Article ID Journal Published Year Pages File Type
6856043 Fuzzy Sets and Systems 2018 8 Pages PDF
Abstract
In this work we state a number of theorems about fuzzy (quasi-)pseudometrizable algebraic structures. Our most useful results are: (1) a fuzzy semitopological group whose topology is induced by a left-invariant fuzzy (quasi-)pseudometric, then it is a fuzzy (paratopological) topological group, (2) if the topology on a semigroup S is induced by an invariant fuzzy quasi-pseudometric, then S is a fuzzy topological semigroup, and (3) the same conclusion is valid for a left-invariant fuzzy quasi-pseudometric on a monoid G such that the left translations are open and the right translations are continuous at the identity e of G. By means of the standard fuzzy (quasi-)pseudometric Md associated to a (quasi-)pseudometric d, our results apply in the case of semitopological groups, semigroups and monoids in order to obtain new results that allow us to generalize and to strengthen previous outcomes.
Related Topics
Physical Sciences and Engineering Computer Science Artificial Intelligence
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