On the Law of Importation $(x wedge y) longrightarrow z equiv (x longrightarrow (y longrightarrow z))$ in Fuzzy Logic

The law of importation, given by the equivalence (x Lambda y) rarr z equiv (xrarr (y rarr z)), is a tautology in classical logic. In A-implications defined by Turksen et aL, the above equivalence is taken as an axiom. In this paper, we investigate the general form of the law of importation J(T(x, y), z) = J(x, J(y, z)), where T is a t-norm and J is a fuzzy implication, for the three main classes of fuzzy implications, i.e., R-, S- and QL-implications and also for the recently proposed Yager's classes of fuzzy implications, i.e., f- and g-implications. We give necessary and sufficient conditions under which the law of importation holds for R-, S-, f- and g-implications. In the case of QL-implications, we investigate some specific families of QL-implications. Also, we investigate the general form of the law of importation in the more general setting of uninorms and t-operators for the above classes of fuzzy implications. Following this, we propose a novel modified scheme of compositional rule of inference (CRI) inferencing called the hierarchical CRI, which has some advantages over the classical CRI. Following this, we give some sufficient conditions on the operators employed under which the inference obtained from the classical CRI and the hierarchical CRI become identical, highlighting the significant role played by the law of importation.     

A direct method for the numerical solution ofy″=f(x,y)

A direct method has been obtained for the numerical solution ofy″=f(x,y). Stability and error analysis of this method are studied and compared with the classical Runge-Kutta method and Runge-Kutta-Nyström method. Computational examples are also presented.     

一种新的(A,x,y)知识的零知识证明协议

基于线性假设下的Cramer-shoup加密方案和SDH假设,提出一种新的(A,x,y)知识的零知识证明协议。该协议比文献[2]中SDH对(A,x)知识的零知识证明协议多了一个参数。     

Families of fifth order Nyström methods for y″=f(x,y) and intervals of periodicity

In this paper all fifth order Nyström methods fory″=f(x, y) based on four evaluations off are presented. Furthermore, we prove that out of these methods there is only one with a non-vanishing interval of periodicity.     

Ergodic distribution for a fuzzy inventory model of type (s, S) with gamma distributed demands

In this study, a stochastic process (X(t)), which describes a fuzzy inventory model of type (s, S) is considered. Under some weak assumptions, the ergodic distribution of the process X(t) is expressed by a fuzzy renewal function U(x). Then, membership function of the fuzzy renewal function U(x) is obtained when the amount of demand has a Gamma distribution with fuzzy parameters. Finally, membership function and alpha cuts of fuzzy ergodic distribution of this process is derived by using extension principle of L. Zadeh.     

On the system of word equations x i 1 x i 2…x i m=y i 1 y i 2…y i n (i=1, 2, …) in a free monoid

 It is proved that the system of word equations x ⁱ ₁=y ⁱ ₁ y ⁱ ₂…y ⁱ _n , i=1, 2,…, ⌈n/2⌉ +1, has only cyclic solutions. Some sharpenings concerning the cases n=5, 7 and n≥9 are derived as well as results concerning the general system of equations x ⁱ ₁ x ⁱ ₂…x ⁱ _m =y ⁱ ₁ y ⁱ ₂…y ⁱ _n , i=1, 2,… . Applications to test sets of certain bounded languages are considered. Received: 18 May 1995/2 January 1996     

Exact periodic cross-kink wave solutions and breather type of two-solitary wave solutions for the (3 + 1)-dimensional potential-YTSF equation

In this paper, the (3+1)-dimensional potential-YTSF equation is investigated. Exact solutions with three-wave form including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave solutions are obtained using Hirota’s bilinear form and generalized three-wave approach with the aid of symbolic computation. Moreover, the properties for some new solutions are shown with some figures.     

Numerical treatment on digital computers for boundary value problem in ordinary differential equations of the typey' = f(x,y,y')

This paper deals with the numerical solution of boundary value problems of the type: $$y'' = f(x,y,y'); y(a) = A, y(b) = B.$$ In the case when the first derivative does not explicitly appear the problem has been faced by the author in [2], where a new approach has been suggested to improve the results given by the classical methods. In the following pages such an approach is extended to the above complete equation, and a new iterative algorithm is presented to solve the obtained discrete systems.     

A Sufficient Condition for the Existence of Restricted Fractional (g, f)-Factors in Graphs

Problems of Information Transmission - In an NFV network, the availability of resource scheduling can be transformed to the existence of the fractional factor in the corresponding NFV network...     

A computational algorithm for the FFD transitive closure and a complete axiomatization of fuzzy functional dependence (FFD)

This article focuses on the axiomatization of fuzzy functional dependency (FFD) in a fuzzy relational data model, which is considered as a fundamental issue towards building a theory of fuzzy relational database design. As an inference basis, the FFD axiomatic system composed of four FFD inference rules is established, and proven to be correct in terms of FFD logical implication with respect to the relation scheme. Consequently, the concept of the FFD transitive closure is defined, and correspondingly a computational algorithm is developed. This helps to tell whether a specific FFD can be derived from a given FFD set using those inference rules. In addition, some details of the algorithm as well as the aspects of the computational complexity and correctness are investigated. Finally, the soundness and completeness of the axiomatic system are discussed. It is proven that the system is both sound and complete. Importantly, this result enables us to “equate” the concept of FFD logical implication to the concept of FFD derivation using the inference rules. © 1994 John Wiley & Sons, Inc.     

Comparisons of some improving strategies on MOPSO for multi-objective (r, Q) inventory system

This paper presents comparisons of some recent improving strategies on multi-objective particle swarm optimization (MOPSO) algorithm which is based on Pareto dominance for handling multiple objective in continuous review stochastic inventory control system. The complexity of considering conflict objectives such as cost minimization and service level maximization in the real-world inventory control problem needs to employ more exact optimizers generating more diverse and better non-dominated solutions of a reorder point and order size system. At first, we apply the original MOPSO employed for the multi-objective inventory control problem. Then we incorporate the mutation operator to maintain diversity in the swarm and explore all the search space into the MOPSO. Next we change the leader selection strategy used that called geographically-based system (Grids) and instead of that, crowding distance factor is also applied to select the global optimal particle as a leader. Also we use ε-dominance concept to bound archive size and maintain more diversity and convergence in the MOPSO for optimizing the inventory control problem. Finally, the MOPSO algorithms created using these strategies are evaluated and compared with each other in terms of some performance metrics taken from the literature. The results indicate that these strategies have significant influences on computational time, convergence, and diversity of generated Pareto optimal solutions.     

On varieties of optimal algorithms for the computation of bilinear mappings III. Optimal algorithms for the computation of xy and yx where x,yϵM2(K)

In this paper we consider optimal algorithms for the computation of Φ:(x,y)? (xy,yx), where x, y are 2×2-matrices over a field K. It is shown that, if the characteristic of K is different from two, then optimal algorithms for the computation of Φ have length nine. Moreover, there are several different equivalence classes of optimal algorithms for Φ. If K= GF(2), then optimal algorithms for the computation of Φ have length ten.     

A cheating immune (k, n) visual cryptography scheme by using the rotation of shares

Multimedia Tools and Applications - Since Noar and Shamir introduced visual cryptography scheme (VCS), the cheating problem of VCS has absorbed much attention of scholars. The current researches on...     

Construction of solitary wave solutions for variants of the K(n,n) equation

In this paper, variational iteration method and Adomian decomposition are implemented to construct solitary solutions for variants of K(n, n) equation. In these schemes the solution takes the form of a convergent series with easily computable components. The chosen initial solution or trial function plays a major role in changing the physical structure of the solution. Comparison between the two methods is made and many models are approached. The obtained results reveal that the two methods are very effective and convenient for constructing solitary solutions.     

Erratum to: A Simple Derivation of the Hansen-Bliek-Rohn-Ning-Kearfott Enclosure for Linear Interval Equations (Reliable Computing 5(2) (1999))

In the Intlab program for the interval enclosure of the solution set of linear systems of equations with interval data, published in the above-mentioned paper, one rounding is in the wrong direction. A simple change amends this bug.     

Theoretical calculation of the phase diagram between one-dimensional long-period structures in the quasi binary sections: Pd3xRh3(1−x)V, Pt3xRh3(1−x)V, and Pt3VxTi(1−x)

The relative stabilities of L1₂, D0₂₂, D0₂₃, 21, and 3 structures in the Pd₃V, Pt₃V, Rh₃V, and Pt₃Ti compounds are investigated employing the Vienna ab initio simulation package. In the pseudobinary Pd_3xRh_3(1−x)V, Pt_3xRh_3(1−x)V, and Pt₃V_xTi_(1−x) alloys, the energy differences from L1₂ of D0₂₂, D0₂₃, 21, and 3 structures are assumed to be linear as function of the number of electrons per atom. At T=0K, the resulting energy diagram shows that the equilibrium between the limiting binary phases is the most stable state. At high temperature, the Gibbs energy curves are computed assuming a Bragg and Williams entropy of mixing in the pseudobinary sections. The D0₂₃ and 21 structures are stabilized in the pseudobinary Pd_3xRh_3(1−x)V, Pt_3xRh_3(1−x)V, and Pt₃V_xTi_(1−x) alloys. The phase diagram between the various structures is calculated in each pseudobinary section and compared with the experimental one.