مجله سیستم های فازی ایران
سال:1389 | دوره:7 | شماره:2 |تعداد مقالات:21

We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables, As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy LR system lacks exact solutions. vVe show that the fuzzy LR system has an exact solution if and only if the corresponding crisp system is compatible (has a solntion) and the solution of the corresponding least squares problem is equal to zero. In this case, the exact solution is determined by the solutions of the two corresponding problems. On the other hand, if the corresponding crisp system is compatible and the optimal value of the corresponding constrained least squares problem is nonzero, then we characterize approximate solutions of the fuzzy system by solution of the least squares problem. Also, we characterize solutions by defining an appropriate membership function so that an exact solution is a fuzzy LR vector having the membership function value equal to one and, when an exact solution does not exist, an approximate solution is a fuzzy LR vector with a maximal membership function value. We propose a class of algorithms based on ABS algorithm for solving the LR fuzzy systems, the proposed algorithms can also be used to solve the extended dual fuzzy linear systems, and finally, we show that, when the system has more than one solution, the proposed algorithms are flexible enough to compute special solutions of interest. Several examples are worked out to demonstrate the various possible scenarios for the solutions of fuzzy LR linear systems.

The fuzzy linear regression model with fuzzy input-output data and crisp coefficients is studied in this paper. A linear programming model based on goal programming is proposed to calculate the regression coefficients. In contrast with most of the previous works, the proposed model takes into account the centers of fuzzy data’s an important feature as well as their spreads in the procedure of constructing the regression model. Furthermore, the model can deal with both symmetric and non-symmetric triangular fuzzy data as well as trapezoidal fuzzy data which have rarely been considered in the previous works. To show the efficiency of the proposed model, some numerical examples are solved and a simulation study is performed. The computational results are compared with some earlier methods.

In this paper, we define the notions of fuzzy congruence relations and fuzzy convex sub algebras on a commutative resituated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgcbras on a commutative residuatcd lattice. Then we study fuzzy convex sub algebras of an integral commutative residuated lattice and will prove that fuzzy filters and fuzzy convex suhalgebras of an integral commutative residuated lattice coincide.

Fuzzy bi-ideals play an important role in the study of ordered semigroupstructures. The purpose of this paper is to initiate and study the intiuitionistic fuzzybi-ideals in ordered semigroups and investigate the basic theorem of intuitionistic fuzzy bi-ideals. To provide the characterizations of regularordered semigroups in terms of intuitionistic fuzzy bi-ideals and to discuss the relationships of left(resp. right and completely regular) ordered semigroups in terms intuitionistic fuzzy bi-ideals.

This paper presents characterizations of M-fuzzifying matroids by means of two kinds of fuzzy operators, called M-fuzzifying derived operators and m-fuzzifying difference derived operators.

The aim of this paper is the study of the sequence of join spaces and fuzzy subsets associated with a hypergroupoid. In this paper we give some properties of the membership function m~Äcorresponding to the direct product of two hypergroupoids and we determine the fuzzy grade of the hypergroupoid (H x H, Ä) in a particular case.

In this paper, we introduce the concepts of 2-isometry, collinearity, 2-Lipschitzmapping in 2-fuzzy 2-normed linear spaces. Also, we give a new generalization of the Mazur- Ulamtheorem when X is a 2-fuzzy 2-normed linear space or Á(X) is a fuzzy 2-normed linear space, that is, the Mazur-Ulam theorem holds, when the 2-isometry mapped to a 2-fuzzy 2-normedlinear space is affine.

Let S be an ordered semi group. A fuzzy subset of S is an arbitrary mapping from S into [0,1], where [0,1] is the usual interval of real numbers. In this paper, the concept of fuzzy generalized bi-ideals of an ordered semi group S is introduced. Regular ordered semi groups are characterized by means of fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals. Finally, two main theorems which characterize regular ordered semi groups and intraregular ordered semi groups in terms of fuzzy left ideals, fuzzy right ideals, fuzzy bi-ideals or fuzzy quasi-ideals are given. The paper shows that one can pass from results in terms of fuzzy subsets in semi groups to ordered semi groups. The corresponding results of unordered semi groups are also obtained.

In the paper, \w introduce the notion of an action Yx as a generalization of the notion of a module, and the notion of a norm D: Yx ®F, where F is a field and D(xg) 6 (g’) = 6 (g) 6 (xg') as well as the notion of fuzzy norm, where D:gx® [0, 1] ÍR, with R the set of all real numbers. A great many standards mappings Oil algebraic systems can be modeled On norms as shown in the examples and it is seen that Ker D= {gl D(g) = O} has many useful properties. Some are explored. In the discussion of the discussion of fuzzy forms as they relate to the complements of sub actions Nx of Yx .

In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the subgroups of maximal chains in a special way which enables us to count the number of fuzzy subgroups.