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 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.

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 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.

Ordered Intuitionistic Fuzzy Soft Sets and Its Application in Decision Making Problem

2018 ◽  
Vol 7 (3) ◽  
pp. 76-98
Author(s):  
Pachaiyappan Muthukumar ◽  
Sai Sundara Krishnan Gangadharan
Keyword(s):  
Decision Making ◽  
Soft Sets ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem ◽  
Algebraic Properties ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Soft Sets

In this article, some new basic operations and results of Ordered Intuitionistic Fuzzy Soft (OIFS) sets, such as equality, complement, subset, union, intersection, OR, and AND operators along with several examples are investigated. Further, based on the analysis of several operations on OIFS sets, numerous algebraic properties and famous De Morgans inclusions and De Morgans laws are established. Finally, using the notions of OIFS sets, an algorithm is developed and implemented in 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.

On lattice ordered intuitionistic fuzzy soft sets

2018 ◽  
Vol 7 (1-2) ◽  
pp. 46-61 ◽  
Author(s):  
Tahir Mahmood ◽  
Muhammad Irfan Ali ◽  
Muhammad Aamir Malik ◽  
Waseem Ahmed
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Soft Sets

Lattices, soft sets, fuzzy sets and their generalizations have always been important for Mathematicians and the researchers working on uncertaities. In this paper our aim is to introduce the concept of lattice ordered intuitionistic fuzzy soft sets. After introducing extended union, extended intersection,  AND-product, OR-product, basic union, basic intersection of intuitionistic fuzzy soft sets, in this paper the affects of lattice ordered intuitionistic fuzzy soft sets and anti-lattice ordered intuitionistic fuzzy soft sets on restricted union, restricted intersection, extended union, extended intersection,AND-product, OR-product, basic union, basic intersection of intuitionistic fuzzy sets are discussed. Further a decision making problem is solved by using these concepts.

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.

scholarly journals Incomplete Fuzzy Soft Sets and Their Application to Decision-Making

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 535 ◽  
Author(s):  
Lu Wang ◽  
Keyun Qin
Keyword(s):  
Decision Making ◽  
Weight Function ◽  
Incomplete Information ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Precise Description ◽  
Soft Sets ◽  
Weighted Function ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets

The research of incomplete fuzzy soft sets is of paramount importance in fuzzy soft sets, where the combination of incomplete fuzzy soft set and decision-making problem is of great significance. Incomplete information in fuzzy soft sets leads to more uncertainty and ambiguity in decision-making. The focus of this paper to propose an algorithm of fuzzy soft set based decision-making problems under incomplete information. On the basis of the weighted function, we introduce the notions of weighted incomplete soft sets and weighted incomplete fuzzy soft sets, and show an approach to weighted incomplete fuzzy soft sets for dealing with decision-making. Considering the missing weight function, the concept of incomplete weighted fuzzy soft sets is presented. Meanwhile, we apply the incomplete weighted fuzzy soft sets to solve the decision-making problem. As modal-style operators for fuzzy soft sets have a precise description of attributes possessed by objects, we apply modal-style operator for incomplete fuzzy soft set to deal with decision-making and propose a new algorithm to make it more accurate and simple.

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.

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