Soft Multiset Research Articles

Generalized Soft Multi Functions

Objectives: To acquaint generalized soft multi functions and graphs. Methods: Generalized semi soft multi sets was introduced using semi closure operators and open soft multi sets. As a consequence, this study acquaints generalized semi soft multi continuous functions with the help of generalized semi soft multi sets. Also the concept of generalized soft multi homeomorphisms are introduced via generalized semi soft multi continuous, open and closed mappings and also the thought of closed soft multi graph is introduced through the open soft multi sets and soft multi points. Findings: This study reveals that composition of two generalized semi soft multi continuous functions do not necessarily generalized semi soft multi continuous but composition of generalized semi soft multi continuous function with any of its stronger forms be a generalized semi soft multi continuous function and also several interesting results are found. Novelty: This study acquaints soft multi graph by using soft multi functions and also acquaint generalized semi closed soft multi graph. Keywords: Generalized Semi Soft Multi Continuous Functions, Generalized Semi Soft Multi Open Functions, Generalized Semi Soft Multi Closed Functions, Generalized Semi Soft Multi Homeomorphisms And Generalized Semi Closed Soft Multi Graphs

An innovative algorithm based on weighted fuzzy soft multisets and its application in selecting optimal construction materials

<p>Effective decision-making is critical across various domains, including technology, medicine, and engineering. To address the complexities of decision-making, particularly in scenarios involving both positive and negative parameters, this paper introduces an innovative algorithm based on weighted fuzzy soft multisets. This algorithm mitigates the issue of counterintuitive results often encountered in existing methods. By incorporating the concept of uniform fuzzy soft multisets and considering the conditional structure of these sets, our approach advances the theoretical framework of decision-making while providing a practical tool for complex scenarios. To demonstrate its practical applicability, we conduct a case study focused on selecting optimal construction materials for a building project, utilizing data from established engineering standards and a comprehensive wood properties database. The key findings of our sensitivity analysis highlight the algorithm's robustness to weight changes and adaptability to different decision sequences. These findings highlight the algorithm's potential to enhance decision support systems across various fields, such as engineering, healthcare, and environmental management. This potential is particularly valuable in complex, multi-criteria scenarios that demand nuanced, context-aware solutions.</p>

Obesity treatment applying effective fuzzy soft multiset-based decision-making process

<p>Nowadays, obesity is recognized as a worldwide epidemic that has become a major cause of death and comorbidities. Recommending appropriate treatment is critical in the global health environment. For obesity treatment to be effective, the person must be able to follow a specific diet that meets his needs so that he can follow it for a long time or forever to maintain fitness. This research aims to determine the best diet among the trusted diets for every person based on his needs and circumstances. This occurs when applying a decision-making technique based on the effective fuzzy soft multiset concept. For this purpose, the definition of the effective fuzzy soft multiset as well as its types, operations, and properties are introduced. Furthermore, a decision-making method is proposed based on the effective fuzzy soft multiset environment. Using matrices operations, one can easily apply the decision-making process based on this new extension of sets to choose the optimal diet for everyone. Finally, an extensive comparative analysis of the previous methods is undertaken and also summarized in a chart to attract focus on the benefits of the suggested algorithm and to demonstrate how they differ from the current one.</p>

Some Types of Neutrosophic Filters in Basic Logic Algebras


 The purpose of this article is to study the neutrosophication of prime and Boolean filters in Basic Logic (BL) algebras. We establish the notions of the neutrosophic prime and Boolean filters of BL-algebras with suitable examples and examine a few of their properties. As a result, we can determine the necessary and sufficient conditions and extension properties of both the neutrosophic prime and Boolean filters of BL-algebras. In addition, by combining both filters we instigate the concept of the neutrosophic prime Boolean filter of BL-algebras with illustration. In the future, the above study can be extended to soft multiset. Moreover, these filters can be applied to various digital image processing techniques.

METRICS AND METRIC SPACES OF SOFT MULTISETS

The theory of Soft set found applications in so many fields including multiset theory to obtain soft multisets. These theories together with some of their properties were presented. Moreover, considering the various applications of metric spaces in various fields; Metrics and metric spaces of soft multisets with some of their attributes were introduced. However, it was discovered that only pseudo-metric spaces could favorably be formulated. Moreover, soft multiset ordering was also presented.

Weighted neutrosophic soft multiset and its application to decision making

In this paper, we procure the idea of weighted neutrosophic soft multiset (WNSMS) as a generalization of neutrosophic soft multiset (NSMS) and its basic properties are to be showed. Besides, we present a new adjustable approach to WNSMS based on decision-making, for solving decision-making in an indeterminacy situation.

Einstein-operations on fuzzy soft multi sets and decision making

In this paper, we define Einstein product and Einstein sum of fuzzy soft multi sets (FSM-sets) and using these products, we introduce an adjustable approach to FSM-set based decision-making, for solving decision-making in an uncertain situation. The feasibility of our proposed FSM-set based decision-making procedure in practical application is shown by some numerical examples.

Soft multi-rough set topology with applications to multi-criteria decision-making problems

Rough set theory introduced by Pawlak (Int J Comput Inf Sci 11:341–356, 1982), multi-set theory proposed by Blizard (Notre Dame J Form Log 30:36–65, 1989) and soft set theory introduced by Molodtsov (Comput Math Appl 37(4–5):19–31, 1999) are fundamental concepts in computational intelligence, which have a myriad of applications in modeling uncertainties and decision making under uncertainty. In this paper, the idea of soft multi-rough set (SMRS) is introduced as a hybrid model of soft set, multi-set and rough set. The SMRS provides roughness of a multi-set in terms of soft multi-approximation space. The novel concept of soft multi-rough topology (SMR-topology) is defined to discuss topological structure of SMRSs by using pairwise SMR-approximations. The proposed models of SMRS and SMR-topology are suitable for modeling uncertainties in the real-life circumstances. SMR-topology is the generalization of crisp topology, soft topology and soft rough set topology. Some fundamental properties of SMR-topology and their related results are studied. Some algorithms for are developed for multi-criteria decision making based on soft multi-sets, soft multi-rough sets and soft multi-rough topology. Based on proposed algorithms, the applications of SMRSs and SMR-topology toward diagnosis of depression and diabetes are illustrated by the numerical examples. A comparison analysis of proposed methods with some existing methods is also given to justify their reliability, feasibility and flexibility.

Certain properties of soft multi-set topology with applications in multi-criteria decision making

The aim of this paper is to introduce the notion of soft multi-set topology (SMS-topology) defined on a soft multi-set (SMS). Soft multi-set and soft multi-set topology are fundamental tools in computational intelligence, which have a large number of applications in soft computing, fuzzy modeling and decision-making under uncertainty. The idea of power whole multi-subsets of a SMS is defined to explore various rudimentary properties of SMS-topology. Certain properties of SMS-topology like SMS-basis, MS-subspace, SMS-interior, SMS-closure and boundary of SMS are explored. Furthermore, the multi-criteria decision-making (MCDM) algorithms with aggregation operators based on SMS-topology are established. Algorithm i (i = 1, 2, 3) are developed for the selection of best alternative for biopesticides, for the selection of best textile company, for the award of performance, respectively. Some real life applications of the proposed algorithms in MCDM problems are illustrated by numerical examples. The the reliability and feasibility of proposed MCDM techniques is shown by comparison analysis with some existing techniques.

Mappings and Connectedness on Hesitant Fuzzy Soft Multispaces

In this paper, we introduce the concept of mapping on hesitant fuzzy soft multisets and present some results for this type of mappings. The notions of inverse image and identity mapping are defined, and their basic properties are investigated. Hence, kinds of mappings and the composition of two hesitant fuzzy soft multimapping with the same dimension are presented. The concept of hesitant fuzzy soft multitopology is defined, and certain types of hesitant fuzzy soft multimapping such as continuity, open, closed, and homeomorphism are presented in detail. Also, their properties and results are studied. In addition, the concept of hesitant fuzzy soft multiconnected spaces is introduced.

On Fuzzy Soft Multi Set and Its Application in Information Systems

On Fuzzy Soft Multi Set and Its Application in Information Systems

Fuzzy soft matrices on fuzzy soft multiset and its applications in optimization problems

Fuzzy soft matrices on fuzzy soft multiset and its applications in optimization problems

An application of fuzzy soft multisets to algebra

In this paper, notions of multi and soft multi LA-?-semigroup are defined. Some generalizations of certain operations on the families of the soft and fuzzy soft multisets are introduced. A concept of fuzzy multi LA-?-semigroup is presented. The concept of fuzzy soft multisets is applied to L?-?-semigroups and various characteristics of these all structures defined on LA-?-semigroups are investigated. Some properties of generalized operations on multi soft and fuzzy multi soft LA-?-semigroups are studied.

Hesitant fuzzy soft multisets and their applications in decision-making problems

In this paper, we introduce some important and basic issues of hesitant fuzzy soft multisets and present some results for hesitant fuzzy sets. The main results of the current branch are studied, and some of its structural properties are established such as the neighborhood hesitant fuzzy soft multisets, interior hesitant fuzzy soft multisets, hesitant fuzzy soft multi-topological spaces and hesitant fuzzy soft multi-basis. Therefore, we show that how to apply the concept of hesitant fuzzy soft multisets in decision-making problems.

Intuitionistic Fuzzy Soft Multisets Theory

Soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. Soft multiset and fuzzy soft multiset are generalization concepts obtained from soft set theory. As a generlazation of fuzzy soft multiset we introduce the definition of intuitionistic fuzzy soft multiset and its operations and study some of their properties. Finally, we give an application in decision making problems.

An adjustable approach to hesitant fuzzy soft multiset based decision making problems

An adjustable approach to hesitant fuzzy soft multiset based decision making problems

Neutrosophic vague soft multiset for decision under uncertainty

The notion of classical soft multisets is extended to neutrosophic vague soft multisets by applying the theory of soft multisets to neutrosophic vague sets to be more effective and useful. We also define its basic operations, namely complement,subset, union, intersection along with illustrative examples, and study some related properties with supporting proofs. Lastly, this notion is applied to a decision making problem and its effectiveness is demonstrated using an illustrative example.

The use of soft matrices on soft multisets and their applications in optimal decision process

In this paper, we introduce a concept of a soft matrix on a soft multiset, and investigate how to use soft matrices to solve decision making problems. An algorithm for a multiple choose selection problem is also provided. Finally, we demonstrate an illustrative example to show the decision making steps.

Soft multi generalized regular sets in soft multi topological spaces

Many researchers have identified some of the basic concepts in soft multi topology and many properties were investigated. The main objective of this study is to provide and study a new class of soft multi closed sets like soft multi generalized regular closed (briefly soft mgr-closed) set and to investigated some of its basic properties in soft multi topological spaces. Furthermore, soft multi α-closed set, soft multi pre-closed set, soft multi semi-closed set, soft multi b-closed set and soft multi β-closed set in soft topological spaces are defined.We show that every soft multi regular closed set is soft multi generalized regular closed set.

Weighted fuzzy soft multiset and decision-making

Fuzzy soft multiset (FSMS) is a substantial and important fuzzy generalization of soft set and multiset (also called bag). In this paper, we have presented the idea of weighted fuzzy soft multiset (WFSMS) as a generalization of FSMS and its basic properties are to be studied. Also, we introduce a new adjustable approach to WFSMS based decision-making, for solving decision-making in an uncertain situation. The feasibility of our proposed WFSMS based decision-making procedure in practical application is read by a mathematical example.