N-soft Sets Research Articles

APLIKASI DARI N-SOFT SET PADA DATA DENGAN OBJEK BERKELOMPOK

In this paper, an application of N-soft set on data with grouped objects will be presented using the construction concept in strait soft set theory to solve a problem in the decision-making process. For each parameter, a weight value will be determined, and from this data, a threshold will be set in such a way that a T-level soft set form is possible. This research is a descriptive qualitative study with a case study approach. An interesting result from this study is that an object with the lowest rank can have the highest rank in a certain group of objects

N-SOFT SETS ASSOCIATION RULE AND ITS APPLICATION FOR PROMOTION STRATEGY IN DISTANCE EDUCATION

In everyday life, we always encounter obstacles in seeing the interrelationships between several events to make the right decisions. Universitas Terbuka is a pioneer in distance education that implements digital transformation for new student registration, student services, and alums. The obstacle faced is determining a suitable promotion strategy for new students. As a result, a representative model is needed to handle such cases. As an extension of soft sets, N-soft sets can handle decision-making for binary and non-binary assessments. However, research has yet to be related to N-soft sets decision-making in data mining, especially association rule classification. This article proposes a new combination of N-soft sets with Association Rule (NSSAR). This article also introduces and applies the decision-making procedure using NSSAR to real. The population is new students of Universitas Terbuka Jakarta in the 2023/2024 odd semester. Samples were taken randomly using a questionnaire—primary data obtained by 201 new students. The following results are obtained based on the processed sample data using the NSSAR algorithm: 1) new students from Universitas Terbuka Jakarta are predominantly from Vocational High Schools domiciled in Bekasi, majoring in Bachelor of Management from the Faculty of Economics and Business; 2) The most favorite media information used by new UT Jakarta students is Instagram. Based on the results, the NSSAR algorithm gave relationship patterns between the number of new students based on region, study program, diploma of origin, and information media. Therefore, policymakers should consider the right promotional strategy to increase the number of students.

Multi-attribute decision-making analysis based on the bipolar N-soft PROMETHEE method

The multi-attribute decision-making (MADM) methods can deeply mine hidden information in data and make a more reliable decision with actual needs and human cognition. For this reason, this paper proposes the bipolar N-soft PROMETHEE (preference ranking organization method for enrichment of evaluation) method. The method fully embodies the advantages of the PROMETHEE method, which can limit the unconditional compensation between attribute values and effectively reflect the priority between attribute values. Further, by introducing an attribute threshold to filter research objects, the proposed method not only dramatically reduces the amount of computation but also considers the impact of the size of the attribute value itself on decision-making. Secondly, the paper proposes the concepts of attribute praise, attribute popularity, total praise, and total popularity for the first time, fully mining information from bipolar N-soft sets, which can effectively handle situations where attribute values have different orders of magnitude. In addition, this paper presents the decision-making process of the new method, closely integrating theoretical models with real life. Finally, this paper analyses and compares the proposed method with the existing ones, further verifying the effectiveness and flexibility of the proposed method.

Aggregation operators on group-based generalized q-rung orthopair fuzzy N-soft sets and applications in solar panel evaluation

Every problem in decision-making has a solution when the information that is available is properly and precisely modeled. This study focuses on non-binary data from N-soft sets and q-rung orthopair fuzzy values, referred to as group-based generalized q-rung orthopair fuzzy N-soft sets (GGq-ROFNSSs). The GGq-ROFNSSs model provides information simultaneously on numerous competing criteria, alternatives, sub-alternatives, and data summarization. We introduce properties of GGq-ROFNSSs such as distinct inclusion features of GGq-ROFNSSs, weak complements of the GGq-ROFNSS, top weak complements the GGq-ROFNSS, bottom weak complements the GGq-ROFNSS. We provide the notion of GGq-ROFNSWA and GGq-ROFNSWG operators as well as their idempotency, monotonicity, and boundedness features. The notion of GGq-ROFNSSs requires a sound methodology of multiple criteria decision making (MCDM) since GGq-ROFNSS combines numerous elements of complex decision-making. We provide a MCDM methodology for the GGq-ROFNSWA and GGq-ROFNSWG operators and depict it in a flowchart. The selection of solar panels for a city is a difficult procedure because it depends on several components such as environment, where the area is located, what kinds of needs are being met, etc. We find a solution to the problem of selecting a suitable solar panel for a city with their underlying characteristics. Finally, we provide a comparison of the suggested method with other techniques to demonstrate its advantages.

A systematic literature review of soft set theory

AbstractSoft set theory, initially introduced through the seminal article “Soft set theory—First results” in 1999, has gained considerable attention in the field of mathematical modeling and decision-making. Despite its growing prominence, a comprehensive survey of soft set theory, encompassing its foundational concepts, developments, and applications, is notably absent in the existing literature. We aim to bridge this gap. This survey delves into the basic elements of the theory, including the notion of a soft set, the operations on soft sets, and their semantic interpretations. It describes various generalizations and modifications of soft set theory, such as N-soft sets, fuzzy soft sets, and bipolar soft sets, highlighting their specific characteristics. Furthermore, this work outlines the fundamentals of various extensions of mathematical structures from the perspective of soft set theory. Particularly, we present basic results of soft topology and other algebraic structures such as soft algebras and $$\sigma$$ σ -algebras. This article examines a selection of notable applications of soft set theory in different fields, including medicine and economics, underscoring its versatile nature. The survey concludes with a discussion on the challenges and future directions in soft set theory, emphasizing the need for further research to enhance its theoretical foundations and broaden its practical applications. Overall, this survey of soft set theory serves as a valuable resource for practitioners, researchers, and students interested in understanding and utilizing this flexible mathematical framework for tackling uncertainty in decision-making processes.

A novel approach to fuzzy N-soft sets and its application for identifying and sanctioning cyber harassment on social media platforms

This study proposes a novel approach to fuzzy N-soft sets for handling cases where membership degree and grade are not related. In the standard model of fuzzy N-soft sets, membership degree and grade are assumed to be directly proportional. This assumption may not hold true in real-world situations, so a more flexible and nuanced approach is necessary. The proposed approach includes two novel algorithms for decision-making problems involving fuzzy N-soft sets. As a result, it is able to be adaptable and sensitive when addressing uncertainties in real-world scenarios, with a particular focus on identifying and sanctioning cyber harassment on social media platforms. Additionally, an innovative perspective and approach to decision-making problems involving fuzzy N-soft sets is introduced by extending an established selection process that prioritizes the dominant parameter, resulting in more precise and dependable outcomes. Our study offers an effective tool for decision-making in various fields, including e-commerce, social media, and product reviews.

Identification of mental disorders in South Africa using complex probabilistic hesitant fuzzy N-soft aggregation information

This paper aims to address the challenges faced by medical professionals in identifying mental disorders. These mental health issues are an increasing public health concern, and middle-income nations like South Africa are negatively impacted. Mental health issues pose a substantial public health concern in South Africa, putting forth extensive impacts on both individuals and society broadly. Insufficient funding for mental health remains the greatest barrier in this country. In order to meet the diverse and complex requirements of patients effective decision making in the treatment of mental disorders is crucial. For this purpose, we introduced the novel concept of the complex probabilistic hesitant fuzzy N-soft set (CPHFNSS) for modeling the unpredictability and uncertainty effectively. Our approach improves the precision with which certain traits connected to different types of mental conditions are recognized by using the competence of experts. We developed the fundamental operations (like extended and restricted intersection, extended and restricted union, weak, top, and bottom weak complements) with examples. We also developed the aggregation operators and their many features, along with their proofs and theorems, for CPHFNSS. By implementing these operators in the aggregation process, one could choose a combination of characteristics. Further, we introduced the novel score function, which is used to determine the optimal choice among them. In addition, we created an algorithm with numerical illustrations for decision making in which physicians employ CPHFNS data to diagnose a specific condition. Finally, comparative analyses confirm the practicability and efficacy of the technique that arises from the model developed in this paper.

Analysis of Buying Decision Making in the Non-Subsidized Fuel Market in Indonesia Using a Soft Sets Approach

The non-subsidized fuel market in Indonesia is very unique, because many world players who are successful in their own countries and successful in other countries fail in Indonesia. One example is that Petronas, which was successful in Malaysia and other Asean countries, has failed in Indonesia. An interesting phenomenon is that BP, in its marketing, cooperates with local player AKR in marketing its products against Pertamina's heavy players. This article will analyze consumers' buying decisions for non-subsidized fuel based on N-Soft Sets, where the object to be analyzed is in the form of non-subsidized fuel brands in Indonesia with the parameters measured being price, quality, location, brand and loyalty. The algorithm that will be used is the Extended Weight Choice Values Algorithm with a single decision type, namely the decision to buy non-subsidized fuel. Weighting of the parameters will be given according to the hierarchy of needs in Maslow's Hierarchy theory, starting from the lowest are physiological needs, security needs, social needs, ego needs and self-actualization needs as the highest level, and Marketing Mix Theory. By implementing N-Soft Sets, it can overcome problems in decision making both in binary and non-binary form so that decision making can be determined in the form of numbers, words or symbols and other forms. A deeper discussion regarding the decision to purchase non-subsidized fuel markets will be able to provide a reference for how consumers choose products for unique markets so that they can be used as a reference when entering a unique market.

Group decision-making methods based on probabilistic hesitant N-soft sets

In this paper, we introduce a new hybrid model called probabilistic hesitant N-soft sets by a suitable combination of probability with hesitant N-soft sets, a model that extends hesitant N-soft sets. Our novel concept extends the ability of hesitant N-soft set by considering the occurrence probability of hesitant grades, which could effectively avoid the loss of decision-making information. Moreover, we investigate some basic properties of probabilistic hesitant N-soft sets and construct fundamental operations on them. Then we describe group decision-making methods including TOPSIS, VIKOR, choice value and weighted choice value based on probabilistic hesitant N-soft sets. The corresponding algorithms are put forward and their validity is proved by examples.

A novel methodology for multi-agent decision-making based on N-soft sets

AbstractMulti-criteria decision analysis with multiple agents provides tools for the research and development of intelligent applications. The solution strategy depends largely on the structure of the data. In this paper we propose a decide-then-merge approach to the problem of multi-agent multi-criteria decision-making when each individual data comes in the form of an N-soft set. To this purpose, we present a methodology that works in two steps. First, with each individual input we associate a ranking. This can be done in several ways, since individual decisions based on N-soft sets are well developed. Then with the help of voting theory, we merge all these rankings and produce a final ranking of the alternatives. The steps of this method are explained with synthetic examples. We argue that the proposed strategy is highly adaptable because both stages of our scheme can be customized by the user. A real case study in the framework of Operational Research illustrates the application of this method in detail. Finally, we perform a comparative analysis with existing methodologies.

Early infectious diseases identification based on complex probabilistic hesitant fuzzy N-soft information.

This paper aims to assess and deal with the challenges experienced by medical professionals caring for infectious diseases. In Pakistan, public health is still a serious concern and the main contributor to morbidity and mortality is infectious diseases. The major issue is a resemblance in the clinical symptoms of infectious diseases such as tuberculosis, hepatitis, COVID-19, dengue, and malaria. Early detection of infectious disease is crucial in order to start treatment with counseling and medication. This can only be done if several infections with similar clinical traits can be diagnosed depending on several criteria, including the availability of various kits, the ability to carry out diagnostic procedures, money, and technical staff. But woefully Pakistan's economy is badly battered due to several circumstances. Therefore, we are unable to provide patients with enough diagnostic testing kits and broadly accessible therapy choices, which makes diagnosis more difficult and create hesitancy with fuzziness and randomness. For this purpose, we introduced the new concept of the complex probabilistic hesitant fuzzy N-soft set. We defined its fundamental operations (like restricted and extended union, restricted and extended intersection, weak, top and bottom weak complements, as well as soft max-AND or soft min-OR) with examples. We also discussed their many properties with their proofs and theorems. Furthermore, we developed the algorithms for decision-making where doctors use the complex probabilistic hesitant fuzzy N-soft information to identify a particular disease. Furthermore, we explained numerical illustration of two case studies. Moreover, a sensitive and comparative analysis is discussed. In the last, we conclude the whole study.

Int N-Soft Substructures of Semigroups

The N-soft sets are newly defined structures with many applications in the real world. We aim for combining the semigroup theory and N-soft sets to provide a comprehensive account of the hybrid framework of N-soft Semigroups. In this paper, we define the γ-inclusive set, int N-soft subsemigroups, int N-soft left [right] ideals of S, int N-soft product and int N-soft characteristic function, θ-Generalized int N-soft subsemigroups and θ-Generalized int N-soft left [right] ideals of S. We also discuss some examples and theorems based on the restricted (extended) union, restricted (extended) intersection, and γ-inclusive set.

Decision-Making by Using TOPSIS Techniques in the Framework of Bipolar Complex Intuitionistic Fuzzy N-Soft Sets

Decision-Making by Using TOPSIS Techniques in the Framework of Bipolar Complex Intuitionistic Fuzzy N-Soft Sets

N-Soft Set Approach Methods For More General Cases

The concept of N-soft set has been introduced in previous studies where the concept is a development of fuzzy sets and soft sets. In its application, the concept of the N-soft set can only be done if the data from the case to be solved are in the form of non-negative integers only. However, in everyday life, a case is not always obtained in the form of integers. This article provides an approach where data from non-integer cases can be solved. This matter opens the opportunity for studying a more general concept than N-soft set by theoretical.

Dual Hesitant N-Soft Sets

In this article, we introduce a new hybrid model called Dual Hesitant N-Soft Sets (DHNSS). This new model is clarified and reformulated as a combination of dual and hesitancy with N-soft sets. We investigate the basic operations of DHNSS. Our novel model is illustrated with real life examples. Moreover, we propose the decision making algorithm to see the application of this model.

The semantics of N-soft sets, their applications, and a coda about three-way decision

This paper presents the first detailed analysis of the semantics of N-soft sets. The two benchmark semantics associated with soft sets are perfect fits for N-soft sets. We argue that N-soft sets allow for an utterly new interpretation in logical terms, whereby N-soft sets can be interpreted as a generalized form of incomplete soft sets. Applications include aggregation strategies for these settings. Finally, three-way decision models are designed with both a qualitative and a quantitative character. The first is based on the concepts of V-kernel, V-core and V-support. The second uses an extended form of cardinality that is reminiscent of the idea of scalar sigma-count as a proxy of the cardinality of a fuzzy set.

Q-Rung orthopair fuzzy N-soft aggregation operators and corresponding applications to multiple-attribute group decision making

In this paper, by integrating the q-rung orthopair fuzzy set (q-ROFS) with the N-soft set, we first propose a q-rung orthopair fuzzy N-soft set (q-ROFNSS). Based on the q-ROFNSS, we explore the q-rung orthopair fuzzy N-soft weighted average (q-ROFNSWA) operator and q-rung orthopair fuzzy N-soft weighted geometric (q-ROFNSWG) operator, and investigate some properties of the q-ROFNSWG operator and q-ROFNSWG operator including idempotency, monotonicity and boundedness. Finally, two kinds of multiple-attribute group decision-making (MAGDM) methods based on q-rung orthopair fuzzy N-soft aggregation operators are established. In addition, a practical example is provided to illustrate the effectiveness and correctness of the new decision-making approaches. Through comparison with existing methods, the advantages of our method are also elaborated.

OWA aggregation operators and multi-agent decisions with [formula omitted]-soft sets

This work improves the theoretical basis of N-soft sets and insists on their practical applications in a multi-agent context. N-soft sets characterize the alternatives in terms of multinary descriptions by attributes. We argue that unlike the basic example of soft set theory, N-soft sets are amenable to various interesting approaches in relation to aggregation. However the literature has not provided mechanisms for the aggregation of N-soft sets. And there exists no multi-agent decision making procedure based on N-soft sets either.Therefore, the goal of this work is twofold. We present a novel theory of aggregation of N-soft sets. The fundamental tools for this purpose are OWA operators. We produce the first scores of alternatives defined by multi-agent, multinary evaluations. Then we apply this theory to multi-agent decision-making. In this way we produce the first algorithms for multi-agent decisions based on N-soft sets. We support our findings with real examples that illustrate the application and versatility of these flexible approaches.

Decision-making analysis based on hesitant fuzzy N-soft ELECTRE-I approach

For the formal expression of uncertain data, hesitant fuzzy set theory has established itself as a distinguished model because it has a broad use in multi-attribute decision-making problems. With the incorporation of features from N-soft sets, a useful framework referred to as hesitant fuzzy N-soft sets has acquired an even greater appeal. This model integrates and associates the hesitant environment with information regarding the existence of grades or star ratings. In this research article, we introduce a multi-attribute decision-making technique known as hesitant fuzzy N-soft ELECTRE-I, which computes the decision-maker assessments in an adjustable and formative manner. The proposed method also improves the robustness and accuracy of the decisions relying on grades or star ratings. Thus it lays a bedrock for subsequent analysis and applications. We justify the relevance and convenience of the proposed technique by testing it in actually existing scenarios. Finally, we give a comparison of this novel methodology with the HFNS-TOPSIS method.

FP-intuitionistic multi fuzzy N-soft set and its induced FP-Hesitant N soft set in decision-making

Intuitionistic fuzzy sets (IFSs) can effectively represent and simulate the uncertainty and diversity of judgment information offered by decision-makers (DMs). In comparison to fuzzy sets (FSs), IFSs are highly beneficial for expressing vagueness and uncertainty more accurately. As a result, in this research work, we offer an approach for solving group decision-making problems (GDMPs) with fuzzy parameterized intuitionistic multi fuzzy N-soft set (briefly, FPIMFNSS) of dimension q by introducing its induced fuzzy parameterized hesitant N-soft set (FPHNSS) as an extension of the multi-fuzzy N-soft set (MFNSS) based group decision-making method (GDMM). In this study, we use the proposed GDMM to solve a real-life GDMP involving candidate eligibility for a single vacant position advertised by an IT firm and compare the ranking performances of the proposed GDMM with the Fatimah-Alcantud method.