Fuzzy set theory is a useful tool to describe situations in which the data are imprecise or vague. Fuzzy sets handle such situation by attributing a degree to which a certain object belongs to a set. The idea of fuzzy norm was initiated by Katsaras in [1984]. Felbin [1992] defined a fuzzy norm on a linear space whose associated fuzzy metric is of Kaleva and Seikkala type [1984]. Cheng and Morde...

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

and Applied Analysis 3 a vector space from various points of view 28–30 . In particular, Bag and Samanta 31 , following Cheng and Mordeson 32 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 33 . They established a decomposition theorem of a fuzzy norm into a family of crisp norms and investigated some properties of fuzzy normed ...

It has been developed a C++ program that generates random fuzzy relations of a given dimension and computes their T-transitive closure (that contains the initial relation) and the new T-transitivized relation (that is contained in the initial relation) for the t-norms minimum, product and Lukasiewicz. It has been computed several distances between both transitive closure and transitivized relat...

We prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of Aliouche, et al. [2], Rao et al. [14] and [15].

Fuzzy relational database handle uncertain and imprecise information for consistent operation on database and manipulate information. In this paper, I introduced fuzzy normal forms for similarity based fuzzy relational database model. First of all I have focused on fuzzy closure of attribute set which can be utilized to find fuzzy key. Next, with the concepts of α -ffd [1], I have defined fuzzy...

In this paper, we present a new method for fuzzy information retrieval based on multi-relationship fuzzy concept networks. There are four kinds of fuzzy relationships in a multi-relationship fuzzy concept network, i.e., “fuzzy positive association” relationship, “fuzzy negative association” relationship, “fuzzy generalization” relationship and “fuzzy specialization” relationship. By performing ...

In this paper, we introduce intuitionistic fuzzy incline (IFI), intuitionistic fuzzy incline matrix (IFIM) and its determinant. Also the transitive closure, power of convergent, nilpotence of IFIM and adjoint of an IFIM are considered here. Some properties of determinant of IFIM and triangular IFIM are also introduced here. 2010 AMS Classification: 03E72, 15A15, 15B15

This article introduces interior and closure operators with inclusion degree considered within a crisp or fuzzy topological framework. First, inclusion degree is introduced in an extension of the interior and closure operators in crisp topology. This idea is then introduced in fuzzy topology by incorporating a relaxed version of fuzzy subsethood. The introduction of inclusion degree leads to a ...