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In this paper, we introduce the concepts of cubic soft (CS) algebra, CS o-subalgebra, and CS ideals within the framework of B-algebra. We provide comprehensive characterizations of these new structures, elucidating their unique properties and interrelationships. Specifically, we present detailed conditions under which a CS subalgebra can be classified as a closed CS ideal. Our analysis explores the intricate relationships among closed cubic soft ideals, cubic soft subalgebras, and cubic soft o-subalgebras. By doing so, we aim to provide a deeper understanding of how these structures interact and coexist within the broader context of B-algebra The findings offer significant insights into the application and theoretical underpinnings of cubic soft sets in algebraic systems, contributing to the ongoing evolution of fuzzy set theory and its applications in various mathematical domains. Our work not only broadens the scope of B-algebra but also enhances its utility in solving complex problems where traditional algebraic approaches may fall short. Through this exploration, we seek to advance the field and open new avenues for research and practical applications in mathematical sciences. [ABSTRACT FROM AUTHOR]

To reduce the threats that wastewater poses to human health and the environment, water treatment techniques must be improved. The use of a procedure that includes preparation, testing, primary and secondary treatments, filtration, disinfection, and continuous monitoring is therefore required. The objective of this research is to create a hybrid notion that extends the idea of an interval-valued neutrosophic fuzzy soft set (IVNFSS) to an interval-valued neutrosophic fuzzy set. Operations like complement, union, and integration are included in the idea. To improve decision-making accuracy, a quality-assessment distance measure is incorporated, offering a numerical representation of the disparity between various factors. Furthermore, the IVNFSS defines distance measures, which are used in the wastewater treatment process. To monitor water quality, IVNFSS, in conjunction with a distance measure, is a potent instrument whose application extends to water waste treatment procedures. This can completely change the way that water quality management is now done by providing a methodical way to guarantee the security and quality of drinking water. [ABSTRACT FROM AUTHOR]

The interval complex single-valued neutrosophic hypersoft set (Ξ-set), together with its features and set-theoretic operations, is a new mathematical structure that is discussed in this article. For managing ambiguous and uncertain knowledge, the suggested structure integrates the interval complex single-valued neutrosophic set and hypersoft set. These two elements have already been regarded as trustworthy settings. The first component has the ability to manage information on interval and periodic types, while the second offers a multi-argument domain for concurrent consideration of numerous sub-attributes. The Ξ-set is used to aggregate these sets, allowing for the fusion of various qualities and any related uncertainty. The resultant aggregated sets, which take into account both the attribute values and the associated uncertainty, give a thorough representation of the decision aspect. To assist in decision-making, the method calculates how similar several options are to the optimum option using a distance-based similarity metric. By contrasting the combined sets of several options, the system determines the best option based on the specified selection criteria. Decision-makers can evaluate how changing attribute values may influence their choices using the suggested strategy’s endorsement of sensitivity analysis. The efficacy of the recommended decision-support mechanism is demonstrated through a case study with a real-world choice dilemma. The results show how well the framework can handle ambiguity and uncertainty while providing decision-makers with meaningful insights and encouraging rational choices. Finally, the multi-attribute decision-support system based on aggregations of Ξ-set provides a reliable framework for dealing with difficult choice issues that are characterized by ambiguity and vagueness. [ABSTRACT FROM AUTHOR]

This study provides an innovative approach to neutrosophic algebraic structures by introducing a new structure called Neutrosophic Soft Cubic T-ideal (NSCTID), which combines T-ideal (TID) and Neutrosophic Soft Cubic Sets (NSCSs) within the framework of PS-Algebra. Within the already-existing neutrosophic cubic structures, the addition of soft sets with the characteristics of TID makes this structure more desirable. The theoretical development of the proposed structure includes the application of fundamental ideas as union, intersection, the Cartesian product, and homomorphism. We also introduce the notions of NSCTID-translation and NSCTID-multiplication to further enhance the structure of NSCTID. By applying the idea of translation and multiplication, we offer improved algorithm for neutrosophic cubic sets to deal with different parameters that are satisying the TID’s distinctive characteristics. Through this thorough research, we offer an elementary understanding of NSCTID and its capabilities, providing the way to new algebraic structures. [ABSTRACT FROM AUTHOR]

There are several decision-making based situations in which it is necessary to categorize the evaluating parameters into their respective sub-parametric values based non-overlapping sets. The existing soft set model is not compatible with such situations therefore hypersoft set (Hs-set) is developed which manages such situations by utilizing a novel mapping called multi-argument approximate mapping which broadens the domain of soft approximate mapping. This research presents the characterization of several essential axiomatic properties and set-based operations of Hs-set which will help the researchers to implement this emerging theory to other fields of study. The brief discussion on some hybridized structures of Hs-set with fuzzy set-like models is also provided. [ABSTRACT FROM AUTHOR]

In multi-criteria decision-making problems, we may have to deal with numbers that are in interval forms, like those of membership, non-membership grades and indeterminacy grades representing unique attributes of elements. When decision-makers come across such an environment, the decisions are harder to make and the most significant factor is that we need to combine these interval numbers to generate a single real number, which can be done using aggregation operators or score functions. To overcome this hindrance, we introduce the notion of interval-valued intuitionistic neutrosophic hypersoft set. This eventually helps the decision-maker to collect the data with no misconceptions. The primary aim of this study is to establish some operational laws for interval-valued intuitionistic neutrosophic hypersoft set. Also, we present the fundamental properties of two aggregation operators, interval-valued intuitionistic neutrosophic weighted average and interval-valued intuitionistic neutrosophic weighted geometric operators. Also, we propose an algorithm for the technique of order of preference by similarity to ideal solution (TOPSIS) method based on correlation coefficients to choose a suitable employee among the alternative using Leipzig leadership model in an organization for an upcoming new project. Finally, we present a comparative study with existing similarity measures to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article aims to introduce a unique hypersoft time-based matrix model that organizes and classifies higher-dimensional information scattered in numerous forms and vague appearances varying on specific time levels. Classical matrices as rank-2 tensors single-handedly relate equations and variables across rows and columns are a limited approach to organizing higher-dimensional information. This Plithogenic Crisp Time Leveled Hypersoft Matrix (PCTLHS-Matrix) model is designed to sort the higher dimensional information flowing in parallel time layers as a combined view of events. This matrix has several parallel layers of time. The time-based level cuts as time layers are introduced to present an explicit view of information on certain required time levels as a separate reality. The sub-layers are formulated as sub-level cuts that represent a partial view of the event or reality. Further subdividing these sub-levels creates sub-sub-level cuts, which are the smallest focused partial view of the event, serving the purpose of zooming. These Level cuts are utilized to construct local aggregation operators for PCTLHSMatrix. And the concept of timelessness is introduced by unifying the time levels of the universe. This means all attributes that exist in various time levels are merged to exist in a unified time called the unified time layer. In this way, the attributes are focused and the layers of time are merged as if there is no time. The particular types of time layers are unified by local operators to introduce the concept of timelessness that is obtained by unifying time levels. Finally, for a precise description of the model, a numerical example is constructed by assuming a classification of various health states with COVID-19 patients in a hospital. [ABSTRACT FROM AUTHOR]

This article aims to introduce some modern algebraic structures as hyper super matrices. The classical algebra and matrices cannot process higher-dimensional information with several levels of ambiguity and uncertainty. Hence, it is necessary to establish such superalgebraic structures that can organize and classify the uncertain and incomplete information floating in parallel higher dimensions as facts, events, or realities. To achieve the desired goal, a particular construction of Hypersoft Matrix (HS-Matrix) and Subjectively Whole Hyper-SuperSoft Matrix (SWHSS-Matrix) is offered in a plithogenic Fuzzy environment initially, and some aggregation operators are formulated. A Local-Global-Universal Combined Consciousness State Ranking Model is formulated as an application. As the classification of non-physical phenomena like state of physical health or Consciousness has not yet been addressed in the area of decision making therefor the proposed model will open a new dimension of classification of the non-physical part of the universe in which one can select the most suitable possible reality from several parallel realities which would be useful in the field of artificial intelligence. This model classifies the accumulated states of matter bodies (subjects). And gives a possible description of the Combined-Consciousness State of a Universe. In addition, it offers a local ranking by observing the information through several angles of vision, just like a human mind does, and a universal ranking by classifying the accumulated states. Furthermore, the final Global Ranking is achieved by constructing a percentage frequency-matrix and an authenticity measure of the order is offered. A numerical example is constructed to describe SWHSS-Matrix and LGU-Ranking Model. Some pie graphs are used to describe the individual states, accumulated states, and the ultimate accumulated universal state of all given subjects (a Combined Conscious State of Universe). [ABSTRACT FROM AUTHOR]

Neutrosophic vague hypersoft set (nVHs-set) is a novel hybrid model that is projected to address the limitations of existing fuzzy vague set-like structures for degree of indeterminacy and multi argument approximate function. This function maps the cartesian product of disjoint attribute valued sets to power set of initial universe. This study aims to characterize nVHs-set to tackle uncertainties more efficiently. Some essential properties and set-theoretic cum aggregation operations of nVHs-set are characterized by employing axiomatic and analytical approaches respectively and explained with the help of suitable examples. An algorithm is proposed based on aggregations of nVHs-set for dealing real-world decision-making issues and problems. The proposed algorithm is validated by its implementation in real-world decision-making problem for the optimal selection of farmhouse. Moreover advantageous aspects of proposed model are assessed with the help of evaluating features through comparison analysis. [ABSTRACT FROM AUTHOR]

Soft set-like models deal with single argument approximate functions while hypersoft set, an extension of the soft set, deals with multi-argument approximate functions. The soft set cannot handle situations when attributes are required to be further divided into disjoint attribute-valued sets. To overcome this situation, a hypersoft set has been developed. In different fields like decision making and medical diagnosis, many researchers developed models based on the soft set for the solution of many problems. But these models deal with only one expert who creates many problems for the users, primarily in designing questionnaires. To remove this discrepancy, we present a neutrosophic hypersoft expert set. This model not only solves the problem of dealing with one expert but also solves the problem of different parametric-valued sets parallel to different characteristics. In this study, we first introduce the concept of neutrosophic hypersoft expert sets, which is a amalgam of both structures i.e., neutrosophic set and hypersoft expert sets. Certain essential basic characteristics (i.e., subset, equal set, agree, disagree set, null set, whole relative set, and whole absolute set), aggregation operations (i.e., complement, restricted union, extended intersection, AND and OR ), and results (i.e., idempotent, absorption, domination, identity, commutative, associative and distributive law) are discussed with examples. Some hybrid structures of the neutrosophic hypersoft expert set are developed with illustrated examples. In the end, a decision-making application is presented for the validity of the proposed theory. [ABSTRACT FROM AUTHOR]

In computational intelligence, machine learning, image processing, neural networks, medical diagnostics, and decision analysis, the ideas of correlation coefficients and entropy have practical applications. By applying hypersoft set (HSS) in neutrosophic environment provides a good model for describing and addressing uncertainties. In statistics, the correlation coefficient between two variables is crucial. Furthermore, the accuracy of the correlation assessment is dependent on data from the discourse set. The main focus of this study, is to develop entropy for (NHSS) and generalized correlation coefficient interval-valued neutrosophic hypersoft-set (IVNHSS). We proposed some theorems on entropy along with algorithms based on correlation and weighted correlation coefficients in the context of NHSs and IVNHSS. The validity and superiority are presented along with application and also comparison is made with existing approaches. [ABSTRACT FROM AUTHOR]

Hypersoft set is an emerging knowledge of study which is projected to address the limitations of soft set for the entitlement of multi-argument approximate function. This function maps sub-parametric tuples to power set of universe. It emphasizes the partitioning of each attribute into its respective attribute-valued set that is missing in existing soft set-like structures. These features make it a completely new mathematical tool for solving problems dealing with uncertainties. In this study, classical concept of weak structures (W-structures) is characterized under hypersoft set environment which will provide a conceptual framework for further characterization of respective topological spaces and other spaces of functional analysis. Some of its important properties and results are investigated. Moreover, new notions of hypersoft weak axioms W-τ0, W-τ1 and W-τ2 are discussed with illustrative examples. [ABSTRACT FROM AUTHOR]

Hypersoft set, an extension of soft set, is more flexible and useful as it tackles the limitation of soft set for dealing with scenarios where distinct attributes are further classified into disjoint attribute-valued sets. It replaces single-argument approximate function of soft set with multi-argument approximate function. The main goal of this research is to align existing literature on single-valued neutrosophic fuzzy soft sets with the need for such a multi-argument function. Firstly, the novel notions of single-valued neutrosophic fuzzy hypersoft sets are characterized. Some of its essential basic properties and set theoretic operations are discussed with illustrated numerical examples. Secondly, fuzzy decision-making algorithm based on single-valued neutrosophic fuzzy hypersoft set matrix is proposed. Explicatory application is presented which depicts the structural validity of proposed structure for successful application to the problems involving vagueness and uncertainties. Lastly, a comparison of the proposed structure with existing structures, is made under appropriate indicators. [ABSTRACT FROM AUTHOR]

Soft set deals with single set of attributes whereas its generalization i.e. hypersoft set deals with multiple disjoint attribute-valued sets corresponding to distinct attributes. In this paper, we first introduced the concept of single valued neutrosophic hypersoft expert sets (SVNHESs) which combines single valued neutrosophic sets and hypersoft expert sets. Some fundamental properties (i.e. subset, not set and equal set), results (i.e. commutative, associative, distributive and D' Morgan Laws) and set-theoretic operations (i.e. complement, union intersection AND, and OR ) are discussed. An algorithm is proposed to solve decisionmaking problems and applied to select the best product. [ABSTRACT FROM AUTHOR]

Neutrosophic hypersoft set is the combination of neutrosophic set and hypersoft set. It resolves the limitations of intuitionistic fuzzy sets and soft sets for the consideration of the degree of indeterminacy and multi-argument approximate function respectively. In this research article, a novel framework i.e. neutrosophic hypersoft graph, is formulated for handling neutrosophic hypersoft information by combining the concept of neutrosophic hypersoft sets with graph theory. Firstly, some of essential and fundamental notions of neutrosophic hypersoft graph are characterized with the help of numerical examples and graphical representation. Secondly, some set theoretic operations i.e. union, intersection and complement, are investigated with illustrative examples and pictorial depiction. [ABSTRACT FROM AUTHOR]

Mapping is a fundamental mathematical concept that is used in many elementary areas of science and mathematics and has numerous applications. The core purpose of this study is to provide a theoretical and analytical approach for carving out a basic structure of composite mappings on the classes of Fuzzy Hypersoft (FHS) sets. It is a comprehensive study of existing concepts regarding mappings on fuzzy soft, soft and hesitant fuzzy soft classes through characterizing of composite mappings on FHS classes. Moreover, certain generalized properties of mappings on FHS classes like FHS images and FHS inverse images, are established. Some related results are verified with the help of illustrative examples. [ABSTRACT FROM AUTHOR]

The main objective of this study is to introduce the notion of plithogenic neutrosophic hypersoft almost topological group. We have defined some new concepts and investigated properties of regularly open set and regularly closed set and then we observed the definitions of plithogenic neutrosophic hypersoft closed mapping, open mapping and finally we have defined the definition of plithogenic neutrosophic hypersoft almost continuous mapping. By observing the definition of plithogenic neutrosophic hypersoft almost continuous mapping we have studied neutrosophic hypersoft topological group and plithogenic neutrosophic hypersoft almost topological group and some of their properties. [ABSTRACT FROM AUTHOR]

Many researchers have created some models based on soft set, to solve problems in decision making and medical diagnosis, but most of these models deal only with one expert. This causes a problem with the users, especially with those who use questionnaires in their work and studies. Therefore we present a new model i.e. Hyper soft Expert Set which not only addresses this limitation of soft-like models by emphasizing the opinion of all experts but also resolves the inadequacy of soft set for disjoint attribute-valued sets corresponding to distinct attributes. In this study, the existing concept of soft expert set is generalized to hyper soft expert set which is more flexible and useful. Some fundamental properties (i.e. subset, not set and equal set), results (i.e. commutative, associative, distributive and D' Morgan Laws) and set-theoretic operations (i.e. complement, union intersection AND, and OR ) are discussed. An algorithm is proposed to solve decision-making problems and applied to recruitment process for hiring "right person for the right job". [ABSTRACT FROM AUTHOR]

Hypersoft set is the generalization of soft set as it converts single attribute function to multiattribute function. The core purpose of this study is to make the existing literature regarding neutrosophic parameterized soft set in line with the need of multi-attribute function. We first conceptualize the neutrosophic parameterized hypersoft set along with some of its elementary properties and operations. Then we propose decision making based algorithm with the help of this theory. Moreover, an illustrative example is presented which depicts its validity for successful application to the problems involving vagueness and uncertainties. [ABSTRACT FROM AUTHOR]

Multi-criteria decision-making (MCDM) focuses on coordination, choice and planning issues, including multi-criteria. the neutrosophic soft set cannot handle environments involving multiple attributes. In order to overcome these obstacles, the neutrosophic hypersoft set (NHSS) and Interval Value neutrosophic hypersoft set (IVNHSS) are defined. In this paper, we extend the concept of IVNHSS with basic properties. We also developed some basic operations on IVNHSS such as union, intersection, addition, difference, Truth-favorite, and False-favorite, etc. with their desirable properties. Finally, the necessity and possibility operations on IVNHSS with properties are presented in the following research. [ABSTRACT FROM AUTHOR]

The complex fuzzy soft set and its generalized hybrids are such effective structures which not only minimize the impediments of all complex fuzzy-like structures for dealing uncertainties but also fulfill all the parametric requirements of soft sets. This feature makes it a completely new mathematical tool for solving problems dealing with uncertainties. Smarandache conceptualized hypersoft set as a generalization of soft set as it transforms the single attribute function into a multi-attribute function. This generalization demands an extension of complex fuzzy soft-like structures to hypersoft structure for more precise results. In this study, hybrids of hypersoft set with complex fuzzy set and its generalized structures i.e. complex intuitionistic fuzzy set and complex neutrosophic set, are developed along with illustrative examples to address the demand of literature. Moreover, some of their fundamentals i.e. subset, equal sets, null set, absolute set etc. and theoretic operations i.e. compliment, union, intersection etc. are discussed. [ABSTRACT FROM AUTHOR]

Convexity plays an imperative role in optimization, pattern classification and recognition, image processing and many other relating topics in different fields of mathematical sciences like operation research, numerical analysis etc. The concept of soft sets was first formulated by Molodtsov as a completely new mathematical tool for solving problems dealing with uncertainties. Smarandache conceptualized hypersoft set as a generalization of soft set (hS, E) as it transforms the function hS into a multi-attribute function hHS. Deli introduced the concept of convexity cum concavity on soft sets to cover above topics under uncertain scenario. In this study, a theoretic and analytical approach is employed to develop a conceptual framework of convexity cum concavity on hypersoft set which is generalized and more effective concept to deal with optimization relating problems. Moreover, some generalized properties like δ-inclusion, intersection and union, are established. The novelty of this work is maintained with the help of illustrative examples and pictorial version first time in literature. [ABSTRACT FROM AUTHOR]

In real life, most of the problems occurred by wrong decision making, while in sports it is mandatory for every player, coach, and technique director to make a good and an ideal decision. In this paper, the concept of similarity measure is used in the neutrosophic environment for decision making in a football game for the selection of players. The data is collected in interval-valued, while the new concept m-polar is illustrated as previous records of m matches played by players. m-polar structures provide multiple data on the concerned problem, so as a result the best solution can be developed for the selection problem. An m-polar Intervalvalued Neutrosophic Set (mIVNS) is derived for the targeted task of player selection problem. Then some operations, properties, and distance measures are introduced on m-polar Interval-valued Neutrosophic Set (mIVNS). Distance-base Similarity Measure is illustrated to each player with an ideal set in mIVNS structure. In the end, the Algorithm is given for ideal decision-making in sports for the selection of players. [ABSTRACT FROM AUTHOR]

Multi-criteria decision making (MCDM) is the technique of selecting the best alternative from multiple alternatives and multiple conditions. The technique for order preference by similarity to an ideal solution (TOPSIS) is a crucial practical technique for ranking and selecting different options by using a distance measure. In this article, we protract the fuzzy TOPSIS technique to neutrosophic fuzzy TOPSIS, and prove the accuracy of the method by explaining the MCDM problem with single-value neutrosophic information, and use the method for supplier selection in the production industry. We hope that this article will promote future scientific research on numerous existence issues based on multi-criteria decision making. [ABSTRACT FROM AUTHOR]

A Similarity measure for Neutrosophic function performs a fundamental role in tackling the prob- lems that include blurred and hazed information but is not able to handle the fuzziness and vagueness of the problems which have numerous information. The objective of this research paper is to generalize neutrosophic soft set to the multi-polar neutrosophic soft set (mNS set), aggregation operators and their properties on mNS sets. It also discusses the distance-based similarity measures that rely on between two mNS sets. It explains with the help of examples that the intended similarity measures of mNS sets are applicable in the field of med- ical diagnosis and decision-making problem for selection of lecturer in universities. Eventually, this proposed method is concluded as an algorithm in the application. [ABSTRACT FROM AUTHOR]

In this paper, we present a single-valued Neutrosophic Hypersoft set, multi-valued Neutrosophic Hypersoft set and tangent similarity measure for single-valued neutrosophic hypersoft sets and its properties. Then we use this technique in an application namely selection of cricket players for different types of matches (ODI, T20, and test) based on Neutrosophic Hypersoft set in decision making of single-valued neutrosophic hypersoft sets. This technique will help us to decide the best option for the players. [ABSTRACT FROM AUTHOR]

Multi-criteria decision making (MCDM) is concerned about organizing and taking care of choice and planning issues including multi-criteria. When attributes are more than one, and further bifurcated, neutrosophic softset environment cannot be used to tackle such type of issues. Therefore, there was a dire need to define a new approach to solve such type of problems, So, for this purpose a new environment namely, Neutrosophic Hypersoft set (NHSS) is defined. This paper includes basics operator's like union, intersection, complement, subset, null set, equal set etc., of Neutrosophic Hypersoft set (NHSS). The validity and the implementation are presented along with suitable examples. For more precision and accuracy, in future, proposed operations will play a vital role is decision-makings like personal selection, management problems and many others. [ABSTRACT FROM AUTHOR]

In this paper, initially a matrix representation of Plithogenic Hypersoft Set (PHSS) is introduced and then with the help of this matrix some local operators for Plithogenic Fuzzy Hypersoft set (PFHSS) are developed. These local operators are used to generalize PFHSS to Plithogenic Fuzzy Whole Hypersoft set (PFWHSS). The generalized PFWHSS set is hybridization of Fuzzy Hypersoft set (which represent multiattributes and their subattributes as a combined whole membership i.e. case of having an exterior view of the event) and the Plithogenic Fuzzy Hypersoft set (in which multi attributes and their subattributes are represented with individual memberships case of having interior view). Thus, the speciality of PFWHSS is its presentation of an exterior and interior view of a situation simultaneously. Later, the PFWHSS is employed in development of multi attributes decision making scheme named as Frequency Matrix Multi Attributes Decision making scheme (FMMADMS). This innovative technique is not only simpler than any of the former MADM techniques, but also has a unique capability of dealing mathematically a variety of human mind psychologies at every level that are working in different environments (fuzzy, intuitionistic, neutrosophic, plithogenic). Besides, FMMADMS also provides the percentage authenticity of the final ranking which in itself is a new idea providing a transparent and unbiased ranking. Moreover, the new introduced idea of frequency matrix handles the ranking ties in the best possible way and has an ability to provide the authenticity comparative analysis of previously developed schemes. Lastly, application of this FMMADMS is described as a numerical example for a case of ranking and selecting the best alternative. [ABSTRACT FROM AUTHOR]

The purpose of MCDM is to determine the best option amongst all the probable options. Due to linguistic assessments, the traditional crisp techniques are not good to solve MCDM problems. This paper deals with the generalization of TOPSIS for neutrosophic hypersoft set primarily based issues explained in section 3. In section 4, the proposed technique is implemented. The proposed technique is easy to implement, and precise and sensible for fixing the MCDM problem with multiple-valued neutrosophic data. In the end, the applicability of the developed method, the problem of parking on which decision maker has normally vague and imprecise knowledge is used. It seems that the outcomes of these examinations are terrific. [ABSTRACT FROM AUTHOR]