Some Properties of Alexandrov Topologies
نویسندگان
چکیده
Alexandrov topologies are the topologies induced by relations. This paper addresses the properties of Alexandrov topologies as the extensions of strong topologies and strong cotopologies in complete residuated lattices. With the concepts of Zhang’s completeness, the notions are discussed as extensions of interior and closure operators in a sense as Pawlak’s the rough set theory. It is shown that interior operators are meet preserving maps and closure operators are join preserving maps in the perspective of Zhang’s definition.
منابع مشابه
Join-meet Approximation Operators Induced by Alexandrov Fuzzy Topologies
In this paper, we investigate the properties of Alexandrov fuzzy topologies and join-meet approximation operators. We study fuzzy preorder, Alexandrov topologies join-meet approximation operators induced by Alexandrov fuzzy topologies. We give their examples.
متن کاملFUZZY PREORDERED SET, FUZZY TOPOLOGY AND FUZZY AUTOMATON BASED ON GENERALIZED RESIDUATED LATTICE
This work is towards the study of the relationship between fuzzy preordered sets and Alexandrov (left/right) fuzzy topologies based on generalized residuated lattices here the fuzzy sets are equipped with generalized residuated lattice in which the commutative property doesn't hold. Further, the obtained results are used in the study of fuzzy automata theory.
متن کاملThe Functorial Relations between Alexandrov Fuzzy Topologies and Upper Approximation Operators
In this paper, we investigate functorial relations between Alexandrov fuzzy topologies and upper approximation operators in complete residuated lattices. We present some examples. AMS Subject Classification: 03E72, 03G10, 06A15, 06F07, 54A40
متن کاملJoin Preserving Maps, Fuzzy Preorders and Alexandrov Fuzzy Topologies
In this paper, we investigate the properties of join preserving maps in complete residuated lattices. We define join approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between join preserving operators and Alexandrov fuzzy topologies. We give their examples. AMS Subject Classification: 03E72, 03G10, 06A15, 06F07
متن کاملSome topologies on the space of quasi-multipliers
Assume that $A$ is a Banach algebra. We define the $beta-$topology and the $gamma-$topology on the space $QM_{el}(A^{*})$ of all bounded extended left quasi-multipliers of $A^{*}.$ We establish further properties of $(QM_{el}(A^{*}),gamma)$ when $A$ is a $C^{*}-$algebra. In particular, we characterize the $gamma-$dual of $QM_{el}(A^{*})$ and prove that $(QM_{el}(A^{*}),gamma)^{*},$...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Int. J. Fuzzy Logic and Intelligent Systems
دوره 15 شماره
صفحات -
تاریخ انتشار 2015