This paper introduces an approach to construct a set of criteria for evaluating alternative options. Content analysis was used to collect criterion elements. Then the elements were classified and organized yielding to hierarchic structure. The reliability of the constructed criteria was evaluated in an experiment. Finally the criteria were used to evaluate alternative options indecision-making....

Several oscillation criteria are established for nonlinear fractional differential equations of the form{ a(t) [( r(t)g ( D−x(t) ))′]η}′ −F(t,∫ ∞ t (v− t)−αx(v)dv ) = 0, where D−x(t) is the Liouville right-side fractional derivative of order α ∈ (0,1) of x(t),η = 2n+1 2m+1 , and n,m∈N . F(t,G)∈C([t0,∞)×R;R) , and there exists function q(t)∈ C([t0,∞);R+) such that F(t,G) Gη q(t) for G = 0 and x ...

The wide ecological area consists of a rangeland with special vegetation and one of the key factors in rangeland management is to select Management Indicator Species (MIS). Management indicator species based on a new method such as Analytical Network Process-Decision Making Trial and Evaluation (ANP-DEMATEL) is one of the most important stages in the successful Range management as choosing a su...

context hamstring acute muscle injuries are prevalent in several sports including afl football (australian football league), sprinting and soccer, and are often associated with prolonged time away from sport. evidence acquisition in response to this, research into prevention and management of hamstring injury has increased, but epidemiological data shows no decline in injury and re-injury rates...

A module $M$ is called $emph{H}$-cofinitely supplemented if for every cofinite submodule $E$ (i.e. $M/E$ is finitely generated) of $M$ there exists a direct summand $D$ of $M$ such that $M = E + X$ holds if and only if $M = D + X$, for every submodule $X$ of $M$. In this paper we study factors, direct summands and direct sums of $emph{H}$-cofinitely supplemented modules. Let $M$ be an $emph{H}...

for the proper use of water resources in agriculture, it is necessary to provide appropriate irrigation system to supply crop water requirement. in the present research, using a hierarchical analysis, different types of irrigation systems were evaluated and prioritized on 1150 hectares of agricultural land of etka organization ​​ located in dorud, iran. hierarchical analysis process is one of t...

in this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function.The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.Based on the ${L}$ukasiewicz triangular norm, we first p...

The purpose of this paper is to present an alternative of a hybrid method based on Saaty’s Analytical Hierarchy Process and on the Technique for Order Preference by using the Similarity to Ideal Solution method (AHP-TOPSIS) and, based on the AHP and its use of pairwise comparisons, to extend it to a new method called α-D MCDMTOPSIS (α-Discounting Method for multi-criteria decision making-TOPSIS...