A non-trivial example of an L-topological space, the L-fuzzy real line is examined. Various L-topological properties and their relationships are developed. Extension theorems on the L-fuzzy real line as well as extension theorems on more general L-topological spaces follow. Finally, a theory of L-fuzzy vector spaces leads up to a fuzzy version of the Hahn-Banach theorem.

One way to increase the power of Qualitative Spatial Reasoning is to introduce proximity operators (such as close and far) that are surrogates for distance measures. These operators appear to be semi-quantitative in nature as opposed to purely qualitative. In the light of observations drawn from psychometric testing of perceived proximity, this paper discusses how a model to support proximal re...

the concept of an $l$-bornology is introduced and the theory of $l$-bornological spacesis being developed. in particular the lattice of all $l$-bornologies on a given set is studied and basic properties ofthe category of $l$-bornological spaces and bounded mappings are investigated.

In this paper, we investigate the properties of join and meet preserving maps in complete residuated lattice using Zhang’s the fuzzy complete lattice which is defined by join and meet on fuzzy posets. We define L-upper (resp. L-lower) approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between L-upper (resp. L-l...

Based on the idea that the closer the query terms in a document are, the more relevant this document is, we propose a information retrieval method based on a fuzzy proximity degree of term occurences to compute document relevance to a query. Our model is able to deal with Boolean queries, but contrary to the traditional extensions of the basic Boolean information retrieval model, it does not ex...

In this paper, the notion of fuzzy semicompactness degrees isintroduced in $L$-fuzzy topological spaces by means of theimplication operation of $L$. Characterizations of fuzzysemicompactness degrees in $L$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.

In this paper, conventional validity indexes are reviewed and the shortcomings of the fuzzy cluster validation index based on intercluster proximity are examined. Based on these considerations, a new cluster validity index is proposed for fuzzy partitions obtained from the fuzzy c-means algorithm. The proposed validity index is defined as the average value of the relative intersections of all p...