A Novel Applications of Complex Intuitionistic Fuzzy Sets in Group Theory

Gulzar, Muhammad; Mateen, M. Haris; Alghazzawi, Dilshad; Kausar, Nasreen

doi:10.1109/access.2020.3034626

Cited by 64 publications

(39 citation statements)

References 30 publications

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“…Garg and Rani [46] achieved some results on information measures for CIFSs. Gulzar et al [47] came up with a novel application of CIFSs in group theory. Quek and Selvachandran [48] talked about the algebraic structure of CIF soft sets associated with groups and subgroups.…”

Section: Figure 2 Evaluation Of Ranges Of Pfs Sfs and Tsfsmentioning

confidence: 99%

Complex T-Spherical Fuzzy Relations With Their Applications in Economic Relationships and International Trades

et al. 2021

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Uncertainty is the unavoidable part of the life. In almost all circumstances, we regularly find ourselves in a state of uncertainty. Several reasons can lead to uncertainty, such as randomness, vagueness and rough knowledge. Fuzzy set (FS) theory deals with these kinds of information. Many generalizations had been made in the theory of FSs, such as intuitionistic FSs (IFSs), q-rung orthopair FSs (qROFSs), complex qROFSs (CqROFSs), spherical FSs (SFSs), T-spherical FSs (TSFSs), and complex TSFSs (CTSFSs). Among these generalizations of FSs, the CTSFSs are the most dominant generalization of the FSs. Although fuzzy relations (FRs), IF relations (IFRs) and complex FRs (CFRs) were defined in the literature, the concepts of relations have not yet been introduced in the CTSFSs. This paper unveils the novel concept of CTSF relations (CTSFRs), which provides the extensive generalizations of FRs. The proposed CTSFRs can give many generalized types of FRs, such as IFRs, CFRs, Pythagorean FRs, qROFRs, SFRs and TSFRs, etc. Additionally, some useful properties and results are obtained for CTSFRs. Moreover, a couple of applications demonstrate the usefulness of the proposed concepts. These CTSFRs can be used to depict the time-related interdependence of global market. Thus, we apply these CTSFRs to analyze the interdependence of the international trades among countries and compare the financial factors affecting business markets. Furthermore, the economic relationships with respect to time lag can be modeled by using the CTSFSs and the CTSFRs. Finally, a comparative analysis illuminates the supremacy of the proposed way in contrast with the existing ones.INDEX TERMS Fuzzy sets (FSs); T-spherical FSs (TSFSs); Complex TSFSs (CTSFSs); CTSF relations (CTSFRs); Cartesian product in CTSFSs; CTSF composite relation; Financial and economic relationships.

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Section: Figure 2 Evaluation Of Ranges Of Pfs Sfs and Tsfsmentioning

confidence: 99%

Complex T-Spherical Fuzzy Relations With Their Applications in Economic Relationships and International Trades

et al. 2021

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“…To explain better the investigated ideas, we briefly recall some fundamental notions such as SSs, CIFSs, and their operational laws. The existing theory of CIFSSs, which was explored by Kumar and Bajaj [32] and Quek et al [33] and the prioritized weighted aggregation operator (PWAO) is also revised. In the overall manuscript, the symbol X UN I is used for fixed set and the terms µ Tf CI and η Tf CI are used to show the grade of positive and the grade of negative.…”

Section: Preliminariesmentioning

confidence: 99%

“…The proposed work is also justified with the help of some numerical examples to show the reliability and effectiveness of the presented work. The existing CIFSSs were explored by Kumar and Bajaj [32] and Quek et al [33]. Based on the above existing ideas, the novel approach is discussed below.…”

Section: A Novel Complex Intuitionistic Fuzzy Soft Setmentioning

confidence: 99%

“…In Section 2, we briefly recall some fundamental notions such as SSs, CIFSs, and their operational laws. The existing theory of CIFSSs, which was explored by Kumar and Bajaj [32] and Quek et al [33] and the prioritized weighted aggregation operator (PWAO) is also revised. In Section 3, we improve the idea of CIFSSs and investigate their fundamental laws.…”

Section: Introductionmentioning

confidence: 99%

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Another View of Complex Intuitionistic Fuzzy Soft Sets Based on Prioritized Aggregation Operators and Their Applications to Multiattribute Decision Making

et al. 2021

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In a conventional interpretation of decision-making based on ambiguity, a decision-maker must prefer the best possible opportunity including various feasible possibilities. However, the dilemma of picking the best possible alternative has continued to be a substantial task to resolve. In this manuscript, we improve the existing complex intuitionistic fuzzy soft set (CIFSS), which includes the grade of truth and falsity with the rule that the sum of the real and imaginary parts of both grades is confined to [0, 1]. CIFS is a valuable procedure to determine the authenticity and consistency of the elaborated approaches. The fundamental laws and their related examples are also determined. Moreover, by using these laws, we investigated the complex intuitionistic fuzzy soft prioritized weighted averaging operator (CIFSPWAO), the complex intuitionistic fuzzy soft prioritized ordered weighted averaging operator (CIFSPOWAO), the complex intuitionistic fuzzy soft prioritized weighted geometric operator (CIFSPWGO), complex intuitionistic fuzzy soft prioritized ordered weighted geometric operator (CIFSPOWGO), and their related properties are also developed. Based on the developed operators, the multiattribute decision-making (MADM) tool is developed by using the explored operators based on CIFSS. Some numerical examples are also illustrated by using the investigated operators to determine the feasibility and consistency of the developed approaches. Finally, the comparative analysis and their geometrical manifestations are also determined to enhance the excellence of the performed explorations.

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“…e theory of complex interval-valued IFS was developed by Garg and Rani [22] which contains the degree of truth and falsity in the form of a subinterval of the unit interval. e idea of the CIFS has received a great deal of attention from the scholars [23][24][25][26] and has been widely used in the different areas. e CIFS is limited in access due to their restriction on the sum of the degrees to be 1, for instance, if a person gives 0.6e i2π (7) for truth grade and 0.5e i2π (6) for falsity, then clearly 0.6 + 0.5 > 1 and hence does not satisfy the properties of CIFS.…”

Section: Introductionmentioning

confidence: 99%

Some Similarity and Distance Measures between Complex Interval-Valued q-Rung Orthopair Fuzzy Sets Based on Cosine Function and their Applications

Garg

Ali

Mahmood

et al. 2021

Mathematical Problems in Engineering

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The purpose of this paper is to present a new method to solve the decision-making algorithm based on the cosine similarity and distance measures by utilizing the uncertain and vague information. A complex interval-valued q-rung orthopair fuzzy set (CIVQROFS) is a reliable and competent technique for handling the uncertain information with the help of the complex-valued membership grades. To address the degree of discrimination between the pairs of the sets, cosine similarity measures (CSMs) and distance measures (DMs) are an accomplished technique. Driven by these, in this manuscript, we defined some CSMs and DMs for the pairs of CIVQROFSs and investigated their several properties. Choosing that the CSMs do not justify the axiom of the similarity measure (SM), then we investigate a technique to developing other CIVQROFSs-based SMs using the explored CSMs and Euclidean DMs, and it fulfills the axiom of the SMs. In addition, we find the cosine DMs (CDMs) by considering the inter-relationship between the SM and DMs; then, we have modified the procedure for the rank of partiality by similarity to the ideal solution method for the CDMs under investigation, which can deal with the associated decision-making problems not only individually from the argument of the opinion of geometry but also the fact of the opinion of algebra. Finally, we provide a numerical example to demonstrate the practicality and effectiveness of the proposed procedure, which is also in line with existing procedures. Graphical representations of the measures developed are also used in this manuscript.

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A Novel Applications of Complex Intuitionistic Fuzzy Sets in Group Theory

Cited by 64 publications

References 30 publications

Complex T-Spherical Fuzzy Relations With Their Applications in Economic Relationships and International Trades

Complex T-Spherical Fuzzy Relations With Their Applications in Economic Relationships and International Trades

Another View of Complex Intuitionistic Fuzzy Soft Sets Based on Prioritized Aggregation Operators and Their Applications to Multiattribute Decision Making

Some Similarity and Distance Measures between Complex Interval-Valued q-Rung Orthopair Fuzzy Sets Based on Cosine Function and their Applications

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