in this paper we prove that each element of any regular baer ring is a sum of two units if no factor ring of r is isomorphic to z_2 and we characterize regular baer rings with unit sum numbers $omega$ and $infty$. then as an application, we discuss the unit sum number of some classes of group rings.

in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

This paper formulates the performance evaluation of cloud services as a multicriteria group decision making problem, and presents a fuzzy multicriteria group decision making method for evaluating the performance of cloud services. Interval-valued intuitionistic fuzzy numbers are used to model the inherent subjectiveness and imprecision of the performance evaluation process. An effective algorit...

Data envelopment analysis (DEA) is a powerful technique for performance evaluation of decision making units (DMUs). One of the main objectives that is followed in performance evaluation is discriminating among efficient DMUs to provide a complete ranking of DMUs. DEA successfully divides them into two categories: efficient DMUs and inefficient DMUs. The DMUs in the efficient category have ident...

This study aims to present a novel approach for determining the weights of decision makers (DMs) based on rough group decision in multiple attribute group decision-making (MAGDM) problems. First, we construct a rough group decision matrix from all DMs' decision matrixes on the basis of rough set theory. After that, we derive a positive ideal solution (PIS) founded on the average matrix of rough...

data envelopment analysis (dea) is a technique based on mathematical programming for evaluating the efficiency of homogeneous decision making units (dmus). in this technique, inefficient dmus are projected onto the frontier, which was constructed by the best performers. centralized resource allocation (cra) is a method in which all dmus are projected onto the efficient frontier through solving ...

an ideal i of a ring r is called right baer-ideal if there exists an idempotent e 2 r such that r(i) = er. we know that r is quasi-baer if every ideal of r is a right baer-ideal, r is n-generalized right quasi-baer if for each i e r the ideal in is right baer-ideal, and r is right principaly quasi-baer if every principal right ideal of r is a right baer-ideal. therefore the concept of baer idea...

Multiple attribute decision making (MADM) methods are very much essential in all fields of engineering, management and other areas where limited alternatives exist and the decision maker has to select the best alternative. Different methods are available in the literature to tackle the MADM problems. The MADM problems are classified as scoring methods, compromising methods and concordance metho...

In this article, we will estimate efficiency amountof decision-making unit by offering the continuous piecewise polynomialextrapolation and interpolation by CCR model input-oriented on the assumptionthat it is constant returns to scale in different times. And finally, we willestimate efficiency amount of decision-making unit indifferent times byoffering an example.