# A New Approach to Fuzzy Soft Set Theory and Its Application in Decision Making

VIT University

^{1}01 Jan 2016-pp 305-313

TL;DR: An application of fuzzy soft sets in decision making is provided which substantially improve and is more realistic than the algorithm proposed earlier by Maji et al.

Abstract: Soft set theory is a new mathematical approach to vagueness introduced by Molodtsov. This is a parameterized family of subsets defined over a universal set associated with a set of parameters. In this paper, we define membership function for fuzzy soft sets. Like the soft sets, fuzzy soft set is a notion which allows fuzziness over a soft set model. So far, more than one attempt has been made to define this concept. Maji et al. defined fuzzy soft sets and several operations on them. In this paper we followed the definition of soft sets provided by Tripathy et al. through characteristic functions in 2015. Many related concepts like complement of a fuzzy soft set, null fuzzy soft set, absolute fuzzy soft set, intersection of fuzzy soft sets and union of fuzzy soft sets are redefined. We provide an application of fuzzy soft sets in decision making which substantially improve and is more realistic than the algorithm proposed earlier by Maji et al.

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VIT University

^{1}TL;DR: This paper follows the approach of Tripathy et al. in redefining IFSS and presents an application of IFSS in decision-making which substantially improve and is more realistic than the algorithms proposed earlier by several authors.

Abstract: Molodtsov introduced soft set theory as a new mathematical approach to handle uncertainty. Hybrid models have been found to be more useful than the individual components. Following this trend fuzzy soft sets (FSS) and intuitionistic fuzzy soft sets (IFSS) were introduced. Recently, soft sets were introduced by Tripathy and Arun (Int J Reasoning-Based Intell Syst 7(3/4):244–253, 2015) [6] using the notion of characteristic function. This led to the redefinitions of concepts like complement, intersection, union of IFSS, Null and absolute IFSS. In this paper, we follow the approach of Tripathy et al. in redefining IFSS and present an application of IFSS in decision-making which substantially improve and is more realistic than the algorithms proposed earlier by several authors.

61 citations

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VIT University

^{1}TL;DR: A new algorithm is proposed by following this approach which provides an application of FSSs in group decision making and the performance is substantially improved than that of the earlier algorithm.

Abstract: Soft set theory was introduced by Molodtsov to handle uncertainty. It uses a family of subsets associated with each parameter. Hybrid models have been found to be more useful than the individual components. Earlier fuzzy set and soft set were combined to form fuzzy soft sets (FSS). Soft sets were defined from a different point of view in Tripathy et al. (Int J Reasoning-Based Intell Syst 7(3/4), 224–253, 2015) where they used the notion of characteristic functions. Hence, many related concepts were also redefined. In Tripathy et al. (Proceedings of ICCIDM-2015, 2015) membership function for FSSs was defined. We propose a new algorithm by following this approach which provides an application of FSSs in group decision making. The performance of this algorithm is substantially improved than that of the earlier algorithm.

37 citations

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VIT University

^{1}TL;DR: IVFSS is defined through the membership function approach to define soft set by Tripathy et al. very recently, and several concepts, such as complement of an IVFSS, null IVF SS, absolute IVFFS, intersection, and union of two IVFsss, are redefined.

Abstract: Soft set (SS) theory was introduced by Molodtsov to handle uncertainty. It uses a family of subsets associated with each parameter. Hybrid models have been found to be more useful than the individual components. Earlier interval-valued fuzzy set (IVFS) was introduced as an extension of fuzzy set (FS) by Zadeh. Yang introduced the concept of IVFSS by combining and soft set models. Here, we define IVFSS through the membership function approach to define soft set by Tripathy et al. very recently. Several concepts, such as complement of an IVFSS, null IVFSS, absolute IVFSS, intersection, and union of two IVFSSs, are redefined. To illustrate the application of IVFSSs, a decision-making (DM) algorithm using this notion is proposed and illustrated through an example.

29 citations

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TL;DR: In this article, the authors focused on the analysis of the key aspects of sustainability projects, namely advanced risk management and project knowledge, which are recommended to the attention of institutions and project managers when designing and executing new projects simultaneously with quality and project status management.

Abstract: The paper is focused on the analysis of the key aspects of sustainability projects, namely advanced risk management and project knowledge. These aspects are recommended to the attention of institutions and project managers when designing and executing new projects simultaneously with quality and project status management. The aim of the paper is to point out the critical factors that have recently affected the success of sustainability projects, which is also its contribution. Empirical research focused on the identification of the application level of the post-project phases in project management in the Czech Republic in 2016 and 2017 was performed. The research was performed as qualitative research employing observation and inquiry methods in the form of a controlled semistructured interview. The research identified 21 most common reasons for not executing post-project phases. Ensuring good and efficient progress of post-project phases, in particular by the means of post-implementation system analysis and compilation of a set of improvement suggestions for subsequent project management, forms the practical background for application of knowledge management and project management principles. A case study focused on the application of fuzzy logic in project risk assessment has been elaborated. In practice, current project management requires the application of advanced risk analysis methods that will replace the simple risk values estimated by calculations of separate risk components.

27 citations

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VIT University

^{1}TL;DR: This paper improves the group decision algorithm proposed by Tripathy et al earlier and provides an application in handling the decision making problem.

Abstract: Soft set theory introduced by Molodtsov is a new mathematical approach to handle the uncertainty problems. It is a family of subsets associated with each parameter in a soft space. Hybrid models have been found to be more useful than the individual components. Earlier fuzzy set and soft set were combined to form fuzzy soft sets and similarly intuitionistic fuzzy soft sets (IFSS) were introduced. Like the soft sets, IFSS is also a notion which allows fuzziness over a soft set model. So far, many attempts have been made to define this concept. Maji et.al defined intuitionistic fuzzy soft sets and several operations on them. Following the definition of soft sets provided by Tripathy et.al (2015) through characteristic function, in this paper we improve the group decision algorithm proposed by Tripathy et al earlier and provide an application in handling the decision making problem.

23 citations

### Cites background from "A New Approach to Fuzzy Soft Set Th..."

...It may be noted that following the same approach we have extended the definition in [7] to the context of FSS....

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...In [7], Tripathy et al introduced membership function of a fuzzy soft set....

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...Similarly, it is expected that defining membership function for FSSs will systematize many operations defined upon them as done in [7]....

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##### References

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01 Aug 1996

TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

52,705 citations

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TL;DR: The main purpose of this paper is to introduce the basic notions of the theory of soft sets, to present the first results of the the theory, and to discuss some problems of the future.

Abstract: The soft set theory offers a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. The main purpose of this paper is to introduce the basic notions of the theory of soft sets, to present the first results of the theory, and to discuss some problems of the future.

3,759 citations

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TL;DR: The authors define equality of two soft sets, subset and super set of a soft set, complement of asoft set, null soft set and absolute soft set with examples and De Morgan's laws and a number of results are verified in soft set theory.

Abstract: In this paper, the authors study the theory of soft sets initiated by Molodtsov. The authors define equality of two soft sets, subset and super set of a soft set, complement of a soft set, null soft set, and absolute soft set with examples. Soft binary operations like AND, OR and also the operations of union, intersection are defined. De Morgan's laws and a number of results are verified in soft set theory.

2,114 citations

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TL;DR: In this article, the theory of soft sets was applied to solve a decision-making problem using rough mathematics, and the results showed that soft sets can be used to solve decision making problems.

Abstract: In this paper, we apply the theory of soft sets to solve a decision making problem using rough mathematics.

1,491 citations