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Proceedings ArticleDOI

On intuitionistic fuzzy soft set and its application in group decision making

01 Feb 2016-pp 1-5
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.
Citations
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Journal ArticleDOI
20 Jan 2020
TL;DR: A new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance is proposed and demonstrated to be rational and practical in applications.
Abstract: As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.

99 citations

Book ChapterDOI
01 Jan 2016
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

Journal ArticleDOI
01 Apr 2019
TL;DR: A case study is presented and a comparative analysis is conducted to illustrate the practicality and effectiveness of the proposed group medical diagnosis model under intuitionistic fuzzy soft environment.
Abstract: This paper is aimed at developing a group decision making (GDM) model for medical diagnosis via determining weights of experts based on a new similarity measure of intuitionistic fuzzy soft sets (IFSSs), and integrating the evaluation information by the weighted intuitionistic fuzzy soft Bonferroni mean (WIFSBM) operator. To address this problem, we first investigate the existing similarity measure and find out that it may lead to counter-intuitive results. Then we define an improved similarity measure for IFSSs and investigate its properties. A new model to estimate the weights of experts is based on similarity measure where the weights of experts are completely unknown. The weights of parameters are computed using the standard evaluation matrix by the maximizing deviation method. Considering the interactions among parameters, the integrated information for each alternative is obtained by the WIFSBM and the ranking index for each alternative is calculated by the score function. A case study is presented and a comparative analysis is conducted to illustrate the practicality and effectiveness of the proposed group medical diagnosis model under intuitionistic fuzzy soft environment.

49 citations

Book ChapterDOI
01 Jan 2016
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

Journal ArticleDOI
TL;DR: This paper presents a review on different parameter reduction and decision making techniques for soft set and hybrid soft sets under unpleasant set of hypothesis environment as well as performance analysis of the their derived algorithms.
Abstract: Many real world decision making problems often involve uncertainty data, which mainly originating from incomplete data and imprecise decision. The soft set theory as a mathematical tool that deals with uncertainty, imprecise, and vagueness is often employed in solving decision making problem. It has been widely used to identify irrelevant parameters and make reduction set of parameters for decision making in order to bring out the optimal choices. In this paper, we present a review on different parameter reduction and decision making techniques for soft set and hybrid soft sets under unpleasant set of hypothesis environment as well as performance analysis of the their derived algorithms. The review has summarized this paper in those areas of research, pointed out the limitations of previous works and areas that require further research works. Researchers can use our review to quickly identify areas that received diminutive or no attention from researchers so as to propose novel methods and applications.

32 citations


Cites background from "On intuitionistic fuzzy soft set an..."

  • ...[73] presented another work on hybrid intuitionistic fuzzy set and soft sets and its application in group decision making....

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References
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Journal ArticleDOI
TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.

13,376 citations

Journal ArticleDOI
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


"On intuitionistic fuzzy soft set an..." refers background in this paper

  • ...In order to bring topological flavor into the models of uncertainty and associate family of subsets of a universe to parameters, Molodtsov [5] introduced the concept of soft sets in 1999....

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  • ...APPLICATION OF INTUITIONISTIC FUZZY SOFT SET IN GROUP DECISION MAKING In [5] Molodtsov has given several applications of soft set....

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  • ...Many of Soft set theory have been discussed by Molodtsov in [5]....

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  • ...In [5] Molodtsov has given several applications of soft set....

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Journal ArticleDOI
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


"On intuitionistic fuzzy soft set an..." refers background in this paper

  • ...Subsequently, many new operations on soft sets were introduced by Maji et al [3, 4]....

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  • ...Following this trend, [2] Maji et al. put forward the concept of fuzzy soft set (FSS) by combining the notions of fuzzy set and soft set....

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Journal ArticleDOI
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

01 Jan 2001

1,100 citations


"On intuitionistic fuzzy soft set an..." refers methods in this paper

  • ...Among several approaches, in [2], FSS and operationson it are defined....

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