کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
394767 665841 2011 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Some remarks on the lattice of fuzzy intervals
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
Some remarks on the lattice of fuzzy intervals
چکیده انگلیسی

In this paper we study the connections between three related concepts which have appeared in the fuzzy literature: fuzzy intervals, fuzzy numbers and fuzzy interval numbers (FIN’s). We show that these three concepts are very closely related. We propose a new definition which encompasses the three previous ones and proceeds to study the properties ensuing from this definition. Given a reference lattice (X, ⊑), we define fuzzy intervals to be the fuzzy sets such that their p-cuts are closed intervals of (X, ⊑). We show that, given a complete lattice (X, ⊑), the collection of its fuzzy intervals is a complete lattice. Furthermore we show that, if (X, ⊑) is completely distributive, then the lattice of its fuzzy intervals is distributive. Finally we introduce a new inclusion measure, which can be used to quantify the degree in which a fuzzy interval is contained in another, an approach which is particularly valuable in engineering applications.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Information Sciences - Volume 181, Issue 10, 15 May 2011, Pages 1863–1873
نویسندگان
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