An extended soft set model: Type-2 fuzzy soft sets

2011 ◽  
Author(s):  
Xir;ao Ma ◽  
Guoyin Wang
Keyword(s):  
Soft Set ◽  
Soft Sets ◽  
Model Type ◽  
Fuzzy Soft Sets

scholarly journals Representation and application of Fuzzy soft sets in type-2 environment

2021 ◽  
Author(s):  
Biplab Paik ◽  
Shyamal Kumar Mondal
Keyword(s):  
Fuzzy Set ◽  
Decision Procedure ◽  
Soft Set ◽  
Decision Makers ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Weighted Type

AbstractThis paper has represented a soft-set in the type-2 environment by its simplest form as an augmentation to soft-set theories. Furthermore, we have applied the type-2 fuzzy soft set(T2FSS) by using our most straightforward representation to find the solution of a decision-making-problem (DMP) based-on T2FSS as well as weighted type-2 fuzzy soft set (WT2FSS). We have proposed two definitions, namely, Mid-$$\alpha $$ α -threshold fuzzy-set of a T2FSS and Mid-$$\lambda $$ λ -threshold fuzzy-set of a T2FSS. Furthermore, we have presented the definition, namely, level fuzzy-soft-set(LFSS) of a T2FSS. Using this concept, we have prepared two algorithms to select one object in T2FSS as well as WT2FSS based on DMP, which take regret disinclination and expectation preference of decision-makers into consideration in the decision procedure. Also, we have presented two numerical examples at the end.

scholarly journals Type-2 Fuzzy Soft Sets and Their Applications in Decision Making

2012 ◽  
Vol 2012 ◽  
pp. 1-35 ◽  
Author(s):  
Zhiming Zhang ◽  
Shouhua Zhang
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Soft Set ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets ◽  
Weighted Type

Molodtsov introduced the theory of soft sets, which can be used as a general mathematical tool for dealing with uncertainty. This paper aims to introduce the concept of the type-2 fuzzy soft set by integrating the type-2 fuzzy set theory and the soft set theory. Some operations on the type-2 fuzzy soft sets are given. Furthermore, we investigate the decision making based on type-2 fuzzy soft sets. By means of level soft sets, we propose an adjustable approach to type-2 fuzzy-soft-set based decision making and give some illustrative examples. Moreover, we also introduce the weighted type-2 fuzzy soft set and examine its application to decision making.

scholarly journals Generalised Interval-Valued Fuzzy Soft Set

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Interval Valued

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in a medical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised fuzzy soft set; generalised interval-valued fuzzy soft set; interval-valued fuzzy set; interval-valued fuzzy soft set.

scholarly journals An algorithm for fuzzy soft set based decision making approach

2020 ◽  
Vol 30 (1) ◽  
pp. 59-70
Author(s):  
Shehu Mohammed ◽  
Akbar Azam
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Group Decision Making ◽  
Group Decision ◽  
Soft Set ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets ◽  
Priority Table

The notion of soft set theory was initiated as a general mathematical tool for handling ambiguities. Decision making is viewed as a cognitive-based human activity for selecting the best alternative. In the present time, decision making techniques based on fuzzy soft sets have gained enormous attentions. On this development, this paper proposes a new algorithm for decision making in fuzzy soft set environment by hybridizing some existing techniques. The first novelty is the idea of absolute scores. The second concerns the concept of priority table in group decision making problems. The advantages of our approach herein are stronger power of objects discrimination and a well-determined inference.

scholarly journals On Fuzzy Soft Sets

2009 ◽  
Vol 2009 ◽  
pp. 1-6 ◽  
Author(s):  
B. Ahmad ◽  
Athar Kharal
Keyword(s):  
Set Theory ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets

We further contribute to the properties of fuzzy soft sets as defined and studied in the work of Maji et al. ( 2001), Roy and Maji (2007), and Yang et al. (2007) and support them with examples and counterexamples. We improve Proposition 3.3 by Maji et al., (2001). Finally we define arbitrary fuzzy soft union and fuzzy soft intersection and prove DeMorgan Inclusions and DeMorgan Laws in Fuzzy Soft Set Theory.

scholarly journals Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1361 ◽  
Author(s):  
Ahmed Mostafa Khalil ◽  
Dunqian Cao ◽  
Abdelfatah Azzam ◽  
Florentin Smarandache ◽  
Wedad R. Alharbi
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Soft Set ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Numerical Example ◽  
Fuzzy Soft Sets ◽  
Novel Concept

In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example.

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.

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