Fuzzy Soft Environment Research Articles

Multi-Attribute Three-Way Decision Approach Based on Ideal Solutions under Interval-Valued Fuzzy Soft Environment

The interval-valued fuzzy soft set (IVFSS) model, which combines the benefits of the soft set model with the interval-valued fuzzy set (IVFS) model, is a growing and effective mathematical tool for processing hazy data. In detail, this model is characterized by symmetry, which has the lower and upper membership degree. The study of decision-making based on IVFSS has picked up more steam recently. However, existing multi-attribute decision-making (MADM) methods can only sort alternative schemes, but are not able to classify them, which is detrimental to decision-makers’ efficient decision-making. In this paper, we propose a multi-attribute three-way decision-making (MATWDM) algorithm based on ideal solutions for IVFSS. MATWDM is extended to the IVFSS environment by incorporating the concept of the ideal solution, offering a more adaptable and comprehensive approach for addressing uncertain MADM issues. The method not only obtains the ranking results of the alternatives, but also divides them into acceptance domain, rejection domain, and delayed-decision domain, which makes the decision results more reasonable and effective, facilitating decision-makers to make better decisions. We apply the proposed three-way decision algorithm to two practical cases as diverse as mine emergency decision and Homestay selection decision. Additionally, the effectiveness and viability of the suggested method are confirmed by experimental findings.

Supplier selection in green supply chain management using correlation-based TOPSIS in a q-rung orthopair fuzzy soft environment

Fuzzy hybrid models are efficient mathematical tools for managing unclear and vague data in real-world scenarios. This research explores the q-rung orthopair fuzzy soft set (q-ROFSS), which presents incomplete and ambiguous details in decision-making problems. The main intention of this study is to describe and evaluate the characteristics of the correlation coefficient (CC) and weighted correlation coefficient (WCC) for q-ROFSS. Also, the technique for order preference should be enhanced by similarity to the ideal solution (TOPSIS) with extended measures in q-ROFSS settings. Furthermore, we integrated mathematical formulations of correlation obstructions to confirm the consistency of the planned technique. It helps handle difficulties involving multi-attribute group decision-making (MAGDM). Moreover, a numerical illustration is presented to clarify how the advocated decision-making methodology can be implemented in evaluating suppliers in green supply chain management (GSCM). As a result, each alternative is assessed using multiple criteria, such as quality and reliability, capacity and scalability, compliance and certifications, and sustainability practices. The technique proposed in this study retains the selected research's specific structure more effectively than current techniques. A comparative analysis further substantiates the feasibility and effectiveness of the proposed approach over other decision-making techniques.

Topological numbers of fuzzy soft graphs and their applications in globalizing the world by mutual trade

In this research draft, by keeping in view, the importance of Zagreb numbers, first we defined some familiar graph families and their degrees in fuzzy soft environment, and then by converting these two novel topological numbers in fuzzy soft framework, their formulae are calculated for these graphical networks. An application of international trade using two kinds of routes is also discussed in the article, and by comparing the results efficiency of both the numbers is compared and analyzed how topological descriptors are useful in examining the progress and profit in the countries, that are a part of the project. Graphs are used in the modeling of links and processes within physical, biological, social, and information systems. A fuzzy graph is the most adaptable tool in mathematics, which describes the fuzzy relationship between objects. Fuzzy graphs are very helpful to give more accuracy to the system as compared to crisp graphs. A classification of the universe with respect to certain specified parameters is known as a soft set. It is a new method for simulating ambiguity and uncertainty. Soft set theory was created by Molodtsov in 1999 as a method for simulating vagueness and uncertainty. Soft set theory is presently used widely in academia to address decision-making issues. The concept of soft graphs is used to provide a parameterized point of view for graphs. In many areas of mathematics and chemistry, as well as in network theory, spectral graph theory, and molecular chemistry, the Zagreb numbers are crucial graph parameters. Due to the importance and significance of Zagreb numbers, in this research article we define these graph parameters in fuzzy soft environment and then derived the fundamental formula for first and second Zagreb numbers of some popular graph families. Also by keeping in view the importance of graph theory in solving decision making problems in business industry, and the most generic behavior of fuzzy soft graph due to its parameterized nature we use our work in application of decision making in trade among different nations.

Decision-making method under the interval-valued complex fuzzy soft environment

Decision-making method under the interval-valued complex fuzzy soft environment

TOPSIS method based on q-rung orthopair picture fuzzy soft environment and its application in the context of green supply chain management

<abstract> <p>Green supplier selection has been an important technique for environmental sustainability and reducing the harm of ecosystems. In the current climate, green supply chain management (GSCM) is imperative for maintaining environmental compliance and commercial growth. To handle the change related to environmental concern and how the company manages and operates, they are integrated the GSCM into traditional supplier selection process. The main aims of this study were to outline both traditional and environmental criteria for selecting suppliers, providing a comprehensive framework to assist decision-maker in prioritizing green supplier effectively. In order to address issue to simulate decision-making problems and manage inaccurate data. A useful technique of fuzzy set was proposed to handle uncertainty in various real-life problems, but all types of data could not be handled such as incomplete and indeterminate. However, several extensions of fuzzy set were considered, such as intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and q-rung orthopair fuzzy soft set considering membership and nonmember ship grade to handle the uncertainty problem. However, there was a lack of information about the neutral degree and parameterization axioms lifted by existing approaches, so to fill this gap and overcome the difficulties Ali et al. proposed a generalized structure by combining the structure of picture fuzzy set and q-rung orthopair fuzzy soft set, known as q-rung orthopair picture fuzzy soft sets, characterized by positive, neutral and negative membership degree with parameterization tools and aggregation operator to solve the multi criteria group decision-making problem. Additionally, the TOPSIS method is a widely utilized to assist individuals and organizations in selecting the most appropriate option from a range of choices, taking into account various criteria. Finally, we demonstrate an illustrative example related to GSCM to enhance competitiveness, based on criteria both in general and with a focus on environmental consideration, accompanied by an algorithm and flow chart.</p> </abstract>

Decision-making techniques based on similarity measures of possibility interval fuzzy soft environment

The fuzzy set (FS) is a powerful logic designed to measure uncertain information and plays a crucial role in solving real-life problems such as decision-making. This article is split into two parts. In the first part, we highlight the notion of possibility for interval-valued fuzzy soft sets (PI-VFSSs) by collecting all interval fuzzy sets (IVFSs) with soft sets (SSs) under possibility properties. A basic set theories, some numerical examples, and some properties for this hybrid model have been created. Then, in order to test the efficiency of the proposed method in solving some real-life problems, we construct an algorithm using a PIV-FSS. On the other hand, in the second part, we apply similarity techniques to the proposed model through the analysis of similarity measures of two PIV-FSSs. After that, a new algorithm based on these measures is applied to the medical diagnosis to find out whether or not a patient has a respiratory disease. Finally, some theories that show the relationship between PIV-FSS with some mathematical operations have been proposed.

A model for emergency supply management under extended EDAS method and spherical hesitant fuzzy soft aggregation information

Due to the frequent occurrence of numerous emergency events that have significantly damaged society and the economy, the need for emergency decision-making has been manifest recently. It assumes a controllable function when it is critical to limit property and personal catastrophes and lessen their negative consequences on the natural and social course of events. In emergency decision-making problems, the aggregation method is crucial, especially when there are more competing criteria. Based on these factors, we first introduced some basic concepts about SHFSS, and then we introduced some new aggregation operators such as the spherical hesitant fuzzy soft weighted average, spherical hesitant fuzzy soft ordered weighted average, spherical hesitant fuzzy weighted geometric aggregation, spherical hesitant fuzzy soft ordered weighted geometric aggregation, spherical hesitant fuzzy soft hybrid average, and spherical hesitant fuzzy soft hybrid geometric aggregation operator. The characteristics of these operators are also thoroughly covered. Also, an algorithm is developed within the spherical hesitant fuzzy soft environment. Furthermore, we extend our investigation to the Evaluation based on the Distance from Average Solution method in multiple attribute group decision-making with spherical hesitant fuzzy soft averaging operators. And a numerical illustration for “supply of emergency aid in post-flooding the situation” is given to show the accuracy of the mentioned work. Then a comparison between these operators and the EDAS method is also established in order to further highlight the superiority of the established work.

An industrial disaster emergency decision-making based on China’s Tianjin city port explosion under complex probabilistic hesitant fuzzy soft environment

Emergency decision-making is vital for nations or communities because it increases emergency management’s effectiveness and legitimacy, which in turn greatly minimizes environmental damage, fatalities, and economic loss. The evaluation of emergency judgements must take into account significant inaccuracy, fuzzyness, and ambiguity. While high risk and uncertainty are frequently characteristics of emergency decision-making (EDM) circumstances. The current EDM methodologies do not take into account the psychological behavior of the decision makers in addition to the various emergency situations and the various responses. In this paper, we presented a new method based on a Complex Probabilistic Hesitant Fuzzy Soft Set (CPHFSS) as represented by membership in 2-D with hesitant probability. The idea that is being put forth captures the ambiguity and takes into account emergency situations while also taking into account the psychological state of the decision-makers involved in the EDM procedure. The introduction of a new score function for the CPHFSS serves as the second objective of this paper, which is to address a number of comparability issues. We examine a novel family of hybrid operators for CPHFSS that utilize numerous independent variables as a solution to these unforeseen issues. The group decision-making strategy and EDAS technique are then suggested employing these operators. Later, an emergency decision-making situation involving a major fire in China is used to demonstrate the validity of the algorithms.

Granulation of protein–protein interaction networks in Pythagorean fuzzy soft environment

Granulation of protein–protein interaction networks in Pythagorean fuzzy soft environment

Aggregation and Interaction Aggregation Soft Operators on Interval-Valued q-Rung Orthopair Fuzzy Soft Environment and Application in Automation Company Evaluation

In several practical decision procedures, it is not accessible to denote assessments by a single crisp number due to a lack of information. However, representing information by an interval number within [0, 1] is a more credible approach. In multi-criteria decision making (MCDM) such an interval number can significantly catch information. In addition, the combination of soft sets with interval-valued q-rung orthopair fuzzy sets can be viewed as interval-valued q-rung orthopair fuzzy soft sets (IVq-ROFSs). It can be a reliable tool to cope with uncertainties. Usually, aggregation operators are functional in MCDM techniques; therefore, aggregation operators on IVq-ROFSs can significantly aggregate pieces of information in intervals with IVq-ROFSs. In this paper, we investigated some crucial properties of interval valued q-rung orthopair fuzzy soft sets (IVq-ROFSSs) and expressed a different representation of IVq-ROFSS in the form of IVq-ROFS number. Based on this representation, we investigated IVq-ROF weighted averaging, IVq-ROF weighted geometric operators and given their basic properties. Moreover, we consider interactions between non-memberships and memberships of different interval-valued q-rung orthopair fuzzy values and defined IVq-ROF weighted interaction averaging, IVq-ROF weighted interaction geometric aggregation operators in IVq-ROFS environments. A decision-making process is given, and an illustration is provided by tackling application in automation company evaluation.

MCDM method on complex picture fuzzy soft environment

In this paper the concept of complex picture fuzzy soft set is defined. The MCDM problem considered consists of two methods. In the first method called CPFS CRITIC method complex picture fuzzy soft matrix is constructed. Normalized CPFS decision function is defined and using this function the normalized CPFS decision matrix is constructed and the weights of the parameters are determined. In the second method the weights of CPFS CRITIC method are taken to find CPFS decision matrix using selected parameters and their alternatives. The utility function depending on the beneficial and non-beneficial alternatives are defined and the integrated utility of each parameter is determined. This method is illustrated by taking four types of chillies as the alternatives and five nutrients as parameters and the best yielding variety of chilli is found. The proposed method is compared with CPFS-TOPSIS method. It is found that the best variety of chilli is the same in both the methods. However, the ranking of the other types of chilli differ.

Interaction aggregation operators to solve multi criteria decision making problem under pythagorean fuzzy soft environment

In this article, we investigate the multi-criteria decision-making complications under Pythagorean fuzzy soft information. The Pythagorean fuzzy soft set (PFSS) is a proper extension of the Pythagorean fuzzy set (PFS) which discusses the parametrization of the attributes of alternatives. It is also a generalization of the intuitionistic fuzzy soft set (IFSS). The PFSS is used to precisely evaluate the deficiencies, anxiety, and hesitation in decision-making (DM). The most essential determination of the current study is to advance some operational laws along with aggregation operators (AOs) within the Pythagorean fuzzy soft environs such as Pythagorean fuzzy soft interaction weighted average (PFSIWA) and Pythagorean fuzzy soft interaction weighted geometric (PFSIWG) operators with their desirable features. Furthermore, a DM technique has been established based on the developed operators to solve multi-criteria decision-making (MCDM) problems. Moreover, an application of the projected method is presented for the selection of an effective hand sanitizer during the COVID-19 pandemic. A comparative analysis with the merits, effectivity, tractability, along with some available research deduces the effectiveness of this approach.

Inter-specific competition among trees in pythagorean fuzzy soft environment

A Pythagorean fuzzy set is very effective mathematical framework to represent parameter-wise imprecision which is the property of linguistic communication. A Pythagorean fuzzy soft graph is more potent than the intuitionistic fuzzy soft as well as the fuzzy soft graph as it depicts the interactions among the objects of a system using Pythagorean membership grades with respect to different parameters. This article addresses the content of competition graphs as well as economic competition graphs like k-competition graphs, m-step competition graphs and p-competition graphs in Pythagorean fuzzy soft environment. All these concepts are illustrated with examples and fascinating results. Furthermore, an application which describes the competition among distinct forest trees, that grow together in the mixed conifer forests of California, for plant resources is elaborated graphically. An algorithm is also designed for the construction of Pythagorean fuzzy soft competition graphs. It is worthwhile to express the competing and non-competing interactions in various networks with the help of Pythagorean fuzzy soft competition graphs wherein a variation in competition relative to different attributes is visible.

TOPSIS Method Based on Correlation Coefficient under Pythagorean Fuzzy Soft Environment and Its Application towards Green Supply Chain Management

The correlation coefficient between two variables is an important aspect of statistics. The accuracy of assessments of correlation relies on information from a set of discourses. Data collected in statistical studies are often full of exceptions. Pythagorean fuzzy soft sets (PFSS) are a parametrized family of extended Pythagorean fuzzy sets (PFS). They comprise a generalization of intuitionistic fuzzy soft sets which may be used to accurately assess deficiencies and uncertainties in evaluations. PFSS can accommodate uncertainty more competently than intuitionistic fuzzy soft sets and are the most important strategy when dealing with fuzzy information in decision-making processes. Herein, the concept and characteristics of correlation coefficients and the weighted correlation coefficients in PFSS are discussed. We also introduce the Pythagorean fuzzy soft weighted average (PFSWA) and Pythagorean fuzzy soft weighted geometric (PFSWG) operators and discuss their desirable characteristics. A prioritization technique for order preference by similarity to the ideal solution (TOPSIS) under the PFSS environment based on correlation coefficients and weighted correlation coefficients will be introduced. Through the proposed methodology, a technique for decision-making is developed. Additionally, an application of the proposed TOPSIS technique is presented for green supplier selection in green supply chain management (GSCM). The practicality, efficacy, and flexibility of the proposed approach is proved through comparative analyses, drawing upon existing studies.

Aggregation operators of Pythagorean fuzzy soft sets with their application for green supplier chain management

The Pythagorean fuzzy soft sets (PFSS) is a parametrized family and one of the appropriate extensions of the Pythagorean fuzzy sets (PFS). It’s also a generalization of intuitionistic fuzzy soft sets, used to accurately assess deficiencies, uncertainties, and anxiety in evaluation. The most important advantage of PFSS over existing sets is that the PFS family is considered a parametric tool. The PFSS can accommodate more uncertainty comparative to the intuitionistic fuzzy soft sets, this is the most important strategy to explain fuzzy information in the decision-making process. The main objective of the present research is to progress some operational laws along with their corresponding aggregation operators in a Pythagorean fuzzy soft environment. In this article, we introduce Pythagorean fuzzy soft weighted averaging (PFSWA) and Pythagorean fuzzy soft weighted geometric (PFSWG) operators and discuss their desirable characteristics. Also, develop a decision-making technique based on the proposed operators. Through the developed methodology, a technique for solving decision-making concerns is planned. Moreover, an application of the projected methods is presented for green supplier selection in green supply chain management (GSCM). A comparative analysis with the advantages, effectiveness, flexibility, and numerous existing studies demonstrates the effectiveness of this method.

A similarity measure under Pythagorean fuzzy soft environment with applications

A novel similarity measure (SM) based upon cosine similarity measure and Frobenius inner product of matrices, and a weighted SM for Pythagorean fuzzy soft sets (PFS-sets/PFSSs) are coined in this article. Some fundamental characteristics of the proposed SM are also brought into light, including that SM of any two PFS-sets equals unity iff the two PFS-sets coincide. Employing this SM, a relation $$\thickapprox ^\lambda $$ amongst two PFS-sets is demarcated. Further, it is demonstrated that this relation does not enjoy the status of an equivalence relation. Moreover, the efficacy of the proposed SM is established with the aid of numerical examples. Comparison analysis of the proposed method with some of the prevailing similarity measures is also given, both numerically and diagrammatically. In the end, an application from psychological disorder accompanied by algorithm and flow chart have been put on display through a conjectural case study.

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.

Granulation of ecological networks under fuzzy soft environment

The main idea of this work is the exploration of granular structures by applying the hybrid models of fuzzy soft sets and fuzzy soft graphs to discuss the indiscernibility partition of set of universe. The information granulation is examined by applying fuzzy soft theory, and the corresponding behavior of granules is reviewed. This article proposes a novel technique of formation of granular structures using fuzzy soft graphs and defines the fuzzy soft granules. Two degree-based models are introduced to explore the abstraction of these granular structure. Then, we use these two degree-based models to granulate the certain relationships between different species in an ecological system. Further, we develop and implement some algorithms of our proposed models to granulate the underconsideration networks. Finally, a comprehensive comparison of our proposed model with other existing techniques is presented to prove the applicability and effectiveness of fuzzy soft granulation.

Decision-making approach based on Pythagorean Dombi fuzzy soft graphs

A Pythagorean fuzzy set model is more useful than intuitionistic fuzzy set model to handle the imprecise information involving both membership and nonmembership degrees, and a soft set is an other parameterized point of view for handling the vagueness. A Pythagorean fuzzy soft graph is considered more capable than intuitionistic fuzzy soft graph for representing the parametric relationships between objects, and the Dombi operators with operational parameters have creditable extensibility. Based on these two notions, we propose the concept of Pythagorean Dombi fuzzy soft graph (PDFSG). We describe certain concepts of graph theory under Pythagorean Dombi fuzzy soft environment. Further, we define the degree sequence and degree set in PDFSG, and the concept of edge regular PDFSG with consequential properties. Moreover, we illustrate the examples in decision making including selection of suitable ETL software for a business intelligence project and evaluation of electronics companies. Finally, we present the comparison analysis of our proposed model to show the superiority than existing model.

(1805-4498) A robust aggregation operators for multi-criteria decision-making method with bipolar fuzzy soft environment

Molodtsov initiated soft set theory that provided a general mathematicalframework for handling with uncertainties in which we encounter the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as bipolar fuzzy set theory.The main object of this paper is to lay a foundation for providing a new application of bipolar fuzzy soft tool in considering many problems that contain uncertainties. In present study, aggregation of bipolar fuzzy soft numbers haveso far not yet been applied for ranking of alternatives in decision-making problems.To this propose, bipolar fuzzy soft weighted arithmetic averaging (BFSWAA) operator, bipolar fuzzy soft weighted geometric averaging (BFSWGA) operatorhave been used to compare two bipolar fuzzy soft numbers (BFSNs) for aggregating different bipolar fuzzy soft input arguments in bipolar fuzzy soft environment.Then, their related properties have been investigated.Finally, a practical example for selection of alternatives is given to demonstratethe utility and application of the proposed work.