scholarly journals Interval-Valued Neutrosophic Soft Rough Sets

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Said Broumi ◽  
Flornetin Smarandache
Keyword(s):  
Rough Sets ◽  
Soft Set ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

We first defined interval-valued neutrosophic soft rough sets (IVN-soft rough sets for short) which combine interval-valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of interval-valued intuitionistic fuzzy soft rough sets (IVIF-soft rough sets).

scholarly journals The Interval-Valued Intuitionistic Fuzzy Optimized Weighted Bonferroni Means and Their Application

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ya-ming Shi ◽  
Jian-min He
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Practical Case ◽  
Basic Properties ◽  
Bonferroni Mean ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Aggregation Techniques ◽  
Interval Valued

We investigate and propose two new Bonferroni means, that is, the optimized weighted BM (OWBM) and the generalized optimized weighted BM (GOWBM), whose characteristics are to reflect the preference and interrelationship of the aggregated arguments and can satisfy the basic properties of the aggregation techniques simultaneously. Further, we propose the interval-valued intuitionistic fuzzy optimized weighted Bonferroni mean (IIFOWBM) and the generalized interval-valued intuitionistic fuzzy optimized weighted Bonferroni mean (GIIFOWBM) and detailed study of their desirable properties such as idempotency, monotonicity, transformation, and boundary. Finally, based on IIFOWBM and GIIFOWBM, we give an approach to group decision making under the interval-valued intuitionistic fuzzy environment and utilize a practical case involving the assessment of a set of agroecological regions in Hubei Province, China, to illustrate the developed methods.

scholarly journals Data Analysis Approach for Incomplete Interval-Valued Intuitionistic Fuzzy Soft Sets

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1061
Author(s):  
Hongwu Qin ◽  
Huifang Li ◽  
Xiuqin Ma ◽  
Zhangyun Gong ◽  
Yuntao Cheng ◽  
...  
Keyword(s):  
Missing Data ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Degree Of Membership ◽  
Filling Method ◽  
Fuzzy Soft Sets ◽  
Interval Valued ◽  
Intuitionistic Fuzzy Soft Sets

The model of interval-valued intuitionistic fuzzy soft sets is a novel excellent solution which can manage the uncertainty and fuzziness of data. However, when we apply this model into practical applications, it is an indisputable fact that there are some missing data in many cases for a variety of reasons. For the purpose of handling this problem, this paper presents new data processing approaches for an incomplete interval-valued intuitionistic fuzzy soft set. The missing data will be ignored if percentages of missing degree of membership and nonmember ship in total degree of membership and nonmember ship for both the related parameter and object are below the threshold values; otherwise, it will be filled. The proposed filling method fully considers and employs the characteristics of the interval-valued intuitionistic fuzzy soft set itself. A case is shown in order to display the proposed method. From the results of experiments on all thirty randomly generated datasets, we can discover that the overall accuracy rate is up to 80.1% by our filling method. Finally, we give one real-life application to illustrate our proposed method.

scholarly journals Three-Way Decisions with Interval-Valued Intuitionistic Fuzzy Decision-Theoretic Rough Sets in Group Decision-Making

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 281 ◽  
Author(s):  
Dajun Ye ◽  
Decui Liang ◽  
Pei Hu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Rough Sets ◽  
Group Decision ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Decision ◽  
Grey Correlation ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this article, we demonstrate how interval-valued intuitionistic fuzzy sets (IVIFSs) can function as extended intuitionistic fuzzy sets (IFSs) using the interval-valued intuitionistic fuzzy numbers (IVIFNs) instead of precision numbers to describe the degree of membership and non-membership, which are more flexible and practical in dealing with ambiguity and uncertainty. By introducing IVIFSs into three-way decisions, we provide a new description of the loss function. Thus, we firstly propose a model of interval-valued intuitionistic fuzzy decision-theoretic rough sets (IVIFDTRSs). According to the basic framework of IVIFDTRSs, we design a strategy to address the IVIFNs and deduce three-way decisions. Then, we successfully extend the results of IVIFDTRSs from single-person decision-making to group decision-making. In this situation, we adopt a grey correlation accurate weighted determining method (GCAWD) to compute the weights of decision-makers, which integrates the advantages of the accurate weighted determining method and grey correlation analysis method. Moreover, we utilize the interval-valued intuitionistic fuzzy weighted averaging (IIFWA) operation to count the aggregated scores and the accuracies of the expected losses. By comparing these scores and accuracies, we design a simple and straightforward algorithm to deduce three-way decisions for group decision-making. Finally, we use an illustrative example to verify our results.

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