Dissertations / Theses on the topic 'Ranking triangular fuzzy numbers'

O Gerenciamento Ágil de Projetos é uma abordagem útil para projetos com alto grau de complexidade e incerteza. Duas de suas características são: o envolvimento do consumidor nas tomadas de decisão sobre o projeto do produto; e, o uso de uma visão do produto, artefato que representa e comunica as características prioritárias e fundamentais do produto a ser desenvolvido. Há métodos para apoiar a criação da visão do produto, mas eles apresentam deficiências em operacionalizar o envolvimento do consumidor final. Por outro lado, existe a Engenharia Kansei, uma metodologia que permite capturar as necessidades de um grande número de consumidores e relacioná-las a características do produto. Este trabalho apresenta um estudo aprofundado da metodologia da Engenharia Kansei e analisa como essa pode ser útil para apoiar a descrição da visão do produto, no contexto do Gerenciamento Ágil de Projetos de produtos manufaturados. Em seguida, para verificar essa proposição, apresenta o desenvolvimento de um Sistema de Engenharia Kansei baseado na Teoria de Quantificação Tipo I, Aritmética Fuzzy, e Algoritmos Genéticos, testado para o projeto de uma caneta voltada a alunos de pós-graduação. Para execução do projeto foi utilizado um conjunto de métodos e procedimentos, tais como: revisão bibliográfica sistemática; desenvolvimento matemático; desenvolvimento computacional; e, estudo de caso. Analisa-se o Sistema de Engenharia Kansei proposto, e os resultados no caso aplicado, para averiguar seu potencial. Indica evidencias que o Sistema de Engenharia Kansei é capaz de gerar requisitos sobre configurações de produtos segundo a perspectiva do consumidor potencial, e que essas configurações são úteis para a formulação da visão do produto e na evolução desta visão no decorrer do projeto de produto.
The Agile Project Management is a useful approach for projects with high degree of complexity and uncertainty. Two of its singularities are: costumer involvement in decision making about the product design; and the use of a product vision, an artifact that represents and communicates the fundamental and high-priority features of the product to be developed. There are methods to support the creation of the product vision, but they have shortcomings in operationalizing the costumer involvement. On the other hand, there is the Kansei Engineering, a methodology to capture the needs of a large number of consumers and correlate them to product features. This paper presents a detailed study of the Kansei Engineering methodology and analyzes how this can be useful to support the description of the product vision, in the context of Agile Project Management of manufactured products. Then, to verify this proposition, it presents the development of a Kansei Engineering System based on Quantification Theory Type I, Fuzzy Arithmetic and Genetic Algorithms, tested for the design of a pen aimed at graduate students. To implement the project we used a set of methods and procedures, such as systematic literature review, mathematical development, computational development, and case study. It analyzes the proposed Kansei Engineering System and the results in the case study applied, to ascertain their potential. Evidence indicates that Kansei Engineering System is capable of generating requirements on product configurations from the perspective of the potential consumer, and that these configurations are useful for the description of the product vision and for the progression of this vision during the project of the product.

The concept of ranking fuzzy numbers has received significant attention from the research community due to its successful applications for decision making. It complements the decision maker exercise their subjective judgments under situations that are vague, imprecise, ambiguous and uncertain in nature. The literature on ranking fuzzy numbers show that numerous ranking methods for fuzzy numbers are established where all of them aim to correctly rank all sets of fuzzy numbers that mimic real decision situations such that the ranking results are consistent with human intuition. Nevertheless, fuzzy numbers are not easy to rank as they are represented by possibility distribution, which indicates that they possibly overlap with each other, having different shapes and being distinctive in nature. Most established ranking methods are capable to rank fuzzy numbers with correct ranking order such that the results are consistent with human intuition but there are certain circumstances where the ranking methods are particularly limited in ranking non – normal fuzzy numbers, non – overlapping fuzzy numbers and fuzzy numbers of different spreads. As overcoming these limitations is important, this study develops an intuition based decision methodology for ranking fuzzy numbers using centroid point and spread approaches. The methodology consists of ranking method for type – I fuzzy numbers, type – II fuzzy numbers and Z – numbers where all of them are theoretically and empirically validated. Theoretical validation highlights the capability of the ranking methodology to satisfy all established theoretical properties of ranking fuzzy quantities. On contrary, the empirical validation examines consistency and efficiency of the ranking methodology on ranking fuzzy numbers correctly such that the results are consistent with human intuition and can rank more than two fuzzy numbers simultaneously. Results obtained in this study justify that the ranking methodology not only fulfills all established theoretical properties but also ranks consistently and efficiently the fuzzy numbers. The ranking methodology is implemented to three related established case studies found in the literature of fuzzy sets where the methodology produces consistent and efficient results on all case studies examined. Therefore, based on evidence illustrated in this study, the ranking methodology serves as a generic decision making procedure, especially when fuzzy numbers are involved in the decision process.

El objetivo en esta Memoría ha sido el análisis de eficiencia de un determinado sector empresarial, teniendo en cuenta dos problemas casi siempre presentes, y de naturaleza muy diferente, por una parte, que los datos que se manejan pueden ser imprecisos y, por tanto, afectar al resultado de cualquier estudio de eficiencia y, por otra parte, el deseo de ordenar las empresas (Unidades De Toma de Decisión) atendiendo a la medición de su eficiencia. Para la medición de la eficiencia se ha recurrido a la metodología no paramétrica del Análisis Envolvente de datos (DEA) aplicandola a empresas del sector textil muy cercanas a nosotros. Ahora bien, dado que consideramos que siempre existe alguna incertidumbre o un posible error en la medición de algunos datos (inputs y outputs), introducimos la limitación de la certeza con el tratamiento fuzzy de los datos, métodos que no requieren conocer ni aplicar hipótesis sobre distribuciones de probabilidad de esos datos, que dicho sea de paso, podría no ser fáctible bajo determinados supuestos de incertidumbre. Pero además de la medir la eficiencia pretendemos proporcionar más información que la mera separación dicotómica entre empresas eficientes o no eficientes. Para ello desarrollamos y aplicamos los modelos de super-efficiencyfuzzy y cross-efficiency-fuzzy, que nos permiten establecer una ordenación bajo incertidumbre. Con este trabajo hemos realizado un estudio amplio de la eficiencia bajo incertidumbre. Se observa que los resultados obtenidos aplicando los distintos métodos son similares. Además, estos métodos proporcionan más información sobre las unidades estudiadas que las que proporciona un solo índice de eficiencia. Estos métodos pueden ser aplicables a otros tipos de empresas, aportando nueva información que puede ayudar u orientar en la toma de decisiones de sus gestores
Pla Ferrando, ML. (2013). Modelos flexibles para la valoración de la eficiencia [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/31521
TESIS

La predicció de despeses, vendes o cobraments en l’àmbit de l’emprenedoria planteja la dificultat afegida de treballar amb dades extremadament incertes. Aquest fet ocasiona que la previsió de tresoreria o la previsió de pèrdues i guanys tingui associada un alt grau d’indeterminació. La lògica borrosa propicia la creació de nous models de prognosi que afavoreixen que l’emprenedor obtingui una visió de futur més àmplia. El nucli del treball doctoral està format per tres articles que presenten una proposta completa de solució a problemes actuals i reals de la predicció emprenedora centrats en potenciar la utilització de la lògica borrosa a nivell pràctic. Tanmateix, cada article desenvolupa un recurs informàtic d’implementació de cadascuna de les tècniques per tal de facilitar, en el cas que sigui possible, la seva incorporació a la praxi emprenedora.
The prediction of costs, sales and payments in the field of entrepreneurship presents the added difficulty of working with extremely uncertain data. This means that the estimate of “cash flow forecasting” and the “income statement” contains a high degree of indetermination. The fuzzy logic promotes the creation of new prognostic models that allow the entrepreneur to gain a broader vision. The core of the doctoral thesis is formed by three papers in which everyone presents a full proposal for a solution to real and current problems of prediction focused on promoting the use of fuzzy logic in entrepreneurial practice. Additionally, each paper develops a computer resource implementation of each technique in order to facilitate, if possible, its joining of the entrepreneurial practice.

碩士
國立臺南大學
應用數學系碩士班
102
In many fuzzy decision problems, ranking fuzzy numbers is an important procedure. Because of the imperfection and fuzziness of thinking, we need a method to compare fuzzy numbers. So far, a great deal of research has been obtained. Some of them use the centroid point of fuzzy numbers as an index to rank the fuzzy numbers. Having reviewed the previous researches, we found that almost each of them tried to use a formula to rank the fuzzy numbers. However, most of them hardly can rank with intuition consistently in all cases. Therefore, a new method of ranking fuzzy numbers is proposed and compensates for these shortcomings. The new method uses three indices , vi and Si to differentiate between fuzzy numbers. Each indicator has a different significance. Primary consideration is the index which is the x-coordinate of centroid of the fuzzy number. It means representative location of fuzzy number A. To distinguish between the two fuzzy numbers have the same centroid, we use the second index vi . The index vi which means the place that the largest membership function grade happened. When the two fuzzy numbers have the same , we let if . Finally, when the two have the same and vi, we use the third indicator Si which means the remainder area. We let if , otherwise, . In the end, we used a more effective and convenient way to demonstrate a few examples.

博士
國立成功大學
工業管理學系
89
Decision makers usually perform imprecise evaluations for a set of alternatives in an uncertain environment, because of the lack of precise information, such as unquantifiable information, incomplete information, nonobtainable information and partial ignorance. To resolve this problem, fuzzy set theory has been extensively used. Fuzzy numbers are applied to represent the imprecise measurements of different alternatives. This leads that the evaluations of a set of alternatives are actually the ranking of the aggregated fuzzy numbers. The ranking process leads to determine a decision-maker’s preference order of fuzzy numbers. Adopting the concept of alpha-cut, this research specifically develops three ranking methods, namely the total dominance index, the weighted belief measurement index and Integrated Signal/Noise (S/N) index. The total dominance index is defined as the function of the number of alpha-cuts, the index of optimism and the left and right spreads at some alpha — cuts of fuzzy numbers, while the weighted belief measurement index includes the elements in the total dominance index and the weighted average on the basis of alpha—cuts. In addition, the Integrated Signal/Noise index incorporates the signal/noise (S/N) ratio into the weighted belief measurement index. The proposed three ranking methods are simple and efficient in terms of the calculations and comparisons. Unlike the existing integral approaches and area measurements, in the proposed approaches membership functions are not necessary to be known in advance. Only several alpha-cuts are needed for obtaining the index value. In addition, the proposed methods also can be used for ranking nonlinear fuzzy numbers, discrete fuzzy numbers and a pure number.

碩士
國立臺南大學
應用數學系碩士班
103
Recently, many problems of finding the nearest triangular approximation of a fuzzy number had been solved. The symmetric triangular approximations preserving one condition were done, too. In this paper, we use the Karush-Kuhn-Tucker theorem to find the symmetric triangular approximations of fuzzy numbers preserving the width (the ambiguity) (the value). Finally, we illustrate our method by some examples.

碩士
國立臺南大學
應用數學系碩士班
104
Recently, many scholars studied approximations of fuzzy numbers by specific fuzzy num- bers under preservation of some operators. In fact, these approximations may not exist for some linear operators. In order to study necessary and sufficient conditions of linear operators which are preserved by interval, triangular, symmetric triangular, trapezoidal, or symmetric trapezoidal approximations of fuzzy numbers, an effective method for solving such problems is proposed. In this paper, we will propose a formula for computing symmetric triangular approximation of any fuzzy number preserving a given linear operator.

博士
國立臺灣科技大學
工業管理系
102
Ranking fuzzy numbers, a significant component in decision making process, supports a decision maker in selecting the optimal solution. Althoung there are many existing ranking methods for fuzzy numbers, most of them suffer from some shortcomings. To overcome these shortcomings, this study proposes a new ranking approach for both normal and generalized fuzzy numbers that ensures full consideration of all information of fuzzy numbers. The proposed approach integrates the concept of centroid point, the left and the right (LR) areas between fuzzy numbers, height of a fuzzy number and the degree of decision maker’s optimism. Several numerical examples are presented to illustrate the efficiency and superiority of the proposed. To reduce uncertainty in decision making and avoid loss of information, this study also proposed a new fuzzy multi-criteria decision making (MCDM) approach based on the proposed ranking method for generalized fuzzy numbers. The applicability of the proposed fuzzy MCMD model is illustrated through a case study.

碩士
長庚大學
企業管理研究所
95
Weight is one of the most useful tools and it becomes the core of decision-making and the center of a method for measuring attribute importance. Besides, weight method is often measured by fuzzy numbers. Triangular fuzzy numbers (TFNs) and trapezoidal fuzzy numbers (TrFNs) of the types are the most easily and simply of GLRFN. Moreover, we consider the value of fuzzy measures as a linguistic value and then convert linguistic terms to fuzzy numbers. (z)fuzzy measures constructs membership functions that adequately capture the meanings of linguistic terms. The purpose of this study is to use (z)fuzzy measures to determine attribute importance. Then, we use different fuzzy numbers such as TFNs and TrFNs to analyze the result of the empirical study. Besides, we also use different distance measures to adjust attribute importance. In TFNs, we selected five types about five-scales of fuzzy linguistic scale. In TrFNs, we also selected three types about five-scales of fuzzy linguistic scale. First, respondents will choice the most important attribute and then distance measures can adjust between the most important attribute and others. So, we can get the TFN and TrFN of every attribute. Later, we used (z)fuzzy measures to obtain attribute importance. In next step, we will calculate (z)fuzzy integrals for all alternatives and use centre-index method to get a crisp number. Finally, we establish a priority of alternatives with respondents using Spearman rank-order correlation coefficient, the consistency of the best alternative and the consistency of the better alternative. We collect sixteen samples from college and graduate school. The result showed three points. First, there are no significant difference between five scales of TFNs and three scales of TrFNs. Second, TFNs obtain similar analysis result to TrFNs. Therefore, we can not use more complex TrFNs to determine attributes importance. Finally, there are no significant differences between three distance measures.

碩士
國立臺灣科技大學
資訊工程系
97
In this thesis, we present two new methods for dealing with fuzzy risk analysis problems. We propose a fuzzy risk analysis algorithm based on a new method for ranking generalized fuzzy numbers and propose a fuzzy risk analysis algorithm based on a new similarity measure between interval-valued fuzzy numbers. First, we present a new method for ranking generalized fuzzy numbers. The proposed fuzzy ranking method considers the areas on the positive side, the areas on the negative side and the heights of the generalized fuzzy numbers to evaluate ranking scores of the generalized fuzzy numbers. We also prove the properties of the proposed fuzzy ranking method and show that it can overcome the drawbacks of the existing fuzzy ranking methods. Then, we apply the proposed method for ranking generalized fuzzy numbers to develop a new method for dealing with fuzzy risk analysis problems. Moreover, we also present a new similarity measure between interval-valued fuzzy numbers. The proposed method considers the degrees of closeness between interval-valued fuzzy numbers on the X-axis and the degrees of differences between the shapes of the interval-valued fuzzy numbers on the X-axis and the Y-axis, respectively. We also prove three properties of the proposed similarity measure and make an experiment to compare the experimental results of the proposed method with the existing similarity measures between interval-valued fuzzy numbers. Based on the proposed similarity measure between interval-valued fuzzy numbers, we present a new fuzzy risk analysis algorithm for dealing with fuzzy risk analysis problems. The proposed algorithm is more flexible than Chen and Chen’s method due to the fact that Chen and Chen’s method lacks the capability to let the evaluating values of the risk of each sub-component for fuzzy risk analysis to be represented by interval-valued fuzzy numbers.

碩士
國立臺灣科技大學
資訊工程系
97
In this thesis, we present a new method for fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights. First, we present a method for ranking generalized fuzzy numbers with different left heights and right heights. The proposed method considers the areas of the positive side, the areas of the negative side and the centroid values of generalized fuzzy numbers as the factors for calculating the ranking scores of generalized fuzzy numbers with different left heights and right heights. It can overcome the drawbacks of the existing fuzzy ranking methods. Based on the proposed fuzzy ranking method of generalized fuzzy numbers with different left heights and right heights, we propose a new method for dealing with fuzzy risk analysis problems. The proposed fuzzy risk analysis method provides us with a useful way to deal with fuzzy risk analysis problems based on generalized fuzzy numbers with different left heights and right heights.

碩士
國立臺灣科技大學
資訊工程系
95
In this thesis, we present two methods for fuzzy risk analysis based on ranking generalized fuzzy numbers and similarity measures between interval-valued fuzzy numbers. First, we present a new method for ranking generalized fuzzy numbers for handling fuzzy risk analysis problems. The proposed method considers defuzzified values, the weight and the spreads of generalized fuzzy numbers. Moreover, we also apply the proposed method for ranking generalized fuzzy numbers to present a new method for dealing with fuzzy risk analysis problems. Then, we present a new similarity measure for interval-valued fuzzy numbers. The proposed similarity measure considers five factors, i.e., the degree of similarity on X-axis between the upper fuzzy numbers of the interval-valued fuzzy numbers, the degree of similarity about the weight of the upper fuzzy numbers of the interval-valued fuzzy numbers, the spread between the upper fuzzy numbers of the interval-valued fuzzy numbers, the degree of similarity on the X-axis between the interval-valued fuzzy numbers, and the degree of similarity on the Y-axis between the interval-valued fuzzy numbers. Moreover, we also present new interval-valued fuzzy numbers arithmetic operators and apply the proposed similarity measure to present a new method for dealing with fuzzy risk analysis problems based on interval-valued fuzzy numbers. The proposed fuzzy risk analysis methods provide us a useful way for handling fuzzy risk analysis problems.

博士
國立臺灣科技大學
工業管理系
101
Ranking fuzzy numbers plays an important role in decision analysis and applications. The last few decades have seen a large number of approaches investigated for ranking fuzzy numbers such as maximizing set and minimizing set concept, integral value, centroid point, distance approach, deviation degree, and magnitude concepts. Nevertheless, some of these approaches are non-intuitive and even inconsistent. Therefore, this study indicates the shortcomings of several existing ranking approaches and proposes improved ranking approaches for fuzzy numbers to overcome their shortcomings. Based on the proposed ranking approaches, an extension of fuzzy multi-criteria decision making is developed for supporting the medical provider selection and evaluation selection process. In the proposed fuzzy multi-criteria decision making model, the ratings of alternatives and importance weight of criteria for medical providers are expressed in linguistic terms. This study then can also obtain the membership functions of the final fuzzy evaluation value in the proposed model. To make the procedure easier and more practical, the normalized weighted ratings are defuzzified into crisp values by using the improved ranking approaches to determine the ranking order of alternatives. This study also uses a numerical example to demonstrate the applicability and advantages of the proposed multi-criteria decision making model.