Fuzzy Soft Set Theory Research Articles

Fuzzy Soft Sets and its Application to Decision Making: A Short Case Study Involving the Health Sector

The health sector faces uncertainty and complex decision-making scenarios, making traditional analytical tools insufficient. The fuzzy soft set theory has emerged as a powerful framework for modeling and reasoning with uncertain information, with promising applications in the health domain. This project explores the application of fuzzy soft sets in various decision-making processes in the health sector, including medical diagnosis, disease classification, treatment planning, risk assessment, patient stratification, and predictive modeling. The study reviews historical development of fuzzy set theory and its extension to soft sets, discussing challenges, limitations, and future research directions. The findings aim to contribute to the growing body of knowledge on the practical relevance and potential of fuzzy soft set theory in addressing healthcare decision-making needs.

Fuzzy Soft Set Theory Applications in Medical Diagnosis: A Comprehensive Review and the Roadmap for Future Studies

This paper provides a literature review addressing the use of soft sets in medical diagnosis. Distinguishing itself from the existing literature, the study offers a comprehensive analysis of how fuzzy soft sets can be integrated into diagnostic processes, highlighting a novel fusion of fuzzy and soft sets in medical applications. Any soft set on a countably infinite universe can be regarded as a fuzzy set, recognizing the limitations of traditional diagnostic tools in dealing with vague and incomplete information, our research aims to utilize the flexibility and comprehensiveness of fuzzy soft sets to enhance decision-making accuracy in medical scenarios. The primary objective of this research is to present a thorough and critical analysis of fuzzy soft set theory in medical diagnosis, aiming to establish it as a fundamental approach in the field. By combining all of these results, we can generate a comprehensive picture of the connections between the many theories that account for fuzziness and imprecision, which helps to fill in the blanks left by recent surveys. The review will focus on identifying the main research trends in this field: the primary research topics that soft set theory addresses in medical applications, the community is currently facing and the major theoretical concepts used to study these topics. The primary objective of this review is to assist in the identifying of emerging research directions. Some of these trends are promising and will help shape a new role for soft set theory in the area of medical applications. The fusion of fuzzy and soft sets in medical applications represents a crucial and necessary stage in the research and diagnosis procedures. Key results include the study on development of algorithms and models that outperform traditional methods in accuracy and reliability.

On Intuitionistic Fuzzy Neutrosophic Soft Ideal Topological Spaces

The purpose of this paper is to introduce the notion of intuitionistic fuzzy neutronsophic soft ideal in Intuitionistic fuzzy neutronsophic soft set theory. The concept of intuitionistic fuzzy neutrosophic soft local function is also introduced. These concepts are discussed with a view to find new intuitionistic fuzzy neutronsophic soft topologies from the original one. The basic structure, respecially a basic for such generated Intuitionistic fuzzy neutronsophic soft topologies also studied here. Finally, the notion of compatibility of intuitionistic fuzzy neutronsophic soft ideals with Intuitionistic fuzzy neutrosophic soft topologies is introduced and some equivalent conditions concerning, this topic are established here.

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.

Generalized Ideals of BCK/BCI-Algebras Based on MQHF Soft Set with Application in Decision Making

The purpose of this study is to generalize the concept of Q -hesitant fuzzy sets and soft set theory to Q -hesitant fuzzy soft sets. The Q -hesitant fuzzy set is an admirable hybrid property, specially developed by the new generalized hybrid structure of hesitant fuzzy sets. Our goal is to provide a formal structure for the m -polar Q -hesitant fuzzy soft (MQHFS) set. First, by combining m-pole fuzzy sets, soft set models, and Q -hesitant fuzzy sets, we introduce the concept of MQHFS and apply it to deal with multiple theories in B C K / B C I -algebra. We then develop a framework including MQHFS subalgebras, MQHFS ideals, closed MQHFS ideals, and MQHFS exchange ideals in B C K / B C I -algebras. Furthermore, we prove some relevant properties and theorems studied in our work. Finally, the application of MQHFS-based multicriteria decision-making in the Ministry of Health system is illustrated through a recent case study to demonstrate the effectiveness of MQHFS through the use of horizontal soft sets in decision-making.

Effective Fuzzy Soft Expert Set Theory and Its Applications

Effective Fuzzy Soft Expert Set Theory and Its Applications

Computational bipolar fuzzy soft matrices with applications in decision making problems

A fuzzy soft matrix is a type of mathematical matrix that combines the principles of fuzzy set theory and soft set theory. It is used to handle uncertainty and vagueness in decision-making problems. Fuzzy soft matrix theory cannot handle negative information. To overcome this difficulty, we define the notion of bipolar fuzzy soft (BFS) matrices and study their fundamental properties. We define products of BFS matrices and investigate some useful properties and results. We also give an application of bipolar fuzzy soft matrices to decision-making problems. We propose a decision-making algorithm based on computer programs under the environment of the bipolar fuzzy soft sets.

Application of Fuzzy Membership Value Matrix

Fuzzy set theory plays a dynamic role in medicinal fields. There are varieties of simulations involving fuzzy matrices to deal with different complicated aspects of medical diagnosis. Today may be a world of uncertainty with its associated problems, which may be well handled by fuzzy soft set theory. Sanchez formulated the diagnostic models including intuitionistic fuzzy matrices representing the medical knowledge between the symptoms and diseases. In this paper, an algorithm is developed and a few examples are proposed to construct the decision method for Diagnosis.

Study on Chaotic Multi-Attribute Group Decision Making Based on Weighted Neutrosophic Fuzzy Soft Rough Sets

In this article, we have proposed a multi-attribute group decision making (MAGDM) with a new scenario or new condition named Chaotic MAGDM, in which not only the weights of the decision makers (DMs) and the weights of the decision attributes are considered, but also the familiarity of the DMs with the attributes are considered. Then we applied the weighted neutrosophic fuzzy soft rough set theory to Chaotic MAGDM and proposed a new algorithm for MAGDM. Moreover, we provide a case study to demonstrate the application of the algorithm. Our contributions to the literature are as follows: (1) familiarity is rubbed into MAGDM for the first time in the context of neutrosophic fuzzy soft rough sets; (2) a new MAGDM model based on neutrosophic fuzzy soft rough sets has been designed; (3) a sorting/ranking algorithm based on a neutrosophic fuzzy soft rough set is constructed.

Dynamic Chaotic Multi-Attribute Group Decision Making under Weighted T-Spherical Fuzzy Soft Rough Sets

In this article, the parameter of the decision maker’s familiarity with the attributes of the alternatives is introduced for the first time in dynamic multi-attribute group decision making to avoid the disadvantages arising from the inappropriate grouping of decision makers. We combine it with fuzzy soft rough set theory and dynamic multi-attribute-grouping decision making to obtain a new decision model, i.e., dynamic chaotic multiple-attribute group decision making. Second, we provide an algorithm for solving this model under a weighted T-spherical fuzzy soft rough set, which can not only achieve symmetry between decision evaluation and fuzzy information but also establish a good symmetrical balance between decision makers and attributes (evaluation indexes). Finally, a specific numerical computation case is proposed to illustrate the convenience and effectiveness of our constructed algorithm. Our contributions to the literature are: (1) We introduced familiarity for the first time in dynamic multi-attribute group decision making. This makes our given dynamic chaotic multi-attribute group decision-making (DCMAGDM) model more general and closer to the actual situation; (2) we combined dynamic chaotic multi-attribute group decision making with T-spherical fuzzy soft rough set theory to make the model more realistic and reflect the actual situation. In addition, our choice of T-spherical fuzzy soft rough set allows the decision maker to engage in a sensible evaluation rather than sticking to numerical size choices; and (3) we constructed a new and more convenient sorting/ranking algorithm based on weighted T-spherical fuzzy soft rough sets.

New Possibility Soft Sets with Quality Assurance Application in Distance Education

The probability fuzzy soft set is an approach that is obtained by adding a probability degree to each approximate element of the fuzzy soft set and is formed by combining Fuzzy Set Theory and Soft Set Theory. This idea was later studied in different sets, such as intuitionistic fuzzy sets, neutrosophic fuzzy sets, Pythagorean fuzzy sets, etc. In this paper, a new Possibility Set is defined in the Fermatean Fuzzy environment and the essential features of new sets have been examined. The set-theoretic operations of new possibility sets, such as subset, soft equal, complement, union, intersection, AND, and OR, have been characterized with the help of elaborated examples. Their fundamental laws and properties are also discussed. A practical example concerning quality assurance in distance education is studied to demonstrate the applicability of new similarity measures in decision-making situations. Thus, it has been shown that the newly given similarity measure can be successfully applied to real-world decision problems. Finally, a comparison of the similarity of the proposed model is made with some existing models.

New generalization of fuzzy soft sets: $ (a, b) $-Fuzzy soft sets

<abstract><p>Many models of uncertain knowledge have been designed that combine expanded views of fuzziness (expressions of partial memberships) with parameterization (multiple subsethood indexed by a parameter set). The standard orthopair fuzzy soft set is a very general example of this successful blend initiated by fuzzy soft sets. It is a mapping from a set of parameters to the family of all orthopair fuzzy sets (which allow for a very general view of acceptable membership and non-membership evaluations). To expand the scope of application of fuzzy soft set theory, the restriction of orthopair fuzzy sets that membership and non-membership must be calibrated with the same power should be removed. To this purpose we introduce the concept of $ (a, b) $-fuzzy soft set, shortened as $ (a, b) $-FSS. They enable us to address situations that impose evaluations with different importances for membership and non-membership degrees, a problem that cannot be modeled by the existing generalizations of intuitionistic fuzzy soft sets. We establish the fundamental set of arithmetic operations for $ (a, b) $-FSSs and explore their main characteristics. Then we define aggregation operators for $ (a, b) $-FSSs and discuss their main properties and the relationships between them. Finally, with the help of suitably defined scores and accuracies we design a multi-criteria decision-making strategy that operates in this novel framework. We also analyze a decision-making problem to endorse the validity of $ (a, b) $-FSSs for decision-making purposes.</p></abstract>

Novel distance, similarity and entropy measures for interval valued intuitionistic fuzzy soft set

Soft and fuzzy sets are generic tools to deal with uncertainty. Both contemporary sets are not suitable to deal with all type of uncertain parameters. In this paper the hybridization of soft with extended fuzzy set information measures are derived. Interval-valued intuitionistic fuzzy soft set theory is a powerful tool for dealing with uncertainty of knowledge in information systems. In this paper, firstly some distance and similarity measures for interval-valued intuitionistic fuzzy soft sets were proposed. Further, some new entropy measures are also introduced by using the similarity measures. The validity of these measures is also proved. Applications of the distance measures is also used in the field of multi attribute decision making and medical diagnosis. The proposed measures are also compared with an existing measure to prove its significance.

Type-II generalized Pythagorean bipolar fuzzy soft sets and application for decision making

In the present communication, we introduce the theory of Type-II generalized Pythagorean bipolar fuzzy soft sets and define complementation, union, intersection, AND, and OR. The Type-II generalized Pythagorean bipolar fuzzy soft sets are presented as a generalization of soft sets. We showed De Morgan's laws, associate laws, and distributive laws in Type-II generalized Pythagorean bipolar fuzzy soft set theory. Also, we advocate an algorithm to solve the decision-making problem based on a soft set model.

Effective Fuzzy Soft Set Theory and Its Applications

Fuzzy soft set is the most powerful and effective extension of soft sets which deals with parameterized values of the alternative. It is an extended model of soft set and a new mathematical tool that has great advantages in dealing with uncertain information and is proposed by combining soft sets and fuzzy sets. Many fuzzy decision making algorithms based on fuzzy soft sets were given. However, these do not consider the external effective on the decision it depends on the parameters without considering any external effective. In order to solve these problems, in this paper, we introduce the concept of effective fuzzy soft set and its operation and study some of its properties. We also give an application of this concept in decision making (DM) problem. Finally, we give an application of this theory to medical diagnosis (MD) and exhibit the technique with a hypothetical case study.

Using optimization method for determining lactic acid bacteria counts in white cheese with different salt concentrations

Total lactic acid bacteria, Lactococcus spp., yeast, and mold counts in white cheese were determined during 55 days of storage in brine solutions with 4%, 6%, 8%, 10%, 12%, 14%, and 16% (w/v) salt concentrations at 4°C. In addition to salt content, dry matter, acidity, protein, fat contents, and sensory evaluations of cheese were also determined. Lactococcus spp. numbers in cheese salted with 4% and 14% brines (w/v salt concentrations) were 9.32 and 8.48 log cfu/g at the 55 days of storage, respectively. The lowest total lactic acid number was 7.24 for cheese in brine with 16% (w/v) salt concentration after 55 days of storage. Yeast numbers were 7.01 and 6.71 log cfu/g for cheese in brines with 4% and 16% (w/v) salt concentrations. Cheese samples salted in 12% and 14% (w/v) concentrations of brines have the highest sensory scores. Analysis results were interpreted mathematically by “fuzzy soft set” modeling. Novelty impact statement This research is a novel study detailing mathematical modeling related to optimizing the salt concentration to preserve the viability of lactic acid starter culture bacteria in the white cheese. Also, it covers the first optimizing method for process control in the cheese industry with the application of “fuzzy soft set theory.”

Decision-making methods based on fuzzy soft competition hypergraphs

Fuzzy soft set theory is an effective framework that is utilized to determine the uncertainty and plays a major role to identify vague objects in a parametric manner. The existing methods to discuss the competitive relations among objects have some limitations due to the existence of different types of uncertainties in a single mathematical structure. In this research article, we define a novel framework of fuzzy soft hypergraphs that export the qualities of fuzzy soft sets to hypergraphs. The effectiveness of competition methods is enhanced with the novel notion of fuzzy soft competition hypergraphs. We study certain types of fuzzy soft competition hypergraphs to illustrate different relations in a directed fuzzy soft network using the concepts of height, depth, union, and intersection simultaneously. We introduce the notions of fuzzy soft k-competition hypergraphs and fuzzy soft neighborhood hypergraphs. We design certain algorithms to compute the strength of competition in fuzzy soft directed graphs that reduce the calculation complexity of existing fuzzy-based non-parameterized models. We analyze the significance of our proposed theory with a decision-making problem. Finally, we present graphical, numerical, as well as theoretical comparison analysis with existing methods that endorse the applicability and advantages of our proposed approach.

(α, β)-cuts and inverse (α, β)-cuts in bipolar fuzzy soft sets

Bipolar fuzzy soft set theory, which is a very useful hybrid set in decision making problems, is a mathematical model that has been emphasized especially recently. In this paper, the concepts of (α,β)-cuts, first type semi-strong (α,β)-cuts, second type semi-strong (α,β)-cuts, strong (α,β)-cuts, inverse (α,β)-cuts, first type semi-weak inverse (α,β)-cuts, second type semi-weak inverse (α,β)-cuts and weak inverse (α,β)-cuts of bipolar fuzzy soft sets were introduced together with some of their properties. In addition, some distinctive properties between (α,β)-cuts and inverse (α,β)-cuts were established. Moreover, some related theorems were formulated and proved. It is further demonstrated that both (α,β)-cuts and inverse (α,β)-cuts of bipolar fuzzy soft sets were useful tools in decision making.

Fuzzy-soft set approach for ranking the functional requirements of software

Software requirements are the need of the stakeholders which are determined by the requirements elicitation techniques. Different fuzzy based methods have been developed to select the software requirements based on the ranking order so that high priority requirements can be implemented during the development process. Based on our review, we found that in these methods’ prior information about the data such as grades of membership during the computation is required and these methods are also incompatible with the parameterization tools. To address this issue, we proposed an approach for ranking the functional requirements of software using fuzzy-soft set theory. The relative deviation between counts of non-functional requirements has been used to construct the fuzzy-soft sets. The weights of the non-functional requirements and the ranking order of the functional requirements are computed from fuzzy soft-set derived from raw data in which no prior information about data is required. An example is presented to illustrate the application of the proposed approach.

A Novel Approach to Decision Making Based on Interval-Valued Fuzzy Soft Set

Interval-valued fuzzy soft set theory is a powerful tool that can provide the uncertain data processing capacity in an imprecise environment. The two existing methods for decision making based on this model were proposed. However, when there are some extreme values or outliers on the datasets based on interval-valued fuzzy soft set for making decisions, the existing methods are not reasonable and efficient, which may ignore some excellent candidates. In order to solve this problem, we give a novel approach to decision making based on interval-valued fuzzy soft set by means of the contrast table. Here, the contrast table has symmetry between the objects. Our proposed algorithm makes decisions based on the number of superior parameter values rather than score values, which is a new perspective to make decisions. The comparison results of three methods on two real-life cases show that, the proposed algorithm has superiority to the existing algorithms for the feasibility and efficiency when we face up to the extreme values of the uncertain datasets. Our proposed algorithm can also examine some extreme or unbalanced values for decision making if we regard this method as supplement of the existing algorithms.