A natural equivalence relation on the set of all fuzzy subsets, generalizing the equality of crisp sets, was recently introduced and studied in various contexts such as finite fuzzy subsets, fuzzy vector space, finite fuzzy subfields and in the classification of finite Abelian groups. In this paper, we restrict this equivalence to the set of fuzzy points and study its effect on the relationship...

Based on the analysis of the rough set model on a tolerance relation and the fuzzy rough set, two types of fuzzy rough sets models on tolerance relations are constructed and researched. Then we propose the optimistic and pessimistic multi-granulation fuzzy rough sets models in a fuzzy tolerance approximation space with the point view of granular computing. In these models, the fuzzy lower and u...

The object of this paper is to introduce the notion of intuitionisticfuzzy continuous mappings and intuitionistic fuzzy bounded linear operatorsfrom one intuitionistic fuzzy n-normed linear space to another. Relation betweenintuitionistic fuzzy continuity and intuitionistic fuzzy bounded linearoperators are studied and some interesting results are obtained.

In this paper, the Cartesian products on fuzzy soft set are defined, and the fuzzy soft relations can be presented based on the Cartesian products, including uni-int decision relation and level fuzzy soft relation. By using these new concepts an unt-int decision making method based on fuzzy soft set is constructed to selects a fuzzy set of optimum elements from the alternatives. Finally, an exa...

Semantic relations between concepts or data are common modelling devices in various knowledge representation approaches. Fuzzy relations can be defined as fuzzy subsets of the cartesian product of a number of domains, extending the notion of crisp relation. Associations in object-oriented modelling – and more specifically in the Unified Modelling Language – can be interpreted as crisp relations...

The representation of imprecise, uncertain or inconsistent information is not possible in relational databases, thus they require addonns to handle these types of information. One possible add-on is to allow the attributes to have values that are fuzzy sets on the attribute domain, which result in fuzzy relational databases (FRDB). From the implementational point of view, values are limited to ...

Fuzzy Formal Concept Analysis (FCA) is a mathematical tool for the effective representation of imprecise and vague knowledge. However, with a large number of formal concepts from a fuzzy context, the task of knowledge representation becomes complex. Hence, knowledge reduction is an important issue in FCA with a fuzzy setting. The purpose of this current study is to address this issue by proposi...

Fuzziness is an important aspect of the uncertainties of spatial data. In this paper, the mechanism and methods of spatial modeling for fuzzy geographical objects are focused and the following two issues are resolved: (1) Modeling fuzzy geographical objects; (2) Modeling the relation between two fuzzy geographical objects. In the first issue, fuzzy geographical objects are defined by the novel ...

In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches. 

This paper is devoted to the discussion of the relationship between fuzzy rough set models and fuzzy topologies on a finite universe. The (TC) axiom for fuzzy topology is proposed. It is proved that the set of all lower approximation sets based on a reflexive and transitive fuzzy relation consists of a fuzzy topology which satisfies (TC) axiom; and conversely, a fuzzy topology which obey (TC) a...