he fuzzy set introduced by L.A.Zadeh [16] in 1965 and the rough set introduced by Pawlak [12] in 1982 are generalizations of the classical set theory. Both these set theories are new mathematical tool to deal the uncertain, vague, imprecise and inexact data. In Zadeh fuzzy set theory, the degree of membership of elements of a set plays the key role, whereas in Pawlak rough set theory, the equiv...

We present a search at the Jefferson Laboratory for new forces mediated by sub-GeV vector bosons with weak coupling α' to electrons. Such a particle A' can be produced in electron-nucleus fixed-target scattering and then decay to an e + e- pair, producing a narrow resonance in the QED trident spectrum. Using APEX test run data, we searched in the mass range 175-250 MeV, found no evidence for an...

If the source of the current accelerating expansion of the universe is a positive cosmological constant, Banks and Fischler argued that there exists an upper limit of the total number of e-foldings of inflation. We further elaborate on the upper limit in the senses of viewing the cosmological horizon as the boundary of a cavity and of the holographic Dbound in a de Sitter space. Assuming a simp...

The papers setting upper bounds on the value of electric charge of the photon are briefly reviewed. The theoretical framework of these bounds is shown to be incomplete. Hence the bounds seem to be unreliable. There exists about a dozen of papers questioning the neutrality of photon and setting an upper limit on its charge. The title of the first paper [1] was " Experimental limit on the " charg...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

in this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

The nondetection of multiple images in the BATSE 4B catalog implies an upper limit to average redshift < z > of gamma ray bursts (GRBs). Here we calculate an upper limit to < z >, independent of the physical model for GRBs, using a filled approximation to compute the lensing rate for GRBs at high z for a variety of cosmologies. The upper limit on < z > depends directly on the cosmological param...

The optimistic multigranulation T-fuzzy rough set model was established based on multiple granulations under T-fuzzy approximation space by Xu et al., 2012. From the reference, a natural idea is to consider pessimistic multigranulation model in T-fuzzy approximation space. So, in this paper, the main objective is to make further studies according to Xu et al., 2012. The optimistic multigranulat...

The non detection of multiple images due to gravitational lensing in the BATSE 4B catalog implies an upper limit to the average redshift < z > of Gamma Ray Bursts (GRBs). Here we calculate an upper limit to < z >, independent of the physical model for GRBs, using a filled approximation to compute the lensing rate for GRBs at high z for a variety of cosmologies. The upper limit on < z > depends ...

In this paper, new definitions of a fuzzy basis and a fuzzy dimension for a fuzzy vector space are presented. A fuzzy basis for a fuzzy vector space (E, μ) is a fuzzy set β on E. The cardinality of a fuzzy basis β is called the fuzzy dimension of (E, μ). The fuzzy dimension of a finite dimensional fuzzy vector space is a fuzzy natural number. For a fuzzy vector space, any two fuzzy bases have t...