We generalise the Weil descent construction of the GHS attack on the elliptic curve discrete logarithm problem (ECDLP) to arbitrary Artin-Schreier extensions. We give a formula for the characteristic polynomial of Frobenius of the obtained curves and prove that the large cyclic factor of the input elliptic curve is not contained in the kernel of the composition of the conorm and norm maps. As a...

The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical hedge algebra. Then, we consider Gödel’s t-norm and t-conorm to define the logical connectives for our logic. Next, we present a resolution inference rule, in ...

There is given an overview on the results related to the generalization of the decision theory to non probabilistic uncertainty based on the characterization of the families of operations involved in generalized mixtures. It turns out that this is based on a previous result on the characterization of the pair of continuous t-norm T and t-conorm S such that the former is conditionally distributi...

In this paper the equation I(U1(x,y),z) = U2(I(x,z), I(y,z)) for all x,y,z ∈ [0,1] is solved where I is a residual implication defined from a uninorm U , and U1,U2 are a conjunctive and a disjunctive uninorm, respectively. Three cases are considered: i) when U is a t-norm, ii) when U1 is a t-norm and/or U2 is a t-conorm, and iii) the general case when the neutral elements of U,U1 and U2 are in ...

This paper presents a critical analysis of conventional operations on intuitionistic fuzzy values (IFVs), and some limitations of the conventional aggregation operator on IFVs are analyzed in detail. In order to overcome these limitations, according to new operation laws on IFVs based on Achimedean t-norm and t-conorm, we propose a new quasi-intuitionistic fuzzy OWA (QIFOWA) operator. Some corr...

Abstract: In this paper, the theory of T-norm and T-conorrn is reviewed and the T-norm, T-conorm and negation function are defined as a set of T-operators. Some typical T-operators and their mathematical properties are presented. Finally, the T-operators are extended to the conventional fuzzy reasoning methods which are based on the MIN and MAX operators. This extended fuzzy reasoning provides ...

In this paper, we introduce the concept of interval pseudo-homegeneous uninorms. We extend the concept of pseudo-homogeneity of specific functions for interval pseudo-homogeneous functions. It is studied two cases of interval pseudo-homogeneous uninorms, that is, interval pseudo-homogeneous tnorms and interval pseudo-homogeneous t-conorms. It is proved a form of interval pseudo-homogeneous t-no...

A new combination rule based on specified fuzzy T-Conorm/T-Norm operators is proposed and analyzed in this article the TCN Rule of Combination. The rule does not belong to the general Weighted Operator Class. The advantages of the new rule could be defined as: very easy to implement, satisfying the impact of neutrality of Vacuous Belief Assignment, commutative, convergent to idempotence, reflec...

A way of incorporating the concepls of fU2.ZY sets into layered neural networks has been described. The inpul can be provided to quanlitative or linguistic fOnTIS while Ihe outpUI may be modeled as membership values. Logical operators, viz., I-norm T and r-conorm S involving And and Or neurons. are employed al the neuronal level, and the conventional back propagarion algorilhm is accordingly mo...

The Weil descent attack, suggested by Frey, has been implemented by Gaudry, Hess and Smart (the so-called GHS attack), on elliptic curves over finite fields of characteristic two of composite degrees. The GHS attack has been extended by Galbraith to hyperelliptic curves of characteristic two. Recently, Diem presented a general treatment of GHS attack to hyperelliptic curves over finite fields o...