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: In this paper we introduce fuzzy det-norm ordering with fuzzy matrices using the structure of M n ( F ) , the set of ( n × n ) fuzzy det-norm ordering with fuzzy matrices is introduced. From this row and column, determinant of the fuzzy norm has been obtained by imposing an equivalence relation on M n ( F ) . We know that the comparability relation on fuzzy matrices is a partial ordering. We prove that det-norm ordering is a partitions ordering on the set of all idempotent matrices in M n ( F ) . We begin with the det-norm ordering on fuzzy matrices as analogue of the ordering on real matrices. Several properties of these orderings are derived. Discuss their relationship between these ordering with det-norm ordering and Also we introduce the concept of Fuzzy norm and partitions of M n ( F ) , Properties of fuzzy det-norm ordering.


Introduction
The concept of fuzzy set was introduced by Zadeh [ Chen. [2] introduced the Fuzzy matrix partial ordering and generalized inverse. Bertoiuzza [1] introduced the distributivity of t-norm and t-conorms. In 1995, Ragab .M. Z. and Emam E. G [7] introduced the determinant and adjoint of a square fuzzy matrix. Meenakshi A.R. and Cokilavany R. [3] introduced the concept of fuzzy 2-normed linear spaces. Nagoorgani A. and Kalyani G. [5] Introduced the Binormed sequences in fuzzy matrices. Nagoorgani A. and Kalyani G. [6] Introduced the Fuzzy matrix m-ordering. ZHOU Minna [9] Introduced the Characterizations of the Minus Ordering in Fuzzy Matrix Set.Nagoorgani A. and Manikandan A. R. [4] introduced the properties of fuzzy det-norm matrices.
In this paper, we introduce the concept of fuzzy det-norm ordering with fuzzy matrices. The purpose of the introduction is to explain det-norm ordering with fuzzy matrices and partitions of M n (F ). In Section 2, fuzzy det-norm ordering with fuzzy matrices is introduced in M n (F ). In Section 3,Properties of det-norm ordering with fuzzy matrices.

Preliminaries
We consider F = [0, 1] the fuzzy algebra with operation [+, ·] and the standard order " ≤ " where a + b = maxa, b, a · b = mina, b for all a, b in F. F is a commutative semi-ring with additive and multiplicative identities 0 and 1 respectively. Let M mn (F ) denote the set of all m × n fuzzy matrices over F.

Fuzzy Det-Norm and Partitions of M n (F )
To analysis more properties of M n (F ) we introduce the concept of norm in M n (F ) and thus we have defined for every A in M n (F ) a non-negative quantity say det-norm is defined in the following way.
Definition 1. An m × n matrix A = [a ij ] whose components are in the unit interval [0, 1] is called a fuzzy matrix.
Definition 2. The determinant |A| of an m × n fuzzy matrix A is defined as follows; |A| = Σ σ∈Sn a 1σ(1) a 2σ(2) · · · a nσ(n) Where S n denotes the symmetric group of all permutations of the indices (1, 2, · · · , n) Definition 3. For every A in M n (F ) the det-norm of A is defined as Clearly M n (F ) = A{1}∪A{2}∪A{3}. The set A{1} is called as det-superior to A and A{2} det-inferior to A. Clearly A{3} is det-equivalent to A. A{4} and A{5} are known as the sets of inner and outer inverses of A.
Theorem 1. For each A in M n (F ) the following results hold true: (ii) For all X ∈ A{5}, X ≤ A . Further for all X in A{4} ∩ A{5} the matrices AX and XA are idempotent.
Therefore reflexivity is true.
Therefore anti symmetry is not true.
Therefore transitivity is true. Thus the det-ordering is not a partial ordering in M n (F ).
Therefore reflexivity is true.
Therefore anti symmetry is not true.
Therefore transitivity is true. Thus the det-ordering is not a partial ordering in M n (F ).
Theorem 4. If A ≤ B, then: Therefore A n ?B n for any positive integer n.

Conclusion
In this paper, a new definition for the det-norm ordering and its properties are suggested in fuzzy environment. A numerical example is given to clarify the developed theory and the proposed det-norm ordering with fuzzy matrix.