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首页> 外文期刊>International journal of general systems >FOUNDATIONS OF FUZZY FUNCTIONS AND VAGUE ALGEBRA BASED ON MANY-VALUED EQUIVALENCE RELATIONS, PART Ⅰ: FUZZY FUNCTIONS AND THEIR APPLICATIONS
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FOUNDATIONS OF FUZZY FUNCTIONS AND VAGUE ALGEBRA BASED ON MANY-VALUED EQUIVALENCE RELATIONS, PART Ⅰ: FUZZY FUNCTIONS AND THEIR APPLICATIONS

机译：基于多值等价关系的模糊函数和Vaue代数的基础，第一部分：模糊函数及其应用

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Strong fuzzy functions and perfect fuzzy functions based on *-fuzzy equalities were studied, and applied to fuzzy control [Demirci, M. (2000) "Fuzzy functions and their applications", J. Math. Anal. Appl. 252, 495―517] and vague algebra [Demirci, M. (1999b) "Vague groups", J. Math. Anal. Appl. 230, 142―156; Demirci, M. (2002a) "Fundamentals of M-vague algebra and M-vague arithmetic operations", Int. J. Uncertainty Fuzziness Knowledge-Based Systems 10 (1), 25―75]. This paper introduces the general theory of strong (perfect) fuzzy functions on the basis of many valued equivalence relations, and establishes the fundamental tools of this theory. Another aim of the present paper is to develop the modelling of input/output systems by strong (perfect) fuzzy functions, and is to propose the description of laws of nature by strong (perfect) fuzzy functions. The present paper also forms the rudimentary base of M-vague algebra on the basis of many-valued equivalence relations, presented in the cognate papers [Demirci, M. (2003d) "Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, Part Ⅱ: Vague algebraic notions", Int. J. General Systems 32, 157―175; Demirci, M. (2003e) "Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, Part Ⅲ: Constructions of vague algebraic notions and vague arithmetic operations", Int. J. General Systems 32, 177―201].
机译：研究了基于*模糊等式的强模糊函数和完美模糊函数，并将其应用于模糊控制[Demirci，M.（2000）“模糊函数及其应用”，J. Math。肛门应用252，495―517]和模糊代数[Demirci，M.（1999b）“ Vague groups”，J. Math。肛门应用230，142―156; Demirci，M.（2002a）“ M-Vague代数和M-Vague算术运算的基础”，国际。 J.基于知识的不确定性模糊系统10（1），25-75]。本文在许多有价值的等价关系的基础上介绍了强（完善）模糊函数的一般理论，并建立了该理论的基本工具。本文的另一个目的是通过强（完美）模糊函数来开发输入/输出系统的建模，并通过强（完美）模糊函数来提出自然定律的描述。本文还根据多值等价关系构成了M-vague代数的基本基础，这些文献在相关论文中提出[Demirci，M.（2003d）“基于多值等价的模糊函数和vague代数的基础关系，第二部分：模糊代数概念”，诠释学。 J.通用系统32，157-175; Demirci，M.（2003e）“基于多值等价关系的模糊函数和模糊代数的基础，第三部分：模糊代数概念和模糊算术运算的构造”，国际。 J.通用系统32，177-201]。

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