in this paper, we investigate the general fuzzy linear system of equations.  the  main aim of this paper is based on the embedding approach. we find the necessary and sufficient conditions for the existence of fuzzy solution of the mentioned systems.  finally, numerical examples are presented to more illustration of the proposed model.

in this paper, a fuzzy version of the analytic form of hahn-banachextension theorem is given. as application, the hahn-banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

In this manuscript, we introduce  a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and   propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between  the fuzzy solution set of a  fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtain...

Example 1.1. A field homomorphism K → F is a character by restricting it to the nonzero elements of K (that is, using G = K×) and ignoring the additive aspect of a field homomorphism. In particular, when L/K is a field extension any element of Aut(L/K) is a field homomorphism L→ L and therefore is a character of L× with values in L×. Example 1.2. For any α ∈ F×, the map Z→ F× by k 7→ αk is a ch...

Obviously, a family of linearly dependent functions has a zero Wronskian. Many standard textbooks on differential equations (e.g., [10, Chap. 5, §5.2], [22, Chap. 1, §4], [9, Chap. 3, §7]) contain the following warning: linearly independent functions may have an identically zero Wronskian! This seems to have been pointed out for the first time by Peano [20, 21], who gave the example of the pair...

The notions of linear and metric independence are investigated in relation to the property: if U is a set of m + 1 independent vectors, and X is a set of m independent vectors, then adjoining some vector in U to X results in a set of m + 1 independent vectors. A weak countable choice axiom is introduced, in the presence of which linear and metric independence are equivalent. Proofs are carried ...

an idea of fuzzy reexivity of felbin's type fuzzy normed linear spaces is introduced and its properties are studied. concept of fuzzy uniform normal structure is given and using the geometric properties of this concept xed point theorems are proved in fuzzy normed linear spaces.

We relate properties of linear systems on X to the question of when I contains I(m) in the case that I is the homogeneous ideal of a finite set of distinct points p1, . . . , pn ∈ P , where X is the surface obtained by blowing up the points. We obtain complete answers for when I contains I(m) when the points pi lie on a smooth conic, or when the points are general and n ≤ 9.