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This book introduces readers to the fundamentals of transportation problems under the fuzzy environment and its extensions. It also discusses the limitations and drawbacks of (1) recently proposed aggregation operators under the fuzzy environment and its various extensions; (2) recently proposed methods for solving transportation problems under the fuzzy environment; and (3) recently proposed methods for solving transportation problems under the intuitionistic fuzzy environment. In turn, the book proposes simplified methods to overcome these limitations.
There is a very simple and fundamental concept· to much of probability and statistics that can be conveyed using the following problem. PROBLEM. Assume a finite set (universe) of N units where A of the units have a particular attribute. The value of N is known while the value of A is unknown. If a proper subset (sample) of size n is selected randomly and a of the units in the subset are observed to have the particular attribute, what can be said about the unknown value of A? The problem is not new and almost anyone can describe several situations where a particular problem could be presented in this setting. Some recent references with different focuses include Cochran (1977); Williams (1978); Hajek (1981); Stuart (1984); Cassel, Samdal, and Wretman (1977); and Johnson and Kotz (1977). We focus on confidence interval estimation of A. Several methods for exact confidence interval estimation of A exist (Buonaccorsi, 1987, and Peskun, 1990), and this volume presents the theory and an extensive Table for one of them. One of the important contributions in Neyman (1934) is a discussion of the meaning of confidence interval estimation and its relationship with hypothesis testing which we will call the Neyman Approach. In Chapter 3 and following Neyman's Approach for simple random sampling (without replacement), we present an elementary development of exact confidence interval estimation of A as a response to the specific problem cited above.
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This volume provides an in-depth analysis of over 100 plant communities of the Dolomite vegetation. The data is based on the phytosociological relevés, which have been collected by the authors in nearly 2000 surveys. The key part consists of approx. 130 association tables presenting plant sociological data for the respective plant communities. Thus, this volume perfectly complements the successful main volume “Plant Life of the Dolomites: Vegetation Structure and Ecology,” which features summarized, synoptic association tables of the twelve habitats. In addition, geo-referenced locations of relevés and detailed ecological measures are provided. A further part describes the individual components of the fascinating dolomitic landscape (Heritage of all Humanity) and presents tables of vegetation complexes, which summarize the more than 400 surveys carried out in the Dolomites. The structure of this supplementary volume corresponds to that of the main volume with a key part consisting of twelve chapters, each describing a specific habitat, and a total of 106 associations. Several topics covered in the main volume, such as the exploration of the flora, ecological factors and syntaxonomy are discussed further here.