The formal system L of fuzzy propositional logic has been successfully applied to the joint research of fuzzy logic and fuzzy reasoning. The current paper further studies the syntactic structure of the system L, presents several new results with respect to this system. Especially, a simplified system which contains only seven axioms is proposed, and the system is found to be equivalent to the o...

For proving linear independence of real numbers, Hermite [6] considered simultaneous approximation to these numbers by algebraic numbers. The point of view introduced by Siegel in 1929 [14] is dual (duality in the sense of convex bodies): he considers simultaneous approximation by means of independent linear forms. We define the height of a linear form L = a0X0 + · · · + amXm with complex coeff...

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

The main aim of this paper is to deal with a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the fuzzy linear programming and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. Keywords Farkas Lemma, Fuzzy Linear Programming, Duality, Ranking Functions.

The object of this paper is to introduce the notion of intuitionisticfuzzy continuous mappings and intuitionistic fuzzy bounded linear operatorsfrom one intuitionistic fuzzy n-normed linear space to another. Relation betweenintuitionistic fuzzy continuity and intuitionistic fuzzy bounded linearoperators are studied and some interesting results are obtained.

Abstract In this paper we have investigated a fuzzy linear programming problem with fuzzy quantities which are LR triangular fuzzy numbers. The given linear programming problem is rearranged according to the satisfactory level of constraints using breaking point method. By considering the constraints, the arranged problem has been investigated for all optimal solutions connected with satisf...

In this paper we introduce the conditional entropy without a fuzzy measure for the union of fuzzy partitions. We recall its properties and we solve the system of functional equations which derives from these conditions, taking into account the locality principle and the independence axiom.

a new approach for pole placement of nonlinear systems using state feedback and fuzzy system is proposed. we use a new online fuzzy training method to identify and to obtain a fuzzy model for the unknown nonlinear system using only the system input and output. then, we linearized this identified model at each sampling time to have an approximate linear time varying system. in order to stabilize...