scholarly journals Possibility Intuitionistic Fuzzy Soft Set

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Maruah Bashir ◽  
Abdul Razak Salleh ◽  
Shawkat Alkhazaleh
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Soft Sets

Possibility intuitionistic fuzzy soft set and its operations are introduced, and a few of their properties are studied. An application of possibility intuitionistic fuzzy soft sets in decision making is investigated. A similarity measure of two possibility intuitionistic fuzzy soft sets has been discussed. An application of this similarity measure in medical diagnosis has been shown.

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 Another View of Aggregation Operators on Group-Based Generalized Intuitionistic Fuzzy Soft Sets: Multi-Attribute Decision Making Methods

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 753 ◽  
Author(s):  
Khizar Hayat ◽  
Muhammad Ali ◽  
Bing-Yuan Cao ◽  
Faruk Karaaslan ◽  
Xiao-Peng Yang
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Soft Set ◽  
Weighted Averaging ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Soft Sets

In this paper, the existing definition of the group-based generalized intuitionistic fuzzy soft set is clarified and redefined by merging intuitionistic fuzzy soft set over the set of alternatives and a group of intuitionistic fuzzy sets on parameters. In this prospect, two new subsets of the group-based generalized intuitionistic fuzzy soft set are proposed and several operations are contemplated. The two new aggregation operators called generalized group-based weighted averaging and generalized group-based weighted geometric operator are introduced. The related properties of proposed operators are discussed. The recent research is emerging on multi-attribute decision making methods based on soft sets, intuitionistic fuzzy soft sets, and generalized intuitionistic fuzzy soft sets. An algorithm is structured and two case studies of multi-attribute decision makings are considered using proposed operators. Further, we provide the comparison and advantages of the proposed method, which give superiorities over recent major existing methods.

scholarly journals Possibility Fuzzy Soft Set

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh ◽  
Nasruddin Hassan
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets

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

scholarly journals Intuitionistic Fuzzy Soft Hyper BCK Algebras

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 399
Author(s):  
Xiaolong Xin ◽  
Rajab Borzooei ◽  
Mahmood Bakhshi ◽  
Young Jun
Keyword(s):  
Decision Making ◽  
Soft Set ◽  
Fuzzy Mathematics ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Soft Sets

Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets, and presented an application of fuzzy soft sets in a decision-making problem. Maji et al. also introduced the notion of intuitionistic fuzzy soft sets in the paper [P.K. Maji, R. Biswas and A.R. Roy, Intuitionistic fuzzy soft sets, The Journal of Fuzzy Mathematics, 9 (2001), no. 3, 677–692]. The aim of this manuscript is to apply the notion of intuitionistic fuzzy soft set to hyper BCK algebras. The notions of intuitionistic fuzzy soft hyper BCK ideal, intuitionistic fuzzy soft weak hyper BCK ideal, intuitionistic fuzzy soft s-weak hyper BCK-ideal and intuitionistic fuzzy soft strong hyper BCK-ideal are introduced, and related properties and relations are investigated. Characterizations of intuitionistic fuzzy soft (weak) hyper BCK ideal are considered. Conditions for an intuitionistic fuzzy soft weak hyper BCK ideal to be an intuitionistic fuzzy soft s-weak hyper BCK ideal are provided. Conditions for an intuitionistic fuzzy soft set to be an intuitionistic fuzzy soft strong hyper BCK ideal are given.

Application of Bipolar Intuitionistic Fuzzy Soft Sets in Decision Making Problem

2018 ◽  
Vol 7 (3) ◽  
pp. 32-55 ◽  
Author(s):  
Chiranjibe Jana ◽  
Madhumangal Pal
Keyword(s):  
Decision Making ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Graphs ◽  
Intuitionistic Fuzzy Soft Sets

This article describes how recently, a paper by D. Ezhilmaran and K. Sankar called Morphism of bipolar intuitionistic fuzzy graphs, has introduced bipolar intuitionistic fuzzy sets and morphism of bipolar intuitionistic fuzzy graphs. By using this concept, the authors of this article have combined a bipolar intuitionistic fuzzy set and a soft set. They introduce the notion of bipolar intuitionistic fuzzy soft set and study their basic properties. Also, presented in this article are the basic operations on bipolar intuitionistic fuzzy soft sets, extended unions, and the intersection of two bipolar intuitionistic fuzzy soft sets. An application of bipolar intuitionistic fuzzy soft set provides into a decision-making problem and a general algorithm to solve this decision making problem.

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 Generalized Trapezoidal Fuzzy Soft Set and Its Application in Medical Diagnosis

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Haidong Zhang ◽  
Lan Shu ◽  
Shilong Liao
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets

Soft set theory is a newly emerging mathematical tool to deal with uncertain problems. In this paper, by introducing a generalization parameter, which itself is trapezoidal fuzzy, we define generalized trapezoidal fuzzy soft sets and then study some of their properties. Finally, applications of generalized trapezoidal fuzzy soft sets in a decision making problem and medical diagnosis problem are shown.

Group Decision Making Through Interval Valued Intuitionistic Fuzzy Soft Sets

2018 ◽  
Vol 7 (3) ◽  
pp. 99-117 ◽  
Author(s):  
B. K. Tripathy ◽  
T. R. Sooraj ◽  
R. K. Mohanty ◽  
Abhilash Panigrahi
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Hybrid Models ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Soft Sets ◽  
Interval Valued

This article describes how the lack of adequate parametrization in some of the earlier uncertainty based models like fuzzy sets, rough sets motivated Molodtsov to introduce a new model in soft set. A suitable combination of individual models leads to hybrid models, which are more efficient than their individual components. So, the authors find the introduction of many hybrid models of soft sets, like the fuzzy soft set (FSS), intuitionistic fuzzy soft sets (IFSS), interval valued fuzzy soft set (IVFSS) and the interval valued intuitionistic fuzzy soft set (IVIFSS). Following the characteristic function approach to define soft sets introduced by Tripathy et al., they re-define IVIFSS in this article. One of the most attractive applications of soft set theory and its hybrid models has been decision making in the form of individual decision making or group decision making. Here, the authors propose a group decision making algorithm using IVIFSS, which generalises many of our earlier algorithms. They compute its complexity and establish the computation experimentally with graphical illustrations.

scholarly journals Similarity Measure of Lattice Ordered Multi-Fuzzy Soft Sets Based on Set Theoretic Approach and Its Application in Decision Making

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1255 ◽  
Author(s):  
Sabeena Begam S ◽  
Vimala J ◽  
Ganeshsree Selvachandran ◽  
Tran Thi Ngan ◽  
Rohit Sharma
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Similarity Measure ◽  
Real Life ◽  
Soft Set ◽  
Theoretic Approach ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets

Many effective tools in fuzzy soft set theory have been proposed to handle various complicated problems in different fields of our real life, especially in decision making. Molodtsov’s soft set theory has been regarded as a newly emerging mathematical tool to deal with uncertainty and vagueness. Lattice ordered multi-fuzzy soft set (LMFSS) has been applied in forecasting process. However, similarity measure is not used in this application. In our research, similarity measure of LMFSS is proposed to calculate the similarity between two LMFSSs. Moreover, some of its properties are introduced and proved. Finally, an application of LMFSS in decision making using similarity measure is analysed.

scholarly journals Decision making algorithmic techniques based on aggregation operations and similarity measures of possibility intuitionistic fuzzy hypersoft sets

2021 ◽  
Vol 7 (3) ◽  
pp. 3866-3895
Author(s):  
Atiqe Ur Rahman ◽  
◽  
Muhammad Saeed ◽  
Hamiden Abd El-Wahed Khalifa ◽  
Walaa Abdullah Afifi ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Approximate Function

<abstract><p>Soft set has limitation for the consideration of disjoint attribute-valued sets corresponding to distinct attributes whereas hypersoft set, an extension of soft set, fully addresses this scarcity by replacing the approximate function of soft sets with multi-argument approximate function. Some structures (i.e., possibility fuzzy soft set, possibility intuitionistic fuzzy soft set) exist in literature in which a possibility of each element in the universe is attached with the parameterization of fuzzy sets and intuitionistic fuzzy sets while defining fuzzy soft set and intuitionistic fuzzy soft set respectively. This study aims to generalize the existing structure (i.e., possibility intuitionistic fuzzy soft set) and to make it adequate for multi-argument approximate function. Therefore, firstly, the elementary notion of possibility intuitionistic fuzzy hypersoft set is developed and some of its elementary properties i.e., subset, null set, absolute set and complement, are discussed with numerical examples. Secondly, its set-theoretic operations i.e., union, intersection, AND, OR and relevant laws are investigated with the help of numerical examples, matrix and graphical representations. Moreover, algorithms based on AND/OR operations are proposed and are elaborated with illustrative examples. Lastly, similarity measure between two possibility intuitionistic fuzzy hypersoft sets is characterized with the help of example. This concept of similarity measure is successfully applied in decision making to judge the eligibility of a candidate for an appropriate job. The proposed similarity formulation is compared with the relevant existing models and validity of the generalization of the proposed structure is discussed.</p></abstract>

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