Introduction to Intuitionistic Fuzzy Multisets and Its Applications

2016 ◽  
pp. 43-52
Author(s):  
T. K. Shinoj ◽  
Sunil Jacob John
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Linguistic Variable ◽  
Human Reasoning ◽  
Collaborative Robots ◽  
Intuitionistic Fuzzy

In this chapter a new concept named Intuitionistic Fuzzy Multiset is introduced, which is an attempt to combine the two concepts: Intuitionistic Fuzzy sets and Fuzzy Multisets. The basic operations and their various properties are discussed. The authors discussed two significant applications of Intuitionistic Fuzzy Multisets. Most of human reasoning involves the use of variables whose values are fuzzy sets. This is the basis for the concept of a linguistic variable. But in some situations like decision making problems, the description by a linguistic variable in terms of membership function only is not adequate. There is chance of existing a non-null complement. There are situations that each element has different membership values. In such situations Intuitionistic Fuzzy Multisets is more adequate. Here the authors present Intuitionistic Fuzzy Multisets as a tool for reasoning such a situation through a medical diagnosis problem. As the second application, accuracy of Collaborative Robots using the concept of Intuitionistic Fuzzy Multiset is discussed.

scholarly journals A Dynamic Interval-Valued Intuitionistic Fuzzy Sets Applied to Pattern Recognition

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Zhenhua Zhang ◽  
Min Wang ◽  
Yong Hu ◽  
Jingyu Yang ◽  
Youpei Ye ◽  
...  
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Recognition Accuracy ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Simulation Results ◽  
Interval Valued

We present dynamic interval-valued intuitionistic fuzzy sets (DIVIFS), which can improve the recognition accuracy when they are applied to pattern recognition. By analyzing the degree of hesitancy, we propose some DIVIFS models from intuitionistic fuzzy sets (IFS) and interval-valued IFS (IVIFS). And then we present a novel ranking condition on the distance of IFS and IVIFS and introduce some distance measures of DIVIFS satisfying the ranking condition. Finally, a pattern recognition example applied to medical diagnosis decision making is given to demonstrate the application of DIVIFS and its distances. The simulation results show that the DIVIFS method is more comprehensive and flexible than the IFS method and the IVIFS method.

scholarly journals New Similarity Measure between Intuitionistic Fuzzy Multisets based on Tangent Function and its Application in Medical Diagnosis

2019 ◽  
Vol 8 (2S3) ◽  
pp. 161-165 ◽  
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Tangent Function

In recent years, Intuitionistic fuzzy set is very useful in decision making problems such as medical diagnosis, pattern recognition, clustering etc., which deals with vagueness and uncertainty. Similarity measure is a tool used to find the closeness of the intuitionistic fuzzy sets by considering the membership, nonmembership and hesitation function. In this paper, we propose an effective similarity measure based on tangent function for intuitionistic fuzzy multi sets in which membership, nonmembership, hesitation function occurs more than once and also we apply this measure in medical diagnosis and pattern recognition.

scholarly journals THE SPHERICAL DISTANCE FOR INTUITIONISTIC FUZZY SETS AND ITS APPLICATION IN DECISION ANALYSIS

2016 ◽  
Vol 22 (3) ◽  
pp. 393-415 ◽  
Author(s):  
Zaiwu GONG ◽  
Xiaoxia XU ◽  
Yingjie YANG ◽  
Yi ZHOU ◽  
Huanhuan ZHANG
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Medical Diagnosis ◽  
Group Decision ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Spherical Distance

Different from traditional distances between Intuitionistic Fuzzy Sets (IFS), the spherical distance between two IFSs relies not only on their relative differences but also their absolute values. In this paper, we generalize the properties of spherical distance measures between IFSs, and investigate the applications of spherical distance measures in group decision making, pattern recognition and medical diagnosis. We develop an optimization spherical distance model with IFS preference in group decision making, and demonstrate that this model is feasible and practical with an evaluation model of drought risk. By using comparative analysis method, we show that this new spherical distance can also be applied in other fields such as pattern recognition and medical diagnosis.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

2021 ◽  
pp. 1-13
Author(s):  
Xi Li ◽  
Chunfeng Suo ◽  
Yongming Li
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Dissimilarity Function ◽  
Better Than

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

scholarly journals Towards Better Concordance among Contextualized Evaluations in FAST-GDM Problems

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 93
Author(s):  
Marcelo Loor ◽  
Ana Tapia-Rosero ◽  
Guy De Tré
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Intuitionistic Fuzzy Sets ◽  
Heterogeneous Group ◽  
Intuitionistic Fuzzy ◽  
High Level ◽  
Consensus Reaching ◽  
Novel Algorithm

A flexible attribute-set group decision-making (FAST-GDM) problem consists in finding the most suitable option(s) out of the options under consideration, with a general agreement among a heterogeneous group of experts who can focus on different attributes to evaluate those options. An open challenge in FAST-GDM problems is to design consensus reaching processes (CRPs) by which the participants can perform evaluations with a high level of consensus. To address this challenge, a novel algorithm for reaching consensus is proposed in this paper. By means of the algorithm, called FAST-CR-XMIS, a participant can reconsider his/her evaluations after studying the most influential samples that have been shared by others through contextualized evaluations. Since exchanging those samples may make participants’ understandings more like each other, an increase of the level of consensus is expected. A simulation of a CRP where contextualized evaluations of newswire stories are characterized as augmented intuitionistic fuzzy sets (AIFS) shows how FAST-CR-XMIS can increase the level of consensus among the participants during the CRP.

scholarly journals On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1485
Author(s):  
Pavel Sevastjanov ◽  
Ludmila Dymova ◽  
Krzysztof Kaczmarek
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Short Paper ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Methodological Problems ◽  
Shafer Theory ◽  
Sets Theory

In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form.

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