we present a model and propose an approach to compute an approximate solution of fully fuzzy linear system $(ffls)$ of equations in which all the components of the coefficient matrix are either nonnegative or nonpositive. first, in discussing an $ffls$ with a nonnegative coefficient matrix, we consider an equivalent $ffls$ by using an appropriate permutation to simplify fuzzy multiplications. t...

A matrix R is said to be g-row substochastic if Re ≤ e. For X, Y ∈ Mn,m, it is said that X is sglt-majorized by Y , X ≺sglt Y , if there exists an n-by-n lower triangular g-row substochastic matrix R such that X = RY . This paper characterizes all (strong) linear preservers and strong linear preservers of ≺sglt on Rn and Mn,m, respectively.

Throughout the paper, all rings are associative rings with identity 1. The set of all idempotents of a ring R is denoted by E(R). Also, for a subset X ⊆ R, we denote the right [resp., left] annihilator of X by r(X) [resp., (X)]. We call a ring R a left p.p.-ring [3], in brevity, an l.p.p.-ring, if every principal left ideal of R, regarded as a left R-module, is projective. Dually, we may define...

In this brief note, we suggest that the accumulating neutrino data [1–3], including the recent results from KamLAND [4] and K2K [5], point to a relatively simple neutrino mass matrix. The data can be explained by oscillations between three active neutrinos with the atmospheric neutrino and K2K data explained by oscillation between the muon and the tauon neutrinos, and the solar neutrino and Kam...