scholarly journals DISTANCE AND SIMILARITY MEASURES FOR SOFT SETS

2010 ◽  
Vol 06 (03) ◽  
pp. 321-334 ◽  
Author(s):  
ATHAR KHARAL
Keyword(s):  
Similarity Measure ◽  
Matrix Representation ◽  
Similarity Measures ◽  
Matching Function ◽  
Soft Sets ◽  
Fundamental Assumption ◽  
Set Operations ◽  
Erroneous Result

In Ref. 7, the authors use matrix representation-based distances of soft sets to introduce matching function and distance-based similarity measures. We first give counterexamples to show that their Definition 2.7 and Lemma 3.5(3) contain errors, then improve their Lemma 4.4 making it a corollary of our result. The fundamental assumption of Ref. 7 has been shown to be flawed. This motivates us to introduce set operations-based measures. We present a case (Example 6.7) where Majumdar-Samanta similarity measure produces an erroneous result but the measure proposed here decides correctly. Several properties of the new measures have been presented and finally the new similarity measures have been applied to the problem of financial diagnosis of firms.

scholarly journals Similarity measures of Pythagorean fuzzy soft sets and clustering analysis

2021 ◽  
Author(s):  
Athira T M ◽  
Sunil Jacob John ◽  
Harish Garg
Keyword(s):  
Similarity Measure ◽  
Fuzzy Set ◽  
Clustering Algorithm ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Soft Set ◽  
Soft Sets ◽  
Pythagorean Fuzzy Set ◽  
Fuzzy Soft Sets ◽  
Membership Value

Abstract Pythagorean fuzzy set (PFS) is a broadening of intuitionistic fuzzy set that can represent the situations where the sum of membership and the non-membership values exceeds one. Adding parameterization to PFS we obtain a structure named as Pythagorean fuzzy soft set (PFSS). It has a higher capacity to deal with vagueness as it captures both the structures of a PFS and a soft set. Several practical situations demand the measure of similarity between two structures, whose sum of membership value and non-membership value exceeds one. There are no existing tools to measure the similarity between PFSS and this paper put forward similarity measures for PFSS. An axiomatic definition for similarity measure is proposed for PFSS and certain expressions for similarity measure are introduced. Further, some theorems which express the properties of similarity measures are proved. A comparative study between proposed expressions for similarity measure is carried out. Also, a clustering algorithm based on PFSS is introduced by utilizing the proposed similarity measure.

scholarly journals A New Approach to Entropy and Similarity Measure of Vague Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Dan Hu ◽  
Zhiyong Hong ◽  
Yong Wang
Keyword(s):  
Similarity Measure ◽  
Similarity Measures ◽  
Soft Sets ◽  
New Approach ◽  
Basic Properties ◽  
Uncertainty Measures

We focus our discussion on the uncertainty measures of vague soft sets. We propose axiomatic definitions of similarity measure and entropy for vague soft sets. Furthermore, we present a new category of similarity measures and entropies for vague soft sets. The basic properties of these measures are discussed and the relationships among these measures are analyzed.

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).

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 Similarity Measure and Entropy of Fuzzy Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhicai Liu ◽  
Keyun Qin ◽  
Zheng Pei
Keyword(s):  
Set Theory ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Soft Set ◽  
The Other ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Uncertainty Measures ◽  
Fuzzy Soft Sets

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. Recently, uncertainty measures of soft sets and fuzzy soft sets have gained attentions from researchers. This paper is devoted to the study of uncertainty measures of fuzzy soft sets. The axioms for similarity measure and entropy are proposed. A new category of similarity measures and entropies is presented based on fuzzy equivalence. Our approach is general in the sense that by using different fuzzy equivalences one gets different similarity measures and entropies. The relationships among these measures and the other proposals in the literatures are analyzed.

Some Hybrid Soft Sets and Their Application in Decision Making

2016 ◽  
pp. 86-117 ◽  
Author(s):  
Pinaki Majumdar
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Soft Set ◽  
Soft Sets ◽  
Basic Properties ◽  
Two Hybrid

In this chapter the notions of two hybrid soft sets, namely fuzzy parameterized soft sets and vague soft sets has been discussed and some operations on them are defined. Some properties of these two hybrid soft sets under these operations are also studied. Application of fuzzy parameterized soft sets and vague soft sets in decision making has also been shown. Then the notion of similarity measure between two hybrid soft sets has been introduced and their basic properties are studied. Applications of these similarity measures in various problems like medical diagnosis and decision making have been shown. The idea of entropy of a fuzzy parameterized soft set has been introduced.

MATHURA (MBI) - A NOVEL IMPUTATION MEASURE FOR IMPUTATION OF MISSING VALUES IN MEDICAL DATASETS

2019 ◽  
Vol 13 ◽  
Author(s):  
B. Mathura Bai ◽  
N. Mangathayaru ◽  
B. Padmaja Rani ◽  
Shadi Aljawarneh
Keyword(s):  
Similarity Measure ◽  
Medical Records ◽  
Missing Values ◽  
Similarity Measures ◽  
Common Problems ◽  
Experiment Analysis

: Missing attribute values in medical datasets are one of the most common problems faced when mining medical datasets. Estimation of missing values is a major challenging task in pre-processing of datasets. Any wrong estimate of missing attribute values can lead to inefficient and improper classification thus resulting in lower classifier accuracies. Similarity measures play a key role during the imputation process. The use of an appropriate and better similarity measure can help to achieve better imputation and improved classification accuracies. This paper proposes a novel imputation measure for finding similarity between missing and non-missing instances in medical datasets. Experiments are carried by applying both the proposed imputation technique and popular benchmark existing imputation techniques. Classification is carried using KNN, J48, SMO and RBFN classifiers. Experiment analysis proved that after imputation of medical records using proposed imputation technique, the resulting classification accuracies reported by the classifiers KNN, J48 and SMO have improved when compared to other existing benchmark imputation techniques.

scholarly journals A set theory based similarity measure for text clustering and classification

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Ali A. Amer ◽  
Hassan I. Abdalla
Keyword(s):  
Set Theory ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Text Clustering ◽  
Plagiarism Detection ◽  
K Nearest Neighbor ◽  
Single Measure ◽  
Highly Effective ◽  
Clustering And Classification ◽  
Effectiveness And Efficiency

Abstract Similarity measures have long been utilized in information retrieval and machine learning domains for multi-purposes including text retrieval, text clustering, text summarization, plagiarism detection, and several other text-processing applications. However, the problem with these measures is that, until recently, there has never been one single measure recorded to be highly effective and efficient at the same time. Thus, the quest for an efficient and effective similarity measure is still an open-ended challenge. This study, in consequence, introduces a new highly-effective and time-efficient similarity measure for text clustering and classification. Furthermore, the study aims to provide a comprehensive scrutinization for seven of the most widely used similarity measures, mainly concerning their effectiveness and efficiency. Using the K-nearest neighbor algorithm (KNN) for classification, the K-means algorithm for clustering, and the bag of word (BoW) model for feature selection, all similarity measures are carefully examined in detail. The experimental evaluation has been made on two of the most popular datasets, namely, Reuters-21 and Web-KB. The obtained results confirm that the proposed set theory-based similarity measure (STB-SM), as a pre-eminent measure, outweighs all state-of-art measures significantly with regards to both effectiveness and efficiency.

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 A New Approach to Measuring the Similarity of Indoor Semantic Trajectories

2021 ◽  
Vol 10 (2) ◽  
pp. 90
Author(s):  
Jin Zhu ◽  
Dayu Cheng ◽  
Weiwei Zhang ◽  
Ci Song ◽  
Jie Chen ◽  
...  
Keyword(s):  
Similarity Measure ◽  
Semantic Information ◽  
Edit Distance ◽  
Similarity Measures ◽  
Indoor Positioning ◽  
Synthetic Dataset ◽  
Shopping Mall ◽  
Indoor Space ◽  
Trajectory Similarity ◽  
Indoor Spaces

People spend more than 80% of their time in indoor spaces, such as shopping malls and office buildings. Indoor trajectories collected by indoor positioning devices, such as WiFi and Bluetooth devices, can reflect human movement behaviors in indoor spaces. Insightful indoor movement patterns can be discovered from indoor trajectories using various clustering methods. These methods are based on a measure that reflects the degree of similarity between indoor trajectories. Researchers have proposed many trajectory similarity measures. However, existing trajectory similarity measures ignore the indoor movement constraints imposed by the indoor space and the characteristics of indoor positioning sensors, which leads to an inaccurate measure of indoor trajectory similarity. Additionally, most of these works focus on the spatial and temporal dimensions of trajectories and pay less attention to indoor semantic information. Integrating indoor semantic information such as the indoor point of interest into the indoor trajectory similarity measurement is beneficial to discovering pedestrians having similar intentions. In this paper, we propose an accurate and reasonable indoor trajectory similarity measure called the indoor semantic trajectory similarity measure (ISTSM), which considers the features of indoor trajectories and indoor semantic information simultaneously. The ISTSM is modified from the edit distance that is a measure of the distance between string sequences. The key component of the ISTSM is an indoor navigation graph that is transformed from an indoor floor plan representing the indoor space for computing accurate indoor walking distances. The indoor walking distances and indoor semantic information are fused into the edit distance seamlessly. The ISTSM is evaluated using a synthetic dataset and real dataset for a shopping mall. The experiment with the synthetic dataset reveals that the ISTSM is more accurate and reasonable than three other popular trajectory similarities, namely the longest common subsequence (LCSS), edit distance on real sequence (EDR), and the multidimensional similarity measure (MSM). The case study of a shopping mall shows that the ISTSM effectively reveals customer movement patterns of indoor customers.

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