This paper investigates the solutions of two-point fuzzy boundary value problems as the form x′′ = f(t, x(t)), x(0) = A and x(l) = B, where A and B are fuzzy numbers. There are four different solutions for the problems when the lateral type of H-derivative is employed to solve the problems. As f(t, x) is a monotone function of x, these four solutions are reduced to two different solutions. As f...

Classifications of (α,β )-fuzzy left (right and lateral) ideals of ternary semigroups are discussed. Relations between (∈,∈ ∨q)-fuzzy left (right and lateral) ideals and (q,∈∨q)-fuzzy left (right and lateral) ideals are established. Given special sets, so called t-q-set and t-∈∨q-set, conditions for the t-q-set and t-∈∨q-set to be left (right and lateral) ideals are considered. Conditions for a...

In [1] T. Dent, K. Kearnes and Á. Szendrei define the derivative, Σ′, of a set of equations Σ and show, for idempotent Σ, that Σ implies congruence modularity if Σ′ is inconsistent (Σ′ |= x ≈ y). In this paper we investigate other types of derivatives that give similar results for congruence n-permutable for some n, and for congruence semidistributivity. In a recent paper [1] T. Dent, K. Kearne...

and Applied Analysis 3 is Cauchy. If each Cauchy sequence is convergent, then the fuzzy norm is said to be complete, and the fuzzy normed space is called a fuzzy Banach space. Let X,N be a fuzzy normed space and Y,N ′ a fuzzy Banach space. For a given mapping f : X → Y , we use the abbreviation Df ( x, y ) : f ( 2x y ) f ( 2x − y 2f x − fx y − fx − y − 2f 2x , 2.1 for all x, y ∈ X. Recall Df ≡ ...

The bipolar fuzzy (BF) set is an extension of the used to solve uncertainty having two poles, positive and negative. rough a useful mathematical technique handle vagueness impreciseness. major objective this paper analyze notion approximation BF ideals semirings by combining theories sets. Then, idea subsemirings (ideals, bi-ideals interior ideals) developed. In addition, are characterized uppe...

We are interested in generalizations of the concepts of t-norm and t-conorm. In a companion chapter in this volume [14] we have presented a family of hypert-norms ∧q and a family of hyper-t-conorms ∨p. The prefix hyper is used to indicate multi-valued operations, also known as hyperoperations (see [5, 14]), i.e. operations which map pairs of elements to sets of elements. See [14] for the constr...

The paper presents IF-inference systems of Takagi-Sugeno type. It is based on intuitionistic fuzzy sets (IF-sets), introduced by K.T. Atanassov, fuzzy t-norm and t-conorm, intuitionistic fuzzy t-norm and t-conorm. Thus, an IFinference system is developed for ozone time series prediction. Finally, we compare the results of the IF-inference systems across various operators.

In this paper, we investigate renewal theories in the T -independent random fuzzy environment based on the concept of fuzzy variable and random fuzzy variable. For special cases, we consider the case for T = min and T =Archimedean t-norm. Mathematics Subject Classification: 60A86

-This study addresses a fuzzy Lyapunov method for the stability analysis of time-delay fuzzy systems subject to external disturbances. The Takagi-Sugeno (T-S) fuzzy model and parallel distributed compensation (PDC) scheme are first employed to design a nonlinear fuzzy controller in order to stabilize the time-delay fuzzy systems. According to the controlled system, the H infinity criterion is d...

The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Seikkala in [8] has defined the fuzzy derivative which is the generalization of the Hukuhara derivative in [7], the fuzzy integral which is the same as that of Dubois and prade [1], and by means of the extension principle of...