The multiplicative hesitant fuzzy information proposed by Xia (2012) uses the non-uniform scale to express the preference of the decision makers which has a broad application background. The key difference between multiplicative hesitant fuzzy information and hesitant fuzzy information is the former uses unsymmetrical scale in expressing the preferences about two alternatives but the latter use...

We study the computational complexity of two Boolean non-linearity measures: the nonlinearity and the multiplicative complexity. We show that if one-way functions exist, no algorithm can compute the multiplicative complexity in time 2 O(n) given the truth table of length 2 n , in fact under the same assumption it is impossible to approximate the multiplicative complexity within a factor of (2 −...

Multiplicative monotone span program is one of the important tools to realize secure multiparty computation. It is essential to construct multiplicative monotone span programs for secure multiparty computations. For any access structure, Cramer et al. gave a method to construct multiplicative monotone span programs, but its row size became double, and the column size also increased. In this pap...

In this paper, we introduce the multiplicative zero-divisor graph of a multiplicative lattice and study Beck-like coloring of such graphs. Further, it is proved that for such graphs, the chromatic number and the clique number need not be equal. On the other hand, if a multiplicative lattice L is reduced, then the chromatic number and the clique number of the multiplicative zero-divisor graph of...

The central theme of this paper is multiplicative polynomial dimensional decomposition (PDD) methods for solving high-dimensional stochastic problems. When a stochastic response is dominantly of multiplicative nature, the standard PDD approximation, predicated on additive function decomposition, may not provide sufficiently accurate probabilistic solutions of a complex system. To circumvent thi...

This article investigates multiplicative consistency ascertaining, inconsistency repairing, and weights derivation for hesitant preference relations (HMPRs). First, the completely weakly of HMPRs are defined. Based on them, 0–1 mixed programming models simple algebraic operations proposed to ascertain HMPRs. Then, some goal developed generate from consistent revise inconsistent An integrated pr...

A variety of theories in psychology postulate that the causal variables combine according to a multiplicative rule to determine the value of the dependent variable. To test multiplicative combination rules empirically, applied researchers frequently use an observational method that involves the following procedure: (a) assessment techniques are used to measure the value of each theoretical cons...

Finite quantum groupoids can be described in many equivalent ways [8, 11, 16]: In terms of the weak Hopf C -algebras of Böhm, Nill, and Szlachányi [2] or the finite-dimensional Hopf-von Neumann bimodules of Vallin [14], and in terms of finite-dimensional multiplicative partial isometries [4] or the finite-dimensional pseudo-multiplicative unitaries of Vallin [15]. In this note, we show that in ...

Crawley-Boevey and Shaw recently introduced a certain multiplicative analogue of the deformed preprojective algebra, which they called the multiplicative preprojective algebra. In this paper we study the moduli space of (semi)stable representations of such an algebra (the multiplicative quiver variety), which in fact has many similarities to the quiver variety. We show that there exists a compl...

The weak ergodic theorems of mathematical demography state that the age distribution of a closed population is asymptotically independent of the initial distribution. In this paper, we provide a new proof of the weak ergodic theorem of the multistate population model with continuous time. The main tool to attain this purpose is a theory of multiplicative processes, which was mainly developed by...