Type-۲ lattice-valued preorders: A common framework of lattice-valued preorders and various kinds of metrics

W. Yao; G. X. Zhang; Y. Shi

Type-۲ lattice-valued preorders: A common framework of lattice-valued preorders and various kinds of metrics

محل انتشار: مجله سیستم های فازی، دوره: 20، شماره: 3

سال انتشار: 1402

نوع سند: مقاله ژورنالی

زبان: انگلیسی

مشاهده: 116

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https://civilica.com/doc/1663170

شناسه ملی سند علمی:

JR_IJFS-20-3_013

تاریخ نمایه سازی: 2 خرداد 1402

چکیده مقاله:

The aim of this paper is to introduce a concept of type-۲ L-preorders for L being a complete residuated lattice. It can be considered as a common framework of L-preorders and hemimetrics, and also contains various kinds of fuzzy metrics, including Morsi fuzzy metrics, KM-fuzzy metrics and modular metrics, as natural examples. It is shown that the category of L-preordered sets can be reflectively and coreflectively embedded in that of type-۲ L-preordered sets. A type-۲ L-preorder can be supplied as different models for further study.

کلیدواژه ها:

Fuzzy relation ، L-preorder ، type-۲ L-preorder ، Morsi fuzzy metric ، GV-fuzzy metric ، modular metric ، metric-type topology

نویسندگان

W. Yao

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China

G. X. Zhang

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China

Y. Shi

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China

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