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In this paper, we deal with special generalization of metric spaces by considering the distances between objects as gradual numbers. Firstly, the concept of gradual metric spaces is introduced. The new concept is a generalization of classical metric spaces and gradual linear normed spaces in the sense of Sadeqi and Azart. And then, basic concepts with respect to topology in gradual metric spaces are...
Based on a frame L, fuzzy posets make a good framework of quantitative domain theory. In this paper, we propose the definition of locally order preserving functors between the categories of fuzzy directed-complete posets and show that these functors can preserve adjointness, surjectivity and injectivity of maps having an adjoint.
By means of semi-pre-open L-sets and their inequality, the new countable SP-compactness and SP-Lindelöf property are introduced in L-topological spaces, where L is a complete De Morgan algebra. The new notions do not depend on the structure of basis lattice L which does not require any distributivity. These new notions are good extensions and have many characterizations as well, when L is completely...
By means of semi-pre-open L-sets and their inequality, the new countable SP-compactness and SP-Lindelöf property are introduced in L-topological spaces, where L is a complete De Morgan algebra. The new notions do not depend on the structure of basis lattice L which does not require any distributivity. These new notions are good extensions and have many characterizations as well, when L is completely...
In this paper, we introduce the concepts of Sh-interval valued fuzzy left ideal, Sh-interval valued fuzzy right ideal, Sh-interval valued fuzzy ideal and extension principle of interval valued fuzzy set, investigate some properties and propose some theorems for homomorphic image and its inverse image on Sh-interval valued fuzzy ideal. Finally, we investigate some properties on character of Sh-interval...
The convergence theory is a basic theory of fuzzy mathematics and have very important applications in economics, management science, information technology and computer science. In this paper we introduce the notions of fuzzy PS-upper limit, fuzzy PS-lower limit and the fuzzy PS-convergent nets of fuzzy sets. We also study the properties of fuzzy PS-upper limit, fuzzy PS-lower limit and the fuzzy...
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