Interval-valued intuitionistic fuzzy soft sets and their properties

Jiang, Yuncheng; Tang, Yong; Chen, Qimai; Liu, Hai; Tang, Jianchao

doi:10.1016/j.camwa.2010.05.036

Cited by 265 publications

(129 citation statements)

References 38 publications

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“…More detailed explanations related to this subsection may be found in [6,7,9,21,24,27,36]. There is no restriction on the sum of T A (u); I A (u) and…”

Section: Preliminarymentioning

confidence: 99%

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Interval-valued neutrosophic soft sets and its decision making

Deli̇

2015

Int. J. Mach. Learn. & Cyber.

143

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In this paper, the notion of the interval valued neutrosophic soft sets (ivn−soft sets) is defined which is a combination of an interval valued neutrosophic sets [36] and a soft sets [30]. Our ivn−soft sets generalizes the concept of the soft set, fuzzy soft set, interval valued fuzzy soft set, intuitionistic fuzzy soft set, interval valued intuitionistic fuzzy soft set and neutrosophic soft set. Then, we introduce some definitions and operations on ivn−soft sets sets. Some properties of ivn−soft sets which are connected to operations have been established. Also, the aim of this paper is to investigate the decision making based on ivn−soft sets by level soft sets. Therefore, we develop a decision making methods and then give a example to illustrate the developed approach.

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“…More detailed explanations related to this subsection may be found in [6,7,9,21,24,27,36]. There is no restriction on the sum of T A (u); I A (u) and…”

Section: Preliminarymentioning

confidence: 99%

“…Some properties of ivn−soft sets which are connected to operations have been established. Some of it is quoted from [6,7,10,9,21,24,27,36].…”

Section: Preliminarymentioning

confidence: 99%

Interval-valued neutrosophic soft sets and its decision making

Deli̇

2015

Int. J. Mach. Learn. & Cyber.

143

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“…is called an intuitionistic fuzzy value (I FV) [16]. For notational convenience, we denote in what follows an IFV by a ( , )…”

Section: Preliminariesmentioning

confidence: 99%

The Application of Intuitionistic Fuzzy Soft Opeations to Medical Diagnosis

Zhang¹,

Gao²,

Gao³

2015

Proceedings of the 2015 International Conference on Education, Management, Information and Medicine

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Abstract. Molodtsov first proposed the soft set theory, which can be utilized as a general mathematical tool for dealing with fuzzy and uncertain information. As a generalization of soft set, intuitionistic fuzzy soft set is another soft set structure, it is a combination of an interval-valued fuzzy set and a soft set. The aim of this paper is to explore the decision making based on interval-valued fuzzy soft sets, the operations are carried out to integrate the medical information and expert information together, the optimcal choice is calculated to choose the disease which the patient most likely to suffer, a numberical example shows that the approach is reasonable..

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“…Usually complicated problems take place with uncertainties, and most of these complex situations can not be handled by adopting classical mathematic methods, considering the fact that with classical mathematic tools all notions are requested to be strict. Up to now, abundant mathematic tools such as fuzzy set theory [1] and rough set theory [2,3] have already been developed and proved to be useful in handling several kinds of the problems that contain uncertainties, and all of these theories share a common inherent difficulty, which is mainly the inadequacy of the parametrization tool [4,5]. However, it is noticed that, without proper parametrization tools, sometimes a practical problem can not be described in a way as much as information collected from different aspects could be taken into account.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of Some Soft Rough Sets

2017

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Through the combination of different types of sets such as fuzzy sets, soft sets and rough sets, abundant hybrid models have been presented in order to take advantage of each other and handle uncertainties. A comparative study of relationships and interconnections of some existing hybrid models has been carried out. Some foundational properties of modified soft rough sets (MSR sets) are analyzed. It is pointed out that MSR approximation operators are some kinds of Pawlak approximation operators, whereas approximation operators of Z-soft rough fuzzy sets are equivalent to approximation operators of rough fuzzy sets. The relationships among F-soft rough fuzzy sets, M-soft rough fuzzy sets and Z-soft rough fuzzy sets are surveyed. A new model called soft rough soft sets has been provided as the generalization of F-soft rough sets, and its application in group decision-making has been studied. Various soft rough sets models show great potential as a tool to solve decision-making problems, and a depth study of the connections among these models contributes to the flexible application of soft rough sets based decision-making approaches.

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Interval-valued intuitionistic fuzzy soft sets and their properties

Cited by 265 publications

References 38 publications

Interval-valued neutrosophic soft sets and its decision making

Interval-valued neutrosophic soft sets and its decision making

The Application of Intuitionistic Fuzzy Soft Opeations to Medical Diagnosis

A Comparative Study of Some Soft Rough Sets

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