Medical diagnosis of nephrotic syndrome using m-polar spherical fuzzy sets

2021 ◽  
pp. 2150094
Author(s):  
Muhammad Riaz ◽  
Maryam Saba ◽  
Muhammad Abdullah Khokhar ◽  
Muhammad Aslam
Keyword(s):  
Nephrotic Syndrome ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Score Function ◽  
Membership Degree ◽  
Relationship Analysis ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Special Cases ◽  
Order Preference

The aim of this paper is to introduce the notion of m-polar spherical fuzzy set (mPSFS) as a hybrid model of spherical fuzzy set (SFS) and m-polar fuzzy set (mPFS). The proposed model named as mPSFS is an efficient model to address multi-polarity in a spherical fuzzy environment. That is, an mPSFS assigns [Formula: see text] number of ordered triple of three independent grades (membership degree, neutral-membership degree and non-membership degree) against each alternative in the universe of discourse. The existing models, namely, mPFS and SFS, are the special cases of suggested hybrid mPSFS. In order to ensure the novelty of this robust extension, various operations on the m-polar spherical fuzzy sets (mPSFSs) are introduced with some brief illustrations to understand these concepts. A robust multi-criteria decision-making (MCDM) method is established by using new score function and accuracy function for m-polar spherical fuzzy numbers (mPSFNS). Additionally, the extensions of technique of order preference by similarity to ideal solution (TOPSIS) and gray relationship analysis (GRA) towards m-polar spherical fuzzy environment are proposed. Moreover, an application to nephrotic syndrome which may lead to kidney damage is analyzed by extensions TOPSIS and GRA. The proposed techniques and their algorithms provide a fruitful diagnosis procedure in the treatment of nephrotic syndrome. Lastly, we give a comparison analysis of the suggested models with some existing models as well.

Complex q-rung orthopair fuzzy Schweizer–Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making

2021 ◽  
pp. 1-23
Author(s):  
Peide Liu ◽  
Tahir Mahmood ◽  
Zeeshan Ali
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Imaginary Part ◽  
Fuzzy Set ◽  
Score Function ◽  
Aggregation Operators ◽  
Unit Interval ◽  
Multi Criteria Decision Making ◽  
Accuracy Function ◽  
Special Cases

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed.

scholarly journals TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1739
Author(s):  
Zeeshan Ali ◽  
Tahir Mahmood ◽  
Miin-Shen Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Unit Interval ◽  
Polar Coordinates ◽  
Topsis Method ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Special Cases ◽  
Order Preference ◽  
Multi Attribute Decision Making

The theory of complex spherical fuzzy sets (CSFSs) is a mixture of two theories, i.e., complex fuzzy sets (CFSs) and spherical fuzzy sets (SFSs), to cope with uncertain and unreliable information in realistic decision-making situations. CSFSs contain three grades in the form of polar coordinates, e.g., truth, abstinence, and falsity, belonging to a unit disc in a complex plane, with a condition that the sum of squares of the real part of the truth, abstinence, and falsity grades is not exceeded by a unit interval. In this paper, we first consider some properties and their operational laws of CSFSs. Additionally, based on CSFSs, the complex spherical fuzzy Bonferroni mean (CSFBM) and complex spherical fuzzy weighted Bonferroni mean (CSFWBM) operators are proposed. The special cases of the proposed operators are also discussed. A multi-attribute decision making (MADM) problem was chosen to be resolved based on the proposed CSFBM and CSFWBM operators. We then propose the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method based on CSFSs (CSFS-TOPSIS). An application example is given to delineate the proposed methods and a close examination is undertaken. The advantages and comparative analysis of the proposed approaches are also presented.

scholarly journals A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yafei Song ◽  
Xiaodan Wang ◽  
Lei Lei ◽  
Aijun Xue
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Degree ◽  
Intuitionistic Fuzzy ◽  
Axiomatic Definition

As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns.

scholarly journals Novel concepts of $ m $-polar spherical fuzzy sets and new correlation measures with application to pattern recognition and medical diagnosis

2021 ◽  
Vol 6 (10) ◽  
pp. 11346-11379
Author(s):  
Muhammad Riaz ◽  
◽  
Maryam Saba ◽  
Muhammad Abdullah Khokhar ◽  
Muhammad Aslam ◽  
...  
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Real Life ◽  
Hybrid Structure ◽  
Fuzzy Environment ◽  
Life Problems ◽  
Correlation Measures ◽  
Relationship Of

<abstract><p>In this paper, we introduce the notion of $ m $-polar spherical fuzzy set ($ m $-PSFS) which is a hybrid notion of $ m $-polar fuzzy set ($ m $-PFS) and spherical fuzzy set (SFS). The purpose of this hybrid structure is to express multipolar information in spherical fuzzy environment. An $ m $-PSFS is a new approach towards computational intelligence and multi-criteria decision-making (MCDM) problems. We introduce the novel concepts of correlation measures and weighted correlation measures of $ m $-PSFSs based on statistical notions of covariances and variances. Correlation measures estimate the linear relationship of the two quantitative objects. A correlation may be positive or negative depending on the direction of the relation between two objects and its value lies the interval $ [-1, 1] $. The same concept is carried out towards $ m $-polar spherical fuzzy ($ m $-PSF) information. We investigate certain properties of covariances and the correlation measures to analyze that these concepts are extension of crisp correlation measures. The main advantage of proposed correlation measures is that these notions deal with uncertainty in the real-life problems efficiently with the help of $ m $-PSF information. We discuss applications of $ m $-polar spherical fuzzy sets and their correlation measures in pattern recognition and medical diagnosis. To discuss the superiority and efficiency of proposed correlation measures, we give a comparison analysis of proposed concepts with some existing concepts.</p></abstract>

scholarly journals Extension of competition graphs under complex fuzzy environment

2020 ◽  
Author(s):  
Muhammad Akram ◽  
Aqsa Sattar ◽  
Faruk Karaaslan ◽  
Sovan Samanta
Keyword(s):  
Unit Circle ◽  
Fuzzy Set ◽  
Economic Competition ◽  
Complex Fuzzy Set ◽  
Fuzzy Environment ◽  
Research Article ◽  
Fuzzy Graphs ◽  
Proposed Model ◽  
Present Complex ◽  
Phase Term

Abstract A complex fuzzy set (CFS) is a remarkable generalization of the fuzzy set in which membership function is restricted to take the values from the unit circle in the complex plane. A CFS is an efficient model to deal with uncertainties of human judgement in more comprehensive and logical way due to the presence of phase term. In this research article, we introduce the concept of competition graphs under complex fuzzy environment. Further, we present complex fuzzy k-competition graphs and p-competition complex fuzzy graphs. Moreover, we consider m-step complex fuzzy competition graphs, complex fuzzy neighborhood graphs (CFNGs), complex fuzzy economic competition graphs (CFECGs) and m-step complex fuzzy economic competition graphs with interesting properties. In addition, we describe an application in ecosystem of our proposed model. We also provide comparison of proposed competition graphs with existing graphs.

Multiple criteria decision making based on Hamy mean operators under the environment of spherical fuzzy sets

2021 ◽  
pp. 1-26
Author(s):  
Muhammad Sarwar Sindhu ◽  
Tabasam Rashid ◽  
Agha Kashif
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Closed Interval ◽  
Multiple Criteria Decision Making ◽  
Score Function ◽  
Vital Role ◽  
Multiple Criteria ◽  
Uncertain Information ◽  
Membership Degree ◽  
Picture Fuzzy Sets

Aggregation operators are widely applied to accumulate the vague and uncertain information in these days. Hamy mean (HM) operators play a vital role to accumulate the information. HM operators give us a more general and stretchy approach to develop the connections between the arguments. Spherical fuzzy sets (SpFSs), the further extension of picture fuzzy sets (PcFSs) that handle the data in which square sum of membership degree (MD), non-membership degree (NMD) and neutral degree (ND) always lie between closed interval [0, 1]. In the present article, we modify the HM operators like spherical fuzzy HM (SpFHM) operator and weighted spherical fuzzy HM (WSpFHM) operator to accumulate the spherical fuzzy (SpF) information. Moreover, various properties and some particular cases of SpFHM and the WSpFHM operators are discussed in details. Also, to compare the results obtained from the HM operators a score function is developed. Based on WSpFHM operator and score function, a model for multiple criteria decision-making (MCDM) is established to resolve the MCDM problem. To check the significance and robustness of the result, a comparative analysis and sensitivity analysis is also performed.

Comparative Analysis of Two Different Probabilistic Fuzzy Sets

2013 ◽  
Vol 647 ◽  
pp. 838-842
Author(s):  
Yi Hua Li ◽  
Wen Jing Huang ◽  
Yan Pang
Keyword(s):  
Comparative Analysis ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Potential Application ◽  
Fuzzy Membership ◽  
Membership Degree ◽  
Fuzzy Features

The probabilistic fuzzy set (PFS) is designed for handling the uncertainties with both stochastic and fuzzy features. In this paper, the fundamental analyses are conducted to study influences of random variations to the fuzzy membership degree and its convergence. The analysis clearly discloses that fuzzy membership degree will show Gaussian features. The work presented will improve the potential application of probabilistic fuzzy sets.

CLASSES OF INTUITIONISTIC FUZZY T-NORMS SATISFYING THE RESIDUATION PRINCIPLE

2003 ◽  
Vol 11 (06) ◽  
pp. 691-709 ◽  
Author(s):  
GLAD DESCHRIJVER ◽  
ETIENNE E. KERRE
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Degree ◽  
Important Class ◽  
Triangular Norms ◽  
Intuitionistic Fuzzy

Intuitionistic fuzzy sets constitute an extension of fuzzy sets: while fuzzy sets give a degree to which an element belongs to a set, intuitionistic fuzzy sets give both a membership degree and a non-membership degree. The only constraint on those two degrees is that the sum must be smaller than or equal to 1. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. In the fuzzy case a t-norm satisfies the residuation principle if and only if it is left-continuous. Deschrijver, Cornelis and Kerre proved that for intuitionistic fuzzy t-norms the equivalence between the residuation principle and intuitionistic fuzzy left-continuity only holds for t-representable t-norms.1 In this paper we construct particular subclasses of intuitionistic fuzzy t-norms that satisfy the residuation principle but that are not t-representable and we show that a continuous intuitionistic fuzzy t-norm [Formula: see text] satisfying the residuation principle is t-representable if and only if [Formula: see text].

scholarly journals A Combined Interval Type-2 Fuzzy MCDM Framework for the Resilient Supplier Selection Problem

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 44
Author(s):  
Seyed Amirali Hoseini ◽  
Sarfaraz Hashemkhani Zolfani ◽  
Paulius Skačkauskas ◽  
Alireza Fallahpour ◽  
Sara Saberi
Keyword(s):  
Distance Measure ◽  
Hamming Distance ◽  
Real Life ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Order Preference ◽  
Simple Additive Weighting ◽  
Interval Type ◽  
High Degree

Selecting the most resilient supplier is a crucial problem for organizations and managers in the supply chain. However, due to the inherited high degree of uncertainty in real-life projects, developing a decision-making framework in a crisp or fuzzy environment may not present accurate or reliable results for the managers. For this reason, it is better to evaluate the potential suppliers in an Interval Type-2 Fuzzy (IT2F) environment for better dealing with this ambiguity. This study developed an improved combined IT2F Best Worst Method (BWM) and IT2F technique for Order Preference by Similarity to Ideal Solution (TOPSIS) model “Atieh Sazan” Co. as a case study, such that the IT2FBWM was employed for obtaining the weight of criteria. The IT2FTOPSIS was utilized for ranking the potential suppliers based on Hamming distance measure. In both phases, the opinions of experts as IT2F linguistic terms were employed for weighting the criteria and obtaining the relative importance of the alternatives in terms of the evaluative criteria. After obtaining the final results, the proposed model was validated by replacing Analytical Hierarchy Process (AHP) and Simple Additive Weighting (SAW) approaches separately instead of BWM for weighting the criteria. After executing both new models, it was found that the final ranking was similar to the final ranking of the proposed model, representing the reliability and accuracy of the obtained results. Moreover, it was concluded that the resilient criteria of “Reorganization” and “Redundancy” are the most determinant measures for selecting the best supplier rather than measures in the Iranian Construction Industry.

SMETS-MAGREZ AXIOMS FOR R-IMPLICATORS IN INTERVAL-VALUED AND INTUITIONISTIC FUZZY SET THEORY

2005 ◽  
Vol 13 (04) ◽  
pp. 453-464 ◽  
Author(s):  
GLAD DESCHRIJVER ◽  
ETIENNE E. KERRE
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Intuitionistic Fuzzy Set ◽  
Membership Degree ◽  
Triangular Norms ◽  
Intuitionistic Fuzzy ◽  
Special Lattice ◽  
Interval Valued

Interval-valued fuzzy sets constitute an extension of fuzzy sets which give an interval approximating the "real" (but unknown) membership degree. Interval-valued fuzzy sets are equivalent to intuitionistic fuzzy sets in the sense of Atanassov which give both a membership degree and a non-membership degree, whose sum must be smaller than or equal to 1. Both are equivalent to L-fuzzy sets w.r.t. a special lattice L*. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. In a previous paper5 we gave a construction for t-norms on L* satisfying the residuation principle which are not t-representable. In this paper we investigate the Smets-Magrez axioms and some other properties for the residual implicator generated by such t-norms.

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