In this paper, we initiate the novel concept of complex intuitionistic fuzzy subgroups and prove that every complex intuitionistic fuzzy subgroup generates two intuitionistic fuzzy subgroups. We extend this ideology to define the concept of level subsets of complex intuitionistic fuzzy set and discuss its various fundamental algebraic characteristics. We also show that the level subset of the complex intuitionistic fuzzy subgroups is a subgroup. Furthermore, we investigate the homomorphic image and preimage of complex intuitionistic fuzzy subgroup under group homomorphism. Moreover, we prove that the product of two complex intuitionistic fuzzy subgroups is also a complex intuitionistic fuzzy subgroup and develop some new results about direct product of complex intuitionistic fuzzy subgroups.INDEX TERMS Complex intuitionistic fuzzy set, Complex intuitionistic fuzzy subgroup, Level subsets, Product of complex intuitionistic fuzzy sets, Product of complex intuitionistic fuzzy subgroups.

In this study, the t-intuitionistic fuzzy normalizer and centralizer of t intuitionistic fuzzy subgroup are proposed. The t-intuitionistic fuzzy centralizer is normal subgroup of t-intuitionistic fuzzy normalizer and investigate various algebraic properties of this phenomena. We also introduce the concept of t-intuitionistic fuzzy Abelian and cyclic subgroups and prove that every t-intuitionistic fuzzy subgroup of Abelian (cyclic) group is t-intuitionistic fuzzy Abelian (cyclic) subgroup. We show that the image and preimage of t-intuitionistic fuzzy Abelian (cyclic) subgroup are t-intuitionistic fuzzy Abelian (cyclic) subgroup under group homomorphism. INDEX TERMS t-intuitionistic fuzzy set, t-intuitionistic fuzzy subgroup, t-intuitionistic fuzzy Abelian subgroup, t-intuitionistic fuzzy cyclic subgroup AMS(MOS) Subject Classifications: 03F55, 08A72, 20N25

N. Palaniappan et. al [20,28] have investigated the concept of intuitionistic fuzzy normal subrings in associative rings. In this study we extend these notions for a class of non-associative rings.

Shal et. al cite:SKR, have introduced the concept of intuitionistic fuzzy normal subrings over a non-associative ring. In this paper, we investigate the concept of intuitionistic anti fuzzy normal subrings over non-associative rings and give some properties of such subrings

The fundamentals of neutrosophic statistics provide a new basis for working with indeterminate data problems. In this study, the notion of the neutrosophic Rayleigh distribution () has been introduced. The neutrosphic extension of the classical Rayleigh model with several application areas is highlighted. The major characteristics of the proposed distribution are described in a way that suggested model can be utilized in different situations involving undetermined, vague and fuzzy data. The usage of proposed distribution notably in the domain of statistical process control () is considered. The classical structure of -chart is not capable of capturing uncertainty on studied variables. The mathematical structure of the -chart based on the proposed neutrosophic distribution has been developed. The neutrosphic parameters of the proposed -chart with other related performance metrics such as neutrosophy run length () and neutrosophy power curve ( ) are established. The proposed chart's performance in a neutrosophic environment is also evaluated to the existing model. Results from this comparative analysis reveal that the suggested Vchart outperforms its current equivalent in terms of neutrosophic statistical power. Finally, a charting structure of proposed design for service life of ball bearings data is considered with a view to support implementation procedure of the proposed neutrosophic design in real-world scenarios.

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One of the most important innovations brought by digitization is the cryptocurrency, also called virtual or digital currency, which has been discussed in recent years and in particular is a new platform for investors. Different types of cryptocurrencies such as Bitcoin, Ethereum, Binance Coin, and Tether do not depend on a central authority. Decision making is complicated by categorization and transmission of uncertainty, as well as verification of digital currency. The weighted average and weighted geometric aggregation operators are used in this article to define a multi-attribute decision-making approach. This work investigates the uniqueness of q-rung orthopair fuzzy hypersoft sets (q-ROFHSS), which respond to instabilities, uncertainty, ambiguity, and imprecise information. This research also covers some fundamental topics of q-ROFHSS. The model offered here is the best option for learning about electronic currency. This study validates the complexity of decision-making problems with different attributes and subattributes to obtain an optimal choice. We conclude that Bitcoin has a diverse set of applications and that crypto assets are well positioned to become an important asset class in decision making.

In this paper, we extend the characterizations of Kuroki [Regular fuzzy duo rings. Inform Sci. 1996;96:119-139], by initiating the concept of fuzzy left (resp. right, interior, quasi-, bi-, generalized bi-) ideals in a class of non-associative and non-commutative rings (LA-ring). We characterize regular (intra-regular, both regular and intra-regular) LA-rings in terms of such ideals.