‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

We begin with formulating the stationary equations of the Kuramoto model as a system of polynomial equations in a novel way. Then, based on an algebraic geometric root count, we give a prescription of computing an upper bound on the number of equilibria of the Kuramoto model for the most general case, i.e., defined on an arbitrary graph and having generic values of natural frequencies and inhom...

In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches. 

Consensus creation is a complex challenge in decision making for conflicting or quasi-conflicting evaluator groups. The problem even more difficult to solve, if one respondents are non-expert and provide uncertain hesitant responses survey. This paper presents methodological approach, the Interval-valued Spherical Fuzzy Analytic Hierarchy Process, with objective handle both types of problems si...

Probability theory is an important tool of modeling randomness in a practical problem. But besides randomness, in the real world, there exists other kind of uncertainties such as impreciseness or vagueness. Set-valued functions are employed to model the impreciseness in applied field such as in Economics, control theory (see for example [1]). Integrals of set-valued functions have been received...

solving a large sparse set of linear equations is of the problems widely seen in every numerical investigation in the entire range of engineering disciplines. employing a finite element approach in solving partial derivative equations, the resulting stiffness matrices would contain many zero-valued elements. moreover, storing all these sparse matrices in a computer memory would slower the compu...