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>

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.

Generalized Entropy and Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets With Application in Decision Making

2021 ◽  
Vol 10 (1) ◽  
pp. 64-93
Author(s):  
Pratiksha Tiwari
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Extended Family ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Optimal Point ◽  
Generalized Entropy ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Interval-valued intuitionistic fuzzy environment is appropriate for most of the practical scenarios involving uncertainty, vagueness, and insufficient information. Entropy, similarity, distance, inclusion, and cross entropy measures are a few methods used for measuring uncertainty and classifying fuzzy sets and its generalizations. Entropy of a fuzzy set describes fuzziness degree of the set and similarity measure measures similarity between two fuzzy or members of its extended family. This paper presents generalized entropy and similarity measures for interval-valued intuitionistic fuzzy sets. Further, the proposed similarity measure is compared with some existing measure of similarity with the help of an illustrative example, and a method is used to define optimal point using the existing information. Finally, entropy and similarity measures are used to identify best alternatives to solve multi-attribute decision making.

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 On Interval-Valued Hesitant Fuzzy Soft Sets

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Haidong Zhang ◽  
Lianglin Xiong ◽  
Weiyuan Ma
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Soft Set ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Numerical Examples ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Interval Valued

By combining the interval-valued hesitant fuzzy set and soft set models, the purpose of this paper is to introduce the concept of interval-valued hesitant fuzzy soft sets. Further, some operations on the interval-valued hesitant fuzzy soft sets are investigated, such as complement, “AND,” “OR,” ring sum, and ring product operations. Then, by means of reduct interval-valued fuzzy soft sets and level hesitant fuzzy soft sets, we present an adjustable approach to interval-valued hesitant fuzzy soft sets based on decision making and some numerical examples are provided to illustrate the developed approach. Finally, the weighted interval-valued hesitant fuzzy soft set is also introduced and its application in decision making problem is shown.

A New Similarity Measure of Intuitionistic Fuzzy Sets Considering Abstention Group Influence and Its Applications

2016 ◽  
Vol 25 (2) ◽  
pp. 197-208 ◽  
Author(s):  
Bei Zhou
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Group Decision ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Group Influence ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Group A ◽  
Multicriteria Group Decision Making

AbstractThe issue of similarity measures of intuitionistic fuzzy sets (IFSs) is considered in this paper. Many existing similarity measures for two IFSs fail to take the abstention group influence into consideration and may lead to counterintuitive results in some cases. To deal with the problem, this paper first discusses the limitations of the existing similarity measures by some numerical examples, then, by considering the influence of abstention group, a new similarity measure of intuitionistic fuzzy sets is proposed, and the same numerical examples are given to demonstrate the validity of the proposed measure. Finally, the proposed similarity measure is applied to pattern recognition, multicriteria group decision making, and medical diagnosis.

scholarly journals A Novel Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 441 ◽  
Author(s):  
Minxia Luo ◽  
Jingjing Liang
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Fuzzy Numbers ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems.

scholarly journals n-Valued Refined Neutrosophic Soft Sets and their Applications in Decision Making Problems and Medical Diagnosis

2018 ◽  
Vol 8 (1) ◽  
pp. 79-86 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Ayman A. Hazaymeh
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Soft Set ◽  
Soft Sets ◽  
Numerical Example

Abstract In this work we use the concept of a ‘n’-valued refined neutrosophic soft sets and its properties to solve decision making problems, Also a similarity measure between two ‘n’-valued refined neutrosophic soft sets are proposed. A medical diagnosis (MD) method is established for ‘n’-valued refined neutrosophic soft set setting using similarity measures. Lastly a numerical example is given to demonstrate the possible application of similarity measures in medical diagnosis (MD).

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.

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