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 ...

in this paper we classify fuzzy subgroups of a rank-3 abelian group $g = mathbb{z}_{p^n} + mathbb{z}_p + mathbb{z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. we present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...

in this paper we introduce the root of a fuzzy number, and we present aniterative method to nd it, numerically. we present an algorithm to generatea sequence that can be converged to n-th root of a fuzzy number.

A right ternary N -group (RTNG) over a right ternary near-ring N is a generalization of its binary counterpart and fuzzy soft sets are generalization of soft sets which are parameterized family of subsets of a universal set. In this paper fuzzy soft N -subgroups and N -ideals over right ternary N -groups are defined and their basic algebraic properties are studied. Fuzzy soft N -subgroups and N...

n-Dimensional fuzzy sets is a fuzzy set extension where the membership values are n-tuples of real numbers in the unit interval [0, 1] orderly increased, called n-dimensional intervals. The set of n-dimensional intervals is denoted by Ln([0, 1]). This paper aims to investigate a special extension from [0, 1] – n-representable fuzzy negations on Ln([0, 1]), summarizing the class of such function...

In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuz...

For any two points P = (p (1) ,p (2) ,...,p (n)) and Q = (q (1) ,q (2) ,...,q (n)) of R n , we define the crisp vector → PQ = (q (1) −p (1) ,q (2) −p (2) ,...,q (n) −p (n)) = Q(−)P. Then we obtain an n-dimensional vector space E n = { → PQ | for all P,Q ∈ R n }. Further, we extend the crisp vector into the fuzzy vector on fuzzy sets of R n. Let D, E be any two fuzzy sets on R n and define the f...

this paper presents a mathematical model for a flow shop scheduling problem consisting of m machine and n jobs with fuzzy processing times that can be estimated as independent stochastic or fuzzy numbers. in the traditional flow shop scheduling problem, the typical objective is to minimize the makespan). however,, two significant criteria for each schedule in stochastic models are: expectable m...

This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Lukasiewicz n-valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n-valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the al...