Introduction to fuzzy arithmetic : theory and applications
Introduction to fuzzy arithmetic : theory and applications
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DOI：
10.2307/2008199
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发表时间：
1986-10
期刊：
影响因子：
--
通讯作者：
A. Kaufmann;M. Gupta
中科院分区：
文献类型：
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作者：
A. Kaufmann;M. Gupta
我们很高兴地阅读了我们的书的评论，介绍模糊算术：理论与应用。这篇评论是由Caroline M.南卡罗来纳州大学的伊士曼，我们很感谢她指出了我们这本书的许多有趣的，积极的方面以及一些缺点。作为模糊社会的成员，我们关注的是概念和技术的研究和发展，这些概念和技术是分析人类感知、思维和推理过程中产生的不确定性的基础。在本书中，我们提出了这些概念和一些处理不确定性的新工具。我们从置信区间[al，a2]的定义开始介绍，其中al和a2分别表示我们的（主观）置信度的下限和上限。接下来，我们将介绍对这些数字的一些算术运算。然后，我们引入了假设的水平[13，1]，并使用它，引入了在我们的推理过程中如此普遍的不确定或模糊数。评论家正确地指出，在某些情况下，区间运算可以被认为是模糊运算的一个子集，这是我们这本书的主要主题。然而，我们故意不想通过引入区间算术然后给出推广来混淆这个问题。我们喜欢我们的方法，就像许多其他使用过这本书的研究人员和学生一样。在我们的方法中，我们一直被引导的愿望，奠定了坚实的基础，模糊数的定义使用的基本概念的置信水平。我们已经介绍了许多新的数学运算的基础上这个概念，并提出了许多推广。此外，我们还介绍了模糊数的一些运算和函数，如整数模运算、三角函数和双曲函数。这些研究已包括为学生以及研究人员谁希望有一个扩展的观点的理论。我们试图对模糊数作一个全面的阐述，用大约115个算例、150个图表和90个表格来说明这一阐述。我们没有包括问题或练习，这将使这本书在教科书的类别。这本书的副标题是“理论与应用”，但正如正确的那样，
We were rather pleased to read the review of our book, Introduction to Fuzzy Arithmetic: Theory and Applications. This review was done quite carefully by Caroline M. Eastman of the University of South Carolina, and we are grateful to her for pointing out many interesting, positive aspects as well as some shortcomings of our book. As members of the fuzzy community, we are concerned with studies and developments of concepts and techniques basic to the analysis of uncertainty arising from human perception, thinking, and reasoning processes. In this book we present such concepts and some novel tools for dealing with uncertainties. We start our introduction with the definition for the interval of confidence [al, a2], where al and a2 represent, respectively, the lower and upper bounds of our (subjective) confidence. Next, we introduce some arithmetic operations on these numbers. We then introduce the level of presumption ue [13, 1] and, using it, introduce the uncertain or fuzzy number that is so pervasive in our reasoning process. The reviewer has rightly pointed out that in certain situations, interval arithmetic can be considered a subset of fuzzy arithmetic, the main topic of our book. However, we intentionally did not want to confuse the issue by introducing interval arithmetic and then giving a generalization. We liked our approach, as have many other researchers and students who have used the book. In our approach, we have been guided throughout by a desire to lay a firm foundation for the definition of fuzzy numbers using the basic concept of level of confidence. We have introduced many novel mathematical operations based on this concept and have presented many generalizations. In addition, we have presented several operations and functions of fuzzy numbers, such as integer modulo operations, trigonometric functions, and hyperbolic functions. These studies have been included for students as well as researchers who wish to have an extended view of the theory. We have attempted to give a thorough exposition of fuzzy numbers; this exposition is illustrated by about 115 worked-out examples, 150 diagrams, and 90 tables. We did not include problems or exercises, which would have put this book in the category of a textbook. The subtitle of the book is "Theory and Applications," but as is rightly