Multi-fuzzy Soft Set Research Articles

A Progressive Outlook on Possibility Multi-Fuzzy Soft Ordered Semigroups: Theory and Analysis

The concept of possibility fuzzy soft sets is a step in a new direction towards a soft set approach that can be used to solve decision-making issues. In this piece of research, an innovative and comprehensive conceptual framework for possibility multi-fuzzy soft ordered semigroups by making use of the notions that are associated with possibility multi-fuzzy soft sets as well as ordered semigroups is introduced. Possibility multi-fuzzy soft ordered semigroups mark a newly developed theoretical avenue, and the central aim of this paper is to investigate it. The focus lies on investigating this newly developed theoretical direction, with practical examples drawn from decision-making and diagnosis practices to enhance understanding and appeal to researchers’ interests. We strictly build the notions of possibility multi-fuzzy soft left (right) ideals, as well as l-idealistic and r-idealistic possibility multi-fuzzy soft ordered semigroups. Furthermore, various algebraic operations, such as union, intersection, as well as AND and OR operations are derived, while also providing a comprehensive discussion of their properties. To clarify these innovative ideas, the theoretical constructs are further reinforced with a set of demonstrative examples in order to guarantee deep and improved comprehension of the proposed framework.

An enhanced MADM with Lq* q-Rung orthopair multi-fuzzy soft set in healthcare supplier selection

The global healthcare systems have encountered unparalleled difficulties due to the COVID-19 pandemic, underscoring the crucial significance of effective management within healthcare supply chains. This research contributes to the field of healthcare supply chain management by presenting a robust MADM methodology called lattice ordered(Lq*) q-rung orthopair multi-fuzzy soft set(Lq* q-ROMFS-MADM) for supplier evaluation and ranking amidst the challenges posed by the COVID-19 pandemic. Taking inspiration from multi-fuzzy soft set and q-rung orthopair fuzzy set, the present research article proposes a novel framework known as Lq* q-rung orthopair multi-fuzzy soft set (Lq* qROMFSS), which incorporates lattice ordering in q-rung orthopair multi-fuzzy soft set. The effectiveness of the proposed model is confirmed through successful experimentation on various important operations, including union, intersection, complement, restricted union and intersection. Moreover, the verification of De Morgan’s laws for Lq* qROMFSS is carried out specifically for these operations mentioned above. To highlight the significance of the proposed Lq* qROMFSS, a multi-attribute decision-making (MADM) problem is presented, showcasing its application in the domain of healthcare supply chain management. Furthermore, a comparative analysis is conducted to elucidate the advantages of this model in comparison to existing models.

Selection of healthcare waste disposal strategies with Lq* q-rung orthopair multi-fuzzy soft set similarity measures

The global challenges associated with urbanization and the escalating waste production have been magnified in recent times, particularly in the context of the COVID-19 pandemic. In response to these challenges, municipal authorities, especially in developing nations, are confronted with the imperative task of discerning the most suitable healthcare waste (HCW) disposal methods. These methods are crucial for the effective management of medical waste, both during and after the COVID-19 era. This study introduces a novel similarity measure designed for lattice ordered q-rung orthopair multi-fuzzy soft sets (Lq* q-ROMnFSSs) and exploring some of their essential characteristics. Currently, no established methods are available for gauging the similarity of Lq* q-ROMnFSSs sets. Therefore, this paper takes a pioneering step by presenting similarity measures tailored for Lq* q-ROMnFSSs sets. Moreover, we propose an evaluation methodology that leverages the lattice ordered q-rung orthopair multi-fuzzy soft information to determine the optimal health care waste (HCW) disposal approach. This approach seeks to enhance decision-making within the realm of waste management, facilitating more informed and effective choices in handling healthcare waste.

Linear diophantine multi-fuzzy soft similarity measures: An analysis on alternative-fuel

Every day, the globe becomes more contemporary and industrialized. As a result, the number of vehicles and engines is growing. However, the energy sources utilized in these engines are scarce and dwindling over time. This circumstance prompts the search for alternate fuel. As civilization develops, transportation becomes a need for daily living. The largest issue is the diminishing supply of fossil fuels and the expanding population. As a result, everyone needs alternate energy sources for their automobiles. Therefore, in this investigation, we identify the best substitute for petrol. We offer the similarity measure(SM) for a hybrid structure of a Linear Diophantine Multi-Fuzzy Soft Set(LDMFSS) with the goal of determining this issue. Because the range of grade values has been expanded, decision-makers now have greater freedom in selecting their grade. An exemplary case study is illustrated that shows the appropriateness of our recommended approach. A comparative analysis is provided to show the outcomes of the proposed method are more achievable and beneficial than those of the existing methodologies. Additionally, its applicability and attainability are evaluated by comparing its structure to those of the already used procedures.

Lattice Algebraic Structures on LDMFS Domains

The premise of the soft set was designed to model vague ideas. In this kind of model, where the set of parameters exhibits some degree of order, lattice order theory is quite beneficial. For researchers studying uncertainty, the notion of soft sets, lattices, and fuzzy sets has proven essential. In this study, the postulation of the Lattice ordered Linear Diophantine Multi-Fuzzy Soft Set (LLDMFSS) is laid out. The fundamental objective of this study is the formation of hybrid algebraic structures for LLDMFSS. Particularly, the characteristics of complete lattice, modular lattice, and distributive lattice were inhibited in LLDMFSS, and some pertinent findings were obtained. Subsequently, the modular and distributive LLDMFSS characterization theorem was implemented. The notion of the direct product for two LLDMFSSs was then addressed.

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>

An Abstract Context to Lattice-Based Ideals (Filters) with Multi-Fuzzy Soft Settings

In this study, multi-fuzzy soft ideals (filters) are introduced over the lattice-ordered multi-fuzzy soft set ([Formula: see text]) and their results are shown. The ideas of lattice-ordered multi-fuzzy soft homomorphism ([Formula: see text]) between two [Formula: see text]s are then introduced, along with those of lattice-ordered multi-fuzzy soft isotone map [Formula: see text], lattice-ordered multi-fuzzy soft isomorphism ([Formula: see text]), and kernel of [Formula: see text]. We also look at the principal ideal and soft prime ideal of [Formula: see text].

Medical Diagnosis under Effective Bipolar-Valued Multi-Fuzzy Soft Settings

The Molodtsov-initiated soft set theory plays an important role as a powerful mathematical tool for handling uncertainty. As an extension of the soft set, the fuzzy soft set can be seen to be more generic and flexible than utilizing the soft set only that fails to represent problem parameters fuzziness. Through this progress, the fuzzy soft set theory cannot deal with decision-making problems involving multi-attribute sets, bipolarity, or some effective considered parameters. Therefore, the goal of this article is to adapt effectiveness and bipolarity concepts with the multi-fuzzy soft set of order n. One can see that this approach generates a novel, extended, effective decision-making environment that is more applicable than any previously introduced one. In addition, types, concepts, and operations of effective bipolar-valued multi-fuzzy soft sets of dimension n are provided, each with an example. Furthermore, properties like absorption, associative, distributive, commutative, and De Morgan’s laws of those new sets are investigated. Moreover, a decision-making methodology under effective bipolar-valued multi-fuzzy soft settings is established. This technique facilitates reaching the final decision that this student is qualified to take a certain education level, or this patient is suffering from a certain disease, etc. In addition, a case study represented in a medical diagnosis example is discussed in detail to make the proposed algorithm clearer. Applying matrix techniques in this example as well as using MATLAB®, not only makes it easier and faster in doing calculations, but also gives more accurate, optimal, and effective decisions. Finally, the sensitivity analysis, as well as a comparison with the existing methods, are conducted in detail and are summarized in a chart to show the difference between them and the current one.

Sustainable method for tender selection using linear Diophantine multi-fuzzy soft set

Tender selection is a fundamental issue for the success of construction projects since it contributes to the overall outline’s performance. In reallife problems, the decision-makers cannot express certain crisp data, so there is uncertainty and vagueness in the values. In this paper, a sustainable technique is proposed to find desirable tenderers coherently and fairly under the needed circumstances. This paper presents three methods of an algorithmic approach to evaluate the tendering process and rank the tenderers. The attributes are expressed as Linear Diophantine Multi-Fuzzy Soft numbers (LDMFSN) since the existence of reference parameters makes the DM freely choose their grade values. Some of the rudimentary properties of LDMFSN are presented. An illustrative example is demonstrated to validate our proposed method. The uniqueness of the result in all three algorithms shows the effectiveness of our proposed approach.

Selection of Exemplary Students Using The Concept of Hesitant Multi-Fuzzy Soft Set

The concept of hesitant multi-fuzzy soft set is a concept that can be applied in decision-making problems. In this paper, we use an algorithm with respect to hesitant multi-fuzzy soft set to make the selection of exemplary students. The decision-making process in this case is carried out by following the steps in a constructed algorithm in order to obtain the best possible outcome from the given case study.

Algebraic Hyperstructure of Multi-Fuzzy Soft Sets Related to Polygroups

The combination of two elements in a group structure is an element, while, in a hypergroup, the combination of two elements is a non-empty set. The use of hypergroups appears mainly in certain subclasses. For instance, polygroups, which are a special subcategory of hypergroups, are used in many branches of mathematics and basic sciences. On the other hand, in a multi-fuzzy set, an element of a universal set may occur more than once with possibly the same or different membership values. A soft set over a universal set is a mapping from parameters to the family of subsets of the universal set. If we substitute the set of all fuzzy subsets of the universal set instead of crisp subsets, then we obtain fuzzy soft sets. Similarly, multi-fuzzy soft sets can be obtained. In this paper, we combine the multi-fuzzy soft set and polygroup structure, from which we obtain a new soft structure called the multi-fuzzy soft polygroup. We analyze the relation between multi-fuzzy soft sets and polygroups. Some algebraic properties of fuzzy soft polygroups and soft polygroups are extended to multi-fuzzy soft polygroups. Some new operations on a multi-fuzzy soft set are defined. In addition to this, we investigate normal multi-fuzzy soft polygroups and present some of their algebraic properties.

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.

Application Multi-Fuzzy Soft Sets in Hypermodules

The goal of this paper is to introduce a novel soft hyperstructure called multi-fuzzy soft hyperstructure. We investigate the notion of multi-fuzzy soft hypermodules and some of their structural properties are discussed. We discuss the behavior image and inverse image of a multi-fuzzy soft set under the multi-fuzzy soft function. According to Zadeh’s extension principle, we prove that the image and inverse image of a multi-fuzzy soft hypermodules are further multi-fuzzy soft hypermodule.

Compositions on lattice ordered multi-fuzzy soft matrix and its simulated application in medical diagnosis

The essential goal of the manuscript is to initiate lattice ordered multi-fuzzy soft matrix (ℒℳℱSℳ) using lattice ordered multi-fuzzy soft set (ℒℳℱSS) and discuss the operations and depict rudimentary properties on ℒℳℱSℳ. Moreover, we originate the various compositions of ℒℳℱSℳ and propose algorithm for medical diagnosis by applying score matrix which have been implemented with the numerical example. Finally, the comparitive analysis of three composition methods is also included for improved reasonability and reliability.

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.

Multi-valued picture fuzzy soft sets and their applications in group decision-making problems

Soft set theory initiated by Molodtsov in 1999 has been emerging as a generic mathematical tool for dealing with uncertainty. A noticeable progress is found concerning the practical use of soft set in decision-making problems. The purpose of this manuscript is to explore the novel of multi-valued picture fuzzy set (MPFS) and multi-valued picture fuzzy soft set (MPFSS) which are the generalizations of the notions of picture fuzzy soft set (PFSS) and multi-fuzzy soft set (MFSS). This notion can be used to express fuzzy information in more general and effective way. In particular, some basic operations such as union, intersection, complement and product of the proposed MPFSS are developed, and their properties are investigated. Furthermore, some aggregation operators corresponding to the proposed MPFSSs are called multi-picture fuzzy soft weighted averaging, multi-picture fuzzy soft ordered weighted averaging and multi-picture soft hybrid weighted averaging operators for a collections of MPFSSs are also developed. Moreover, based on these operators, we presented a new method to deal with the multi‐attribute group decision-making problems under the multi-valued picture fuzzy soft environment. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods. The graphical interpretation of the explored approaches is also utilized with future directions.

Similarity Measure of Lattice Ordered Multi-Fuzzy Soft Sets Based on Set Theoretic Approach and Its Application in Decision Making

Many effective tools in fuzzy soft set theory have been proposed to handle various complicated problems in different fields of our real life, especially in decision making. Molodtsov’s soft set theory has been regarded as a newly emerging mathematical tool to deal with uncertainty and vagueness. Lattice ordered multi-fuzzy soft set (LMFSS) has been applied in forecasting process. However, similarity measure is not used in this application. In our research, similarity measure of LMFSS is proposed to calculate the similarity between two LMFSSs. Moreover, some of its properties are introduced and proved. Finally, an application of LMFSS in decision making using similarity measure is analysed.

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