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Bekir Tanay

Bio: Bekir Tanay is an academic researcher from Muğla University. The author has contributed to research in topics: Soft set & Topological group. The author has an hindex of 7, co-authored 24 publications receiving 607 citations.

Papers
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Journal ArticleDOI
TL;DR: Initial concepts of soft rings are introduced and some operations on soft sets are defined in this paper.
Abstract: Molodtsov (1999) introduced the concept of soft sets in [1]. Then, Maji et al. (2003) defined some operations on soft sets in [2]. Aktas and Ca@?man (2007) defined the notion of soft groups in [3]. Finally, soft semirings are defined by Feng et al. (2008) in [5]. In this paper, we have introduced initial concepts of soft rings.

348 citations

Journal ArticleDOI
TL;DR: In this paper, the concept of fuzzy soft topology is introduced and some of its structural properties such as neighborhood of a fuzzysoft set, interior fuzzy soft set, fuzzy soft basis, and fuzzy soft subspace topology are studied.
Abstract: In this paper, the concept of fuzzy soft topology is introduced and some of its structural properties such as neighborhood of a fuzzy soft set, interior fuzzy soft set, fuzzy soft basis, fuzzy soft subspace topology are studied.

215 citations

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TL;DR: In this paper, the fuzzy cone metric space and the topology induced by this space were defined and some related results of fuzzy cone Banach contraction theorem were proved. But these results are restricted to fuzzy cone metrics.
Abstract: In this study, we define the fuzzy cone metric space, the topology induced by this space and some related results of them. Also we state and prove the fuzzy cone Banach contraction theorem. c ⃝2015 All rights reserved.

31 citations

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TL;DR: A numerical method for solving the higher order linear difference equations with variable coefficients and mixed argument under the mixed conditions is presented, based on the hybrid Legendre and Taylor polynomials.
Abstract: A numerical method for solving the higher order linear difference equations with variable coefficients and mixed argument under the mixed conditions is presented. The method is based on the hybrid Legendre and Taylor polynomials. The solution is obtained in terms of Legendre polynomials. IIIustrative examples are included to demonstrate the validity and applicability of the technique.

12 citations


Cited by
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Journal ArticleDOI
TL;DR: The properties of soft open, soft nbd and soft closure are investigated and the properties ofsoft interior, soft exterior and soft boundary are defined which are fundamental for further research on soft topology and will strengthen the foundations of the theory of soft topological spaces.
Abstract: For dealing with uncertainty researchers introduced the concept of soft sets. Shabir and Naz (2011) [28], defined several basic notions on soft topology and studied many properties. In this paper, we continue investigating the properties of soft open (closed), soft nbd and soft closure. We also define and discuss the properties of soft interior, soft exterior and soft boundary which are fundamental for further research on soft topology and will strengthen the foundations of the theory of soft topological spaces.

283 citations

Journal ArticleDOI
TL;DR: It is proved that certain De Morgan's law hold in soft set theory with respect to different operations on soft sets and the notion of restricted symmetric difference of soft sets is defined and investigated.
Abstract: Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, first we prove that certain De Morgan's law hold in soft set theory with respect to different operations on soft sets. Then, we discuss the basic properties of operations on soft sets such as intersection, extended intersection, restricted union and restricted difference. Moreover, we illustrate their interconnections between each other. Also we define the notion of restricted symmetric difference of soft sets and investigate its properties. The main purpose of this paper is to extend the theoretical aspect of operations on soft sets.

262 citations

Journal ArticleDOI
TL;DR: This paper generalizes the adjustable approach to fuzzy soft sets based decision making by using level soft sets of intuitionistic fuzzysoft sets and introduces the weighted intuitionistic soft sets and investigates its application to decision making.
Abstract: Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. There has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. In this paper we generalize the adjustable approach to fuzzy soft sets based decision making. Concretely, we present an adjustable approach to intuitionistic fuzzy soft sets based decision making by using level soft sets of intuitionistic fuzzy soft sets and give some illustrative examples. The properties of level soft sets are presented and discussed. Moreover, we also introduce the weighted intuitionistic fuzzy soft sets and investigate its application to decision making.

198 citations

Journal ArticleDOI
01 Mar 2015
TL;DR: This work first defines intuitionistic fuzzy parameterized soft sets (intuitionistic FP-soft sets) and study some of their properties, and introduces an adjustable approaches to intuitionistic FP -soft sets based decision making.
Abstract: HighlightsWe define a intuitionistic fuzzy parameterized soft sets for dealing with uncertainties that is based on both soft sets and intuitionistic fuzzy sets.We investigated their operations and properties.We introduce a decision making method based on intuitionistic FP-soft sets. In this work, we first define intuitionistic fuzzy parameterized soft sets (intuitionistic FP-soft sets) and study some of their properties. We then introduce an adjustable approaches to intuitionistic FP-soft sets based decision making. Finally, we give a numerical example which shows that this method successfully works.

197 citations

Journal ArticleDOI
TL;DR: Some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets are reviewed, providing several novel algorithms in decision making problems by combining these kinds of hybrid models.
Abstract: Fuzzy set theory, rough set theory and soft set theory are all generic mathematical tools for dealing with uncertainties. There has been some progress concerning practical applications of these theories, especially, the use of these theories in decision making problems. In the present article, we review some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets. In particular, we provide several novel algorithms in decision making problems by combining these kinds of hybrid models. It may be served as a foundation for developing more complicated soft set models in decision making.

178 citations