Similarity Measure of Complex Vague Soft Sets and Its Application to Pattern Recognition

Selvachandran, Ganeshsree; Garg, Harish; Alaroud, Mohammad; Salleh, Abdul Razak

doi:10.1007/s40815-018-0492-5

Cited by 33 publications

(15 citation statements)

References 55 publications

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“…Hu et al [17] proposed some distance measures for CFSs and studied the continuity of operations of CFSs. Some similarity measures of CVSSs are proposed by Selvachandran et al [18] and their applications in pattern recognitions are studied. In [19], Quek and Selvachandran studied the algebraic structures of CIFS associated with groups, while [20] discussed the application of CFS in E-commerce.…”

Section: Introductionmentioning

confidence: 99%

On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition

Ullah

Mahmood

Ali

et al. 2019

Complex Intell. Syst.

280

148

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The concept of complex fuzzy set (CFS) and complex intuitionistic fuzzy set (CIFS) is two recent developments in the field of fuzzy set (FS) theory. The significance of these concepts lies in the fact that these concepts assigned membership grades from unit circle in plane, i.e., in the form of a complex number instead from [0, 1] interval. CFS cannot deal with information of yes and no type, while CIFS works only for a limited range of values. To deal with these kinds of problems, in this article, the concept of complex Pythagorean fuzzy set (CPFS) is developed. The novelty of CPFS lies in its larger range comparative to CFS and CIFS which is demonstrated numerically. It is discussed how a CFS and CIFS could be CPFS but not conversely. We investigated the very basic concepts of CPFSs and studied their properties. Furthermore, some distance measures for CPFSs are developed and their characteristics are studied. The viability of the proposed new distance measures in a building material recognition problem is also discussed. Finally, a comparative study of the proposed new work is established with pre-existing study and some advantages of CPFS are discussed over CFS and CIFS.

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Section: Introductionmentioning

confidence: 99%

On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition

Ullah

Mahmood

Ali

et al. 2019

Complex Intell. Syst.

280

148

View full text Add to dashboard Cite

show abstract

“…These distance measures in [30,31] are defined by using Hamming and Euclidean metrics. Recently, several concepts including the parallelity [32,33] and entropy measures [34] of complex fuzzy sets and distances of complex intuitionistic fuzzy sets [35], complex vague soft sets [7,36,37] and complex multi-fuzzy soft set [5] have been developed. Since Greenfield et al [8,9] introduced the concept of an interval-valued complex fuzzy sets (IVCFSs), which is a generalization of the complex fuzzy set introduced by Ramot et al [1], some progress has been made in various subjects related to the IVCFS.…”

Section: Introductionmentioning

confidence: 99%

Distance Measures between the Interval-Valued Complex Fuzzy Sets

Dai

2019

Mathematics

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Complex fuzzy set (CFS) is a recent development in the field of fuzzy set (FS) theory. The significance of CFS lies in the fact that CFS assigned membership grades from a unit circle in the complex plane, i.e., in the form of a complex number whose amplitude term belongs to a [ 0 , 1 ] interval. The interval-valued complex fuzzy set (IVCFS) is one of the extensions of the CFS in which the amplitude term is extended from the real numbers to the interval-valued numbers. The novelty of IVCFS lies in its larger range comparative to CFS. We often use fuzzy distance measures to solve some problems in our daily life. Hence, this paper develops some series of distance measures between IVCFSs by using Hamming and Euclidean metrics. The boundaries of these distance measures for IVCFSs are obtained. Finally, we study two geometric properties include rotational invariance and reflectional invariance of these distance measures.

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“…In future research, we shall extend the present study to some more generalized environment and applied it to many other fields such as graph theory, transportation evaluation, resource management using different uncertain environments [57][58][59][60][61][62].…”

Section: Discussionmentioning

confidence: 99%

Symmetric Triangular Interval Type-2 Intuitionistic Fuzzy Sets with Their Applications in Multi Criteria Decision Making

Singh

Garg

2018

Symmetry

Self Cite

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Type-2 intuitionistic fuzzy set (T2IFS) is a powerful and important extension of the classical fuzzy set, intuitionistic fuzzy set to measure the vagueness and uncertainty. In a practical decision-making process, there always occurs an inter-relationship among the multi-input arguments. To deal with this point, the motivation of the present paper is to develop some new interval type-2 (IT2) intuitionistic fuzzy aggregation operators which can consider the multi interaction between the input argument. To achieve it, we define a symmetric triangular interval T2IFS (TIT2IFS), its operations, Hamy mean (HM) operator to aggregate the preference of the symmetric TIT2IFS and then shows its applicability through a multi-criteria decision making (MCDM). Several enviable properties and particular cases together with following different parameter values of this operator are calculated in detail. At last a numerical illustration is to given to exemplify the practicability of the proposed technique and a comparative analysis is analyzed in detail.

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Similarity Measure of Complex Vague Soft Sets and Its Application to Pattern Recognition

Cited by 33 publications

References 55 publications

On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition

On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition

Distance Measures between the Interval-Valued Complex Fuzzy Sets

Symmetric Triangular Interval Type-2 Intuitionistic Fuzzy Sets with Their Applications in Multi Criteria Decision Making

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