Fuzzy relation equations are becoming extremely important in order to investigate the optimal solution of the inverse problem even though there is a restrictive condition for the availability of the solution of such inverse problems. We discussed the methods for finding the optimal (maximum and minimum) solution of inverse problem of fuzzy relation equation of the form $R \circ Q = T$ where for both cases R and Q are kept unknown interchangeably using different operators (e.g. alpha, sigma etc.). The aim of this study is to make an in-depth finding of best project among the host of projects, depending upon different factors (e.g. capital cost, risk management etc.) in the field of civil engineering. On the way to accomplish this aim, two linguistic variables are introduced to deal with the uncertainty factor which appears in civil engineering problems. Alpha-composition is used to compute the solution of fuzzy relation equation. Then the evaluation of the projects is orchestrated by defuzzifying the obtained results. The importance of adhering to such synopsis, in the field of civil engineering, is demonstrated by an example.

Eigen fuzzy sets of fuzzy relation can be used for the estimation of highest and lowest levels of involved variables when applying max-min composition on fuzzy relations. By the greatest eigen fuzzy sets (set which can be greater anymore) maximum membership degrees of any fuzzy set can be found, with the help of least eigen fuzzy set (set which can be less anymore) minimum membership degrees of any fuzzy sets can be found as well.The lowest and highest level, impact or e ffect of anything can be found by applying eigen fuzzy set theory. The implicational aspect of this research study is medical and customer satisfaction level measurement. By applying methods of eigen fuzzy set theory the e ffectiveness of medical cure and customer satisfaction can be found with high precision.

We are living in a world full of uncertainty and ambiguity. We usually ask ourselves questions that we are uncertain about their answers. Is it going to rain tomorrow? What will be the exchange rate of euro next month? Why, where and how should I invest? Type-1 Fuzzy sets are characterized by the membership function whose value for a given element x is said to be the grade of membership having a value in the interval [0, 1]. In addition, type-1 fuzzy sets have limited capabilities to deal with uncertainty. In our thesis, we study another concept of a fuzzy description of uncertainty which is called Type-2 fuzzy sets. According to this concept, for any given element x, we can’t speak of an unambiguously specified value of the membership function. Moreover, Type-2 fuzzy sets constitute a powerful tool for handling uncertainty. The aim of our thesis is to examine the potential of the Type-2 fuzzy sets especially in decision making. So, we present basic definitions concerning Type-2 fuzzy sets, and operations on these sets are to be discussed too. Then, Type-2 fuzzy relations and methods of transformation of Type-2 fuzzy sets will be introduced. Also, the theory of Type-2 Fuzzy sets will serve for the construction of the fuzzy inference system. Finally, we utilize interval type-2 fuzzy sets in the application of Multiple Attributes Group Decision Making which is called TOPSIS.

本研究的主要目的，在應用模糊理論，建立改進傳統系統分析模式。並以高中教科書評選為例，首先使用評鑑因素重要程度模糊問卷及教科書評鑑表，建立因素模糊相對權重矩陣與模糊評估矩陣，同時以模糊眾數和模糊評估與傳統方法進行比較分析。我們經由實際評選發現，應用模糊評選教科書，比傳統評選教科書來得合理。在尋求適當的共識時，模糊統計較能適時反應出人們實際的想法。 / The purpose of this study is to develop a system analysis by fuzzy theory. A comparison was made between fuzzy sample mode, fuzzy evaluation and the conventional method about textbook selection. In order to establish the factor fuzzy relation weight matrix and to estimate fuzzy evaluation matrix, we use the fuzzy weight and evaluation questionnaire first. It was found, by way of the actual evaluation, that the application of fuzzy evaluation is better than the traditional evaluation. While looking for appropriate consensus, fuzzy statistics is a better reflection of popular idea.

In recent years the greater emphasis is placed on the renewable energy sources that are environmentally friendly. Demand for renewable energy sources is supported by government incentives, which leads to an increasing pace of investment in this sector. Prices for electricity from renewable energies are far higher than the prices of conventional electricity. If the current trend continues, it is only a matter of time before they meet. According to this fact, PRE Company decided to invest in hydropower. This thesis deals with identifying of potential investment opportunities in small hydropower plants from the PRE point of view and the subsequent evaluation of these variants on the basis of multi-criteria decision making.

本文嘗試以模糊理論的觀念，應用到時間數列分析上。研究重點包括模糊關係、模糊規則庫和模糊時間數列模式建構與預測等。我們首先給定模糊時間數列模式的概念與一些重要性質。接著提出模糊規則庫的定義，以及模式建構的流程，並以模糊關係方程式的推導，提出模糊時間數列模式建構方法。最後，利用提出的方法，對台灣地區加權股票指數建立模糊時間數列模式，並對未來進行預測，且考慮以平均預測準確度來做預測效果之比較。這對於財務金融的未來走勢分析將深具意義。 / The paper has attempted to apply the concept of fuzzy method on the analysis of time series. This reserch is also to include fuzzy relation, fuzzy rule base, fuzzy time series model constructed and forecasting. First, we'll define the concept of fuzzy time series model and some important properties. Next, the definition of fuzzy rule base will also be put forward, along with procedure of model constructed, the formation of fuzzy relation polynomial, and the methods to construct fuzzy time series model. At last, with the above methods, we'll build up fuzzy time series model on Taiwan Weighted Index and predict future trend while examine the predictive results with average forecasting accuracy. This shall carry profund signifigornce on the analysis of future trend in terms of financialism.

近年來，隨著科技的進步與工商業的發展，預測技術的創新與改進愈來愈受到重視，同樣地，對於預測準確度的要求也愈來愈高。尤其在經濟建設、人口政策、經營規畫、管理控制等問題上，預測更是決策過程中不可或缺的重要資訊。有鑑於此，本論文嘗試應用模糊關係方程式，提出多變量模糊時間數列建構過程及轉折區間檢測模式理論架構。另一方面，多變量模糊時間數列模式建構過程，研究者曾提出很多轉折點之偵測與檢定方法，然而在實際的例子中，時間數列之結構改變所呈現出來的是一種緩慢的改變過程，即轉折點本身就是模糊不確定。這個概念在建構不同模式分析各國經濟活動數據時更顯重要。本論文針對轉折區間之檢測提出一個完整的認定程序。多變量時間數列系統中的隸屬度函數等於在計算成果指標群時的群集中心。應用本論文提出的方法，我們以德國、法國及希臘之總體經濟指標GDP為例，考慮通貨膨脹率、GDP成長率及投資率來進行轉折區間的檢測。 / In recent years, along with the technological advancement and commercial development, the creation and improvement of forecasting techniques have more and more attention. Especially at the economic developments, population policy, management planning and control, forecasting gives necessary and important information in the decision-making process. Regarding stock market as the example, these numerals of closing price are uncertain and indistinct. Again, the factors of influence on quantity are numerous, such as turnover, exchange rate etc. Therefore, if we consider merely the closing price of front day to build and forecast, we will not only misestimate the future trend, but also will cause unnecessary damage. Owing to this reason, we propose the procedure of multivariate fuzzy time series model constructed and theory structure by fuzzy relation equation. Combining closing price with turnover, we apply our methods to build up multivariate fuzzy time series model on Taiwan Weighted Index and predict future trend while examine the predictive results with average forecasting accuracy. A fuzzy time series is defined on averages of cumulative fuzzy entropies of the tree time series. Finally, an empirical study about change periods identification for Germany, France and Greece major macroeconomic indicators are demonstrated.

[pt] A área de química do estado sólido ocupa uma posição cada vez mais importante nas atividades de pesquisa e desenvolvimento farmacêuticas. A compreensão das propriedades do estado sólido de um insumo farmacêutico ativo (IFA) mostra-se crítica no desenvolvimento de formulações em função de seus impactos na biodisponibilidade e solubilidade dos fármacos, sendo essencial para garantir o benefício terapêutico, otimizar o desenvolvimento e garantir a proteção da propriedade intelectual. Esta tese investiga indicadores científicos e tecnológicos na área de química do estado sólido utilizando ferramentas de ciência dos dados a partir de publicações científicas e depósitos de patentes, visando contribuir para o aumento da competitividade da indústria farmoquímica e farmacêutica brasileira e de outros mercados emergentes. A partir da utilização de ferramentas de ciência dos dados é proposta uma metodologia baseada em técnicas de text mining associadas a relações fuzzy. Essa metodologia de identificação de competências específicas aplicada na área de química do estado sólido tem como estudo de caso a descoberta de uma nova forma polimórfica para o IFA acetato de dexametasona. Os resultados revelam que existem competências científicas em química do estado sólido no Brasil. Contudo, quando comparada com a interação universidade-empresa mundial, a indústria farmoquimica e farmacêutica local perde em estágio de competitividade e desenvolvimento. Por outro lado, os resultados demonstram a robustez da metodologia e sua capacidade de identificar pesquisadores em área específicas, oferecendo soluções para apoio a tomada de decisão e identificação de pesquisadores relevantes para o desenvolvimento do setor farmoquímico e farmacêutico. / [en] The solid-state chemistry area has received increased attention in the pharmaceutical research and development activities. The comprehension of the solid-state properties of an active pharmaceutical ingredient (API) is critical in the development of formulations due to their impact on the bioavailability and solubility of the final drug, being essential to ensure therapeutic benefit, optimize development and allow a proper intellectual property protection. This research investigates science and technology indicators in the solid-state chemistry area using data science tools applied to scientific publications and patent documents, aiming to contribute to the increase of the competitiveness of the pharmaceutical industry in Brazil and in other emerging markets. Through data science tools, a methodology based on text mining techniques associated to fuzzy relations is proposed. This methodology for identifying specific competencies is applied in the solid-state chemistry area exploring a case study of the discovery of a new polymorphic form of the API dexamethasone acetate. The results reveal the existence of scientific competencies in solid-state chemistry in Brazil. However, when compared to the global university-company interaction, the local pharmaceutical industry shows a lower stage of competitiveness and development. On the other hand, the results indicates the robustness of the methodology and its ability to identify researchers in specific areas, offering solutions to support the decision making and identification of researchers relevant to the development of the pharmaceutical sector.