In this study, we first introduce the fuzzy sets, soft sets, fuzzy soft sets and their related properties. We then present the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) that is one of classical Multiple Attribute Decision Making (MADM) methods. We also present the Grey Relation Method. In the main part of this study, we extend the TOPSIS method on the fuzzy soft se...

Multiple criteria decision-making (MCDM) research has developed rapidly and has become a main area of research for dealing with complex decision problems. The purpose of the paper is to explore the performance evaluation model. This paper develops an evaluation model based on the fuzzy analytic hierarchy process and the technique for order performance by similarity to ideal solution, fuzzy TOPS...

In this paper, with a new idea, we redefine generalized fuzzy ideal and investigate some of its properties. We generalize fuzzy prime ideals and introduce the notions of (∈,∈ ∨q)−fuzzy prime ideal of ordered semigroups. We characterize (∈,∈ ∨q)−fuzzy prime ideal by its image and level ideals. We establish necessary and sufficient condition for fuzzy set to be a (∈,∈ ∨q)−fuzzy prime ideal. 2010 ...

Multiple criteria decision-making (MCDM) research has developed rapidly and has become a main area of research for dealing with complex decision problems. The purpose of the paper is to explore the performance evaluation model. This paper develops an evaluation model based on the fuzzy analytic hierarchy process and the technique for order performance by similarity to ideal solution, fuzzy TOPS...

This paper extends the technique for order preference by similarity to ideal solution (TOPSIS) for solving multi-attribute group decision making (MAGDM) problems under Atanassov intuitionistic fuzzy set (IFS) environments. In this methodology, weights of attributes and ratings of alternatives on attributes are extracted from fuzziness inherent in decision data and making process and described u...

The goal of this paper is to introduce the notions of , -double fuzzy ideals and , -double fuzzy ideal bases where and are strictly two-sided, commutative quanta and also investigate the relationships between these two structures. Then, we construct a functor from the category of , -double fuzzy ideal spaces to the category of , -double fuzzy cotopological spaces. Furthermore, we show the exist...

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semi...

we consider the semilinear elliptic boundary value problem  = ∈∂ω− δ = ∈ωu x xu x f u x x( ) 0;( ) λ ( ( ));where λ > 0 is a parameter, ω is a bounded region in rn with a smooth boundary, and f is asmooth function. we prove, under some additional conditions, the existence of a positive solution for λlarge. we prove that our solution u for λ large is such that = →∞∈ω|| u ||: sup| u(x) |xas λ ...

The notion of lacunary ideal convergence in intuitionistic fuzzy normed linear space (IFNLS) was introduced by the present corresponding author [P. Debnath, Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Comput. Math. Appl., 63 (2012), 708-715] and an open problem in that paper was whether every lacunary I-convergent sequence is lacunary I-Cauchy. Further, a new concep...

9 This article proposes an approach to handle multi-attribute decision making (MADM) 10 problems under the interval-valued intuitionistic fuzzy environment, in which both 11 assessments of alternatives on attributes (hereafter, referred to as attribute values) and 12 attribute weights are provided as interval-valued intuitionistic fuzzy numbers (IVIFNs). 13 The notion of relative closeness is e...