lee and Park's algorithm is shown numerically generally slightly better than the alternative algorithm due to the simple binary search scheme used. The alternative algorithm also requires fewer comparisons than that of the Guu algorithm. Furthermore, in comparison of the average CPU time requirements, the ranks of the results of these algorithms are consistent with those of the algorithms for the average numbers of calculations. In general, the alternative algorithm may provide an efficient alternative algorithm to the FWAs. In the worse-case situation, the Guu algorithm still may be considered as an efficient alternative

Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment

This paper proposes a fuzzy TOPSIS method based on alpha level sets and presents a nonlinear programming (NLP) solution procedure. The relationship between the fuzzy TOPSIS method and fuzzy weighted average (FWA) is also discussed. Three numerical examples including an application to bridge risk assessment are investigated using the proposed fuzzy TOPSIS method to illustrate its applications and the differences from the other procedures. It is shown that the proposed fuzzy TOPSIS method performs better than the other fuzzy versions of the TOPSIS method.

Application of the Fuzzy Weighted Average in Strategic Portfolio Management*

ABSTRACTWe propose a systematic approach that incorporates fuzzy set theory in conjunction with portfolio matrices to assist managers in reaching a better understanding of the overall competitiveness of their business portfolios. Integer linear programming is also accommodated in the proposed integrated approach to help select strategic plans by using the results derived from the previous portfolio analysis and other financial data. The proposed integrated approach is designed from a strategy‐oriented perspective for portfolio management at the corporate level. It has the advantage of dealing with the uncertainty problem of decision makers in doing evaluation, providing a technique that presents the diversity of confidence and optimism levels of decision makers. Furthermore, integer linear programming is used because it offers an effective quantitative method for managers to allocate constrained resources optimally among proposed strategies. An illustration from a real‐world situation demonstrates the integrated approach. Although a particular portfolio matrix model has been adopted in our research, the procedure proposed here can be modified to incorporate other portfolio matrices.

Application of new fuzzy-weighted average (NFWA) method to engineering design evaluation

Engineering design evaluation is characterized by imprecise (vague) importance and satisfaction levels of criteria, which are better treated as fuzzy variables rather than as subjective crisp variables. Nevertheless, operations on fuzzy numbers tend to increase unnecessarily the imprecision when they are combined for some applications, particularly, when a fuzzy-weighted average (FWA) is calculated. This paper proposes a novel method of operating on fuzzy numbers to obtain a fuzzy-weighted average of desirability levels during design evaluation. The method produces overall desirability levels less imprecise and more realistic than those of the conventional FWA. Furthermore, the balance points of these fuzzy numbers seem to be more credible than those of the FWA. An example is presented, which demonstrates the advantages of the method developed.