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Closed Forms of the Interval Type 2 Fuzzy Sets Additions Based on Archimedean T-norms with Application in Decision Making Aggregation
International Journal of Fuzzy Systems ( IF 4.3 ) Pub Date : 2020-09-15 , DOI: 10.1007/s40815-020-00932-8
Kuo-Ping Chiao

Fuzzy addition is one of the operations widely used in the application of fuzzy systems. The analytical and closed form expressions of the fuzzy additions of the generalized fuzzy numbers and the interval type 2 fuzzy numbers (IT2FS) are developed. The generalized fuzzy numbers is a non-flat and subnormal fuzzy number with different left and right shape functions. Classical fuzzy operations based on the minimum t-norm could lead to uncontrollable fuzziness. Fuzzy addition based on generalized t-norm can better control ambiguity. In order to control the ambiguity of fuzzy addition, this paper is to develop a general type 1 fuzzy set and interval type 2 fuzzy set (IT2FS) additions based on t-norm. The closed forms of the generalized IT2FS additions based on some popular t-norms are formulated. The specific analytical and closed form expressions based on Archimedean t-norms: e.g. drastic, Łukasiewicz, product and the families of Schweizer-Sklar and Yager t-norms are derived. The IT2FS are widely used to characterize the natural words, e.g. the decision making linguistic judgments, the fuzzy real time control systems with linguistic rules. Furthermore, based on the analytical T1FS additions results, the application to the linguistic multiple criteria decision making aggregation of the IT2FS additions based on t-norms is introduced. A comparative MCDM numerical example is demonstrated for the verification of the developed closed form expressions.



中文翻译:

基于阿基米德T范数的区间2型模糊集加法的封闭形式及其在决策聚合中的应用

模糊加法是在模糊系统的应用中广泛使用的运算之一。建立了广义模糊数和区间类型2模糊数(IT2FS)的模糊加法的解析形式和闭式形式。广义模糊数是具有不同左,右形状函数的非平坦且次正规的模糊数。基于最小t范数的经典模糊运算可能会导致不可控制的模糊性。基于广义t范数的模糊加法可以更好地控制歧义。为了控制模糊加法的模糊性,本文将基于t范数开发通用的1型模糊集和区间2型模糊集(IT2FS)加法。制定了基于一些流行的t范数的广义IT2FS加法的封闭形式。推导了基于阿基米德t范式的特定分析式和闭式表达式:例如drastic,Łukasiewicz,乘积以及Schweizer-Sklar和Yager t范式的族。IT2FS被广泛用于表征自然词,例如决策语言判断,具有语言规则的模糊实时控制系统。此外,基于分析的T1FS加法结果,介绍了基于t范数的IT2FS加法在语言多准则决策聚合中的应用。演示了一个比较的MCDM数值示例,用于验证开发的封闭形式表达式。决策语言判断,具有语言规则的模糊实时控制系统。此外,基于分析的T1FS加法结果,介绍了基于t范数的IT2FS加法在语言多准则决策聚合中的应用。演示了一个比较的MCDM数值示例,用于验证开发的封闭形式表达式。决策语言判断,具有语言规则的模糊实时控制系统。此外,基于分析的T1FS加法结果,介绍了基于t范数的IT2FS加法在语言多准则决策聚合中的应用。演示了一个比较的MCDM数值示例,用于验证开发的封闭形式表达式。

更新日期:2020-09-16
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