Concept Of Fuzzy Sets Research Articles

Pythagorean fuzzy DEMATEL method for supplier selection in sustainable supply chain management

The fuzzy DEMATEL (Decision Making Trial and Evaluation Laboratory) method is one of the accepted decision-making methods in uncertain environment. The Pythagorean fuzzy set is a generalized concept of fuzzy set and intuitionistic fuzzy set. In this paper, we develop the Pythagorean fuzzy set based DEMATEL method and apply it to solve the supplier selection problem in sustainable supply chain management. We consider the Pythagorean fuzzy set for handling uncertain and incomplete information while selecting the criteria of a supplier and dealing with ambiguity of human decisions. Considering the independence of the criteria, we put forward the proposed method which gives mutual relationships among the criteria, and identifies cause–effect components of the system. The proposed method is illustrated numerically based on data collected from a group of professional personnel.

Application of MBJ - Neutrosophic Set on Filters of Incline Algebra

The concept of fuzzy set has been generalized to many kinds and one among them is neutrosophic set which is a developed from intuitionistic fuzzy set by adding a components called indeterminate function between truth and falsity membership function. This neutrosophic set also moved a step forward and shows a variation in indeterminate function alone as an interval valued indeterminate function and other functions remains same and this is named as MBJ - neutrosophic set. Here, this work on the MBJ - neutrosophic set merged with incline algbera and introduces the idea of MBJ - neutrosophic filter of an incline algebraic structure and is engrossing with several results. Also, the level, cartesian product, projection, characteristic function and chain conditions are also disputed.

Dombi-Normalized Weighted Bonferroni Mean Operators with Novel Multiple-Valued Complex Neutrosophic Uncertain Linguistic Sets and Their Application in Decision Making

Although fuzzy set concepts have evolved, neutrosophic sets are attracting more attention due to the greater power of the structure of neutrosophic sets. The ability to account for components that are true, false or neither true nor false is useful in the resolution of real-life problems. However, simultaneous variations render neutrosophic sets unsuitable in specific circumstances. To enable the management of these sorts of issues, we combine the principle of multi-valued neutrosophic uncertain linguistic sets and complex fuzzy sets to develop the principle of multi-valued complex neutrosophic uncertain linguistic sets. Multi-valued complex neutrosophic uncertain linguistic sets can contain grades of truth, abstinence, and falsity, and uncertain linguistic terms, which are expressed as complex numbers whose real and imaginary parts are limited to the unit interval. Some important Dombi laws are elaborated along with Bonferroni mean operators, which offer a flexible general structure with modifiable factors. Bonferroni means aggregation operators perform a significant role in conveying the magnitude level of options and characteristics. To determine relationships among any number of attributes, we develop multi-valued complex neutrosophic uncertain linguistic Dombi-normalized weighted Bonferroni mean operators and discuss their important properties with some special cases. By using these laws, we can deploy the multi-attribute decision-making (MADM) technique using the novel principle of multi-valued complex neutrosophic uncertain linguistic sets. To determine the power and flexibility of the elaborated approach, we resolve some numerical examples based on the proposed operator. Finally, the work is validated with the help of comparative analysis, a discussion of its advantages, and geometric expressions of the elaborated theories.

Fractional transportation problem under interval-valued Fermatean fuzzy sets

<abstract><p>The concept of an interval-valued Fermatean fuzzy set (IVFFS), an extension of Fermatean fuzzy sets, is a more resilient and reliable tool for dealing with uncertain and incomplete data in practical applications. The purpose of this paper is to define a triangular interval-valued Fermatean fuzzy number (TIVFFN) and its arithmetic operations. Fractional transportation problems (FTPs) have important implications for cost reduction and service improvement in logistics and supply management. However, in practical problems, the parameters in the model are not precise due to some unpredictable factors, including diesel prices, road conditions, weather conditions and traffic conditions. Therefore, decision makers encounter uncertainty when estimating transportation costs and profits. To address these challenges, we consider a FTP with TIVFFN as its parameter and call it an interval-valued Fermatean fuzzy fractional transportation problem (IVFFFTP). A new method for solving this IVFFFTP is proposed without re-transforming the original problem into an equivalent crisp problem. Illustrative examples are discussed to evaluate the precision and accuracy of the proposed method. Finally, the results of the proposed method are compared with those of existing methods.</p></abstract>

N,m-Rung Orthopair Fuzzy Sets With Applications to Multicriteria Decision Making

A q-rung orthopair fuzzy set is one of the effective generalizations of fuzzy set for dealing with uncertainties in information. Under this environment, in this study, we define a new type of extensions of fuzzy sets called n,m-rung orthopair fuzzy sets and investigate their relationship with Fermatean fuzzy sets, Pythagorean fuzzy sets and intuitionistic fuzzy sets. The n,m-rung orthopair fuzzy sets can supply with more doubtful circumstances than Fermatean fuzzy sets, Pythagorean fuzzy sets and intuitionistic fuzzy sets because of their larger range of depicting the membership grades. There is a symmetry between the values of this membership function and non-membership function. Here, any power function scales are utilized to widen the scope of the decision-making problems. In addition, the novel notion of an n,m-rung orthopair fuzzy set through double universes is more flexible when debating the symmetry between two or more objects that are better than the diffusing concept of an n-rung orthopair fuzzy set, as well as m-rung orthopair fuzzy set. The main advantage of n,m-rung orthopair fuzzy sets is that it can describe more uncertainties than Fermatean fuzzy sets, which can be applie in many decision-making problems. Then, we discover the essential set of operations for the n,m-rung orthopair fuzzy sets along with their several properties. Finally, we introduce a new operator, namely, n,m-rung orthopair fuzzy weighted power average (n,m-ROFWPA) over n,m-rung orthopair fuzzy sets and apply this operator to the MADM problems for evaluation of alternatives with n,m-rung orthopair fuzzy information.

Cubic m-polar fuzzy topology with multi-criteria group decision-making

<abstract><p>The concept of cubic m-polar fuzzy set (CmPFS) is a new approach to fuzzy modeling with multiple membership grades in terms of fuzzy intervals as well as multiple fuzzy numbers. We define some fundamental properties and operations of CmPFSs. We define the topological structure of CmPFSs and the idea of cubic m-polar fuzzy topology (CmPF topology) with P-order (R-order). We extend several concepts of crisp topology to CmPF topology, such as open sets, closed sets, subspaces and dense sets, as well as the interior, exterior, frontier, neighborhood, and basis of CmPF topology with P-order (R-order). A CmPF topology is a robust approach for modeling big data, data analysis, diagnosis, etc. An extension of the VIKOR method for multi-criteria group decision making with CmPF topology is designed. An application of the proposed method is presented for chronic kidney disease diagnosis and a comparative analysis of the proposed approach and existing approaches is also given.</p></abstract>

Linear Diophantine fuzzy graphs with new decision-making approach

<abstract><p>The concept of linear Diophantine fuzzy set (LDFS) is a new mathematical tool for optimization, soft computing, and decision analysis. The aim of this article is to extend the notion of graph theory towards LDFSs. We initiate the idea of linear Diophantine fuzzy graph (LDF-graph) as a generalization of certain theoretical concepts including, q-rung orthopair fuzzy graph, Pythagorean fuzzy graph, and intuitionistic fuzzy graph. We extend certain properties of crisp graph theory towards LDF-graph including, composition, join, and union of LDF-graphs. We elucidate these operations with various illustrations. We analyze some interesting results that the composition of two LDF-graphs is a LDF-graph, cartesian product of two LDF-graphs is a LDF-graph, and the join of two LDF-graphs is a LDF-graph. We describe the idea of homomorphisms for LDF-graphs. We observe the equivalence relation via an isomorphism between LDF-graphs. Some significant results related to complement of LDF-graph are also investigated. Lastly, an algorithm based on LDFSs and LDF-relations is proposed for decision-making problems. A numerical example of medical diagnosis application is presented based on proposed approach.</p></abstract>

Evaluation of Wind Turbine Failure Modes Using the Developed SWARA-CoCoSo Methods Based on the Spherical Fuzzy Environment

Accurately recognizing potential failures in the early stages of providing products or services can prevent the loss of investment and time and reduce the risk of safety hazards. Failure mode and effects analysis (FMEA) is a conventional approach for detecting and prioritizing the probable failures of a product’s design or production process. Nevertheless, the traditional risk priority number (RPN) method has come under criticism for its deficiencies. This paper proposes a modified FMEA method based on fuzzy Multi-Criteria Decision Making (MCDM) techniques to cope with the weaknesses of the previous methodologies and improve the primary method. The concept of spherical fuzzy sets (SFS) is utilized to address the vagueness and impreciseness of the information that allows the experts to have more freedom in making decisions by including membership, non-membership, and hesitation of fuzzy sets. Initially, the procedure of assigning weights to the RPN criteria is implemented with SFS step-wise weight assessment ratio analysis (SWARA). Then, the failure modes are ranked by the SFS combined compromise solution (CoCoSo) method. The effectiveness and practicality of the suggested approach are illustrated through a case study on the Manjil wind farm in Iran. Results show that the suggested model is more reliable and realistic to be utilized in the prioritization of failures than the common FMEA method or other integrated MCDM approaches.

A novel decision making technique based on spherical hesitant fuzzy Yager aggregation information: application to treat Parkinson's disease

<abstract><p>The concept of spherical hesitant fuzzy set is a mathematical tool that have the ability to easily handle imprecise and uncertain information. The method of aggregation plays a great role in decision-making problems, particularly when there are more conflicting criteria. The purpose of this article is to present novel operational laws based on the Yager t-norm and t-conorm under spherical hesitant fuzzy information. Furthermore, based on the Yager operational laws, we develop the list of Yager weighted averaging and Yager weighted geometric aggregation operators. The basic fundamental properties of the proposed operators are given in detail. We design an algorithm to address the uncertainty and ambiguity information in multi-criteria group decision making (MCGDM) problems. Finally, a numerical example related to Parkinson disease is presented for the proposed model. To show the supremacy of the proposed algorithms, a comparative analysis of the proposed techniques with some existing approaches and with validity test is presented.</p></abstract>

SIFAT-SIFAT MATRIKS LUNAK FUZZY INTUISIONISTIK

Fuzzy soft sets is one of the mathematical tools that are used to deal with the problem of uncertainty, such as problems in the field of economic, health, and others. The concept of fuzzy soft sets is extended into intuitiononistic fuzzy soft sets to intuitiononistic fuzzy soft matrices. This article examines the intuitionistic fuzzy soft matrix and defines the various types and operations of the intuitionistic fuzzy soft matrix. In addition, the application of an intuitionistic fuzzy soft matrix is ​​given to decision-making problems such as the selection of swimming athletes who have the best swimming techniques.

Multi-Attribute Decision-Support System Based on Aggregations of Interval-Valued Complex Neutrosophic Hypersoft Set

Hypersoft set is an emerging field of study that is meant to address the insufficiency and the limitation of existing soft-set-like models regarding the consideration and the entitlement of multi-argument approximate function. This type of function maps the multi-subparametric tuples to the power set of the universe. It focuses on the partitioning of each attribute into its attribute-valued set that is missing in existing soft-set-like structures. This study aims to introduce novel concepts of complex intuitionistic fuzzy set and complex neutrosophic set under the hypersoft set environment with interval-valued settings. Two novel structures, that is, interval-valued complex intuitionistic hypersoft set (IV-CIFHS-set) and interval-valued complex neutrosophic hypersoft set (IV-CNHS-set), are developed via employing theoretic, axiomatic, graphical, and algorithmic approaches. After conceptual characterization of essential elementary notions of these structures, decision-support systems are presented with the proposal of algorithms to assist the decision-making process. The proposed algorithms are validated with the help of real-world applications. A comprehensive inter-cum-intra comparison of proposed structures is discussed with the existing relevant models, and their generalization is elaborated under certain evaluating features.

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.

Bipolar Complex Fuzzy Soft Sets and Their Application

We introduce a new computational model to solve efficient problems. This research generalizes the concept of bipolar fuzzy soft sets (BFSS) to the realm of complex numbers. However, the ranges of positive and negative values membership BFSS functions are extended to unit disk instead of [0, 1] and [-1, 0] respectively. The main benefit of bipolar complex fuzzy soft sets BCFSSs appears in the ability to transfer bipolar fuzzy soft information to a mathematical formula without losing the full meaning of information that may appear from different phases. Some basic operations and theorems on BCFSS are defined with numerical examples. This research has extended to illustrate the utilization of BCFSS in decision making problems by generalizing the applications and algorithms.

Complex linear Diophantine fuzzy sets and their cosine similarity measures with applications

In this paper, the concept of complex linear Diophantine fuzzy set (CLDFS), which is obtained by integrating the phase term into the structure of the linear Diophantine fuzzy set (LDFS) and thus is an extension of LDFS, is introduced. In other words, the ranges of grades of membership, non-membership, and reference parameters in the structure of LDFS are extended from the interval [0, 1] to unit circle in the complex plane. Besides, this set approach is proposed to remove the conditions associated with the grades of complex-valued membership and complex-valued non-membership in the framework of complex intuitionistic fuzzy set (CIFS), complex Pythagorean fuzzy set (CPyFS), and complex q-rung orthopair fuzzy set (Cq-ROFS). It is proved that each of CIFS, CPyFS, and Cq-ROFS is a CLDFS, but not vice versa. In addition, some operations and relations on CLDFSs are derived and their fundamental properties are investigated. The intuitive definitions of cosine similarity measure (CSM) and cosine distance measure (CDM) between two CLDFSs are introduced and their characteristic principles are examined. An approach based on CSM is proposed to tackle medical diagnosis issues and its performance is tested by dealing with numerical examples. Finally, a comparative study of the proposed approach with several existing approaches is created and its advantages are discussed.

Application of Pythagorean Fuzzy Digraphs in Package Delivery Robots

The fuzzy set concept was developed to cope with uncertainty, whereas traditional sets are intended to deal with certainty. To address flaws in fuzzy set theory, extensions such as Intuitionistic Fuzzy Set (IFS), neutrosophic fuzzy sets, image fuzzy sets, and Pythagorean fuzzy set (PyFS) were developed. Pythagorean fuzzy set is useful tool for more clearly defining hazy concepts. In comparison to other fuzzy models, Pythagorean fuzzy set-based models allow more flexibility in handling human judgement information. The fuzzy graph structure is used to deal with the uncertainty in a network and to characterize its relationship with the non-empty vertex set. Pythagorean fuzzy graph (PyFG) was one of the Intuitionistic Fuzzy Graph (IFG) extensions. PyFG was created to cope with the uncertainty of an object and its relationship with other objects. PyFS and PyFG are the driving forces behind this innovative concept. This work defines Pythagorean Fuzzy Digraph (PyFDG), and PyFDG's score function. An algorithm is proposed for an issue to find the Pythagorean shortest path in package delivery robots.

New entropy propositions for interval‐valued spherical fuzzy sets and their usage in an extension of ARAS (ARAS‐IVSFS)

AbstractThe spherical fuzzy set (SFS) concept and its interval‐valued version (IVSFS) are among the recent developments aiming at handling the hesitancy representation issue in multiple attribute decision‐making problems. In SFS, decision‐makers can assign independent membership, non‐membership, and hesitancy degrees. IVSFS extends this feature by assigning intervals to these three degrees. In this manner, the uncertainty, vagueness, and ambiguity hidden in human judgements can be quantified and processed more comprehensively. In multiple attribute decision‐making problems, the attribute weights are not commonly known. To determine these weights, there are two families of methods: subjective and objective ones. While subjective methods need expert judgements in weighting, objective methods can reveal the weights from the current dataset. Entropy‐based weighting technique is one of the well‐known objective methods. In the study, two IVSFS entropy expressions are introduced, and their practicality is presented in obtaining objective weights. Then, an IVSFS extension of Additive Ratio Assessment Method is proposed and integrated with the entropy‐based weighting schema. The proposition is applied in solving a 3D printer selection problem and a comparative analysis is conducted to check its robustness and validity.

Fuzzy Sets in Hyper UP-algebra

In this paper, we apply the concept of fuzzy set to hyper UP-subalgebras. We introduce the notions of fuzzy hyper UP-subalgebra and fuzzy hyper UP-filter and establish some of their properties. Furthermore, some properties of hyper homomorphism in relation to fuzzy hyper UP-subalgebras and fuzzy hyper UP-filter are also presented.

Rough q-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making

Yager recently introduced the q-rung orthopair fuzzy set to accommodate uncertainty in decision-making problems. A binary relation over dual universes has a vital role in mathematics and information sciences. During this work, we defined upper approximations and lower approximations of q-rung orthopair fuzzy sets using crisp binary relations with regard to the aftersets and foresets. We used an accuracy measure of a q-rung orthopair fuzzy set to search out the accuracy of a q-rung orthopair fuzzy set, and we defined two types of q-rung orthopair fuzzy topologies induced by reflexive relations. The novel concept of a rough q-rung orthopair fuzzy set over dual universes is more flexible when debating the symmetry between two or more objects that are better than the prevailing notion of a rough Pythagorean fuzzy set, as well as rough intuitionistic fuzzy sets. Furthermore, using the score function of q-rung orthopair fuzzy sets, a practical approach was introduced to research the symmetry of the optimal decision and, therefore, the ranking of feasible alternatives. Multiple criteria decision making (MCDM) methods for q-rung orthopair fuzzy sets cannot solve problems when an individual is faced with the symmetry of a two-sided matching MCDM problem. This new approach solves the matter more accurately. The devised approach is new within the literature. In this method, the main focus is on ranking and selecting the alternative from a collection of feasible alternatives, reckoning for the symmetry of the two-sided matching of alternatives, and providing a solution based on the ranking of alternatives for an issue containing conflicting criteria, to assist the decision-maker in a final decision.

New Generalized Intuitionistic Fuzzy Divergence Measure with Applications to Multi-Attribute Decision Making and Pattern Recognition

Background: The notion of fuzzy set was introduced by Zadeh. After that, many researchers extended the concept of fuzzy sets in different ways. Atanassov introduced the concept of intuitionistic fuzzy sets as an extension of fuzzy sets. This concept is applied in many fields such as bio-informatics, image processing, decision making, feature selection, pattern recognition, etc. Objectives: The prime objective of this paper is to introduce a new generalized intuitionistic fuzzy divergence measure with proof of its validity and discussions on its elegant properties. Applications of the proposed divergence measure in multi-attribute decision making and pattern recognition are also discussed with some numerical illustrations. Further, the proposed divergence measure is compared with other methods for solving MADM and pattern recognition problems which exist in the literature. Methods: The divergence measure method is used to measure the divergence between two given sets. In addition, the results of the other existing measures are also given to compare with the proposed measure. Results: It was observed that the proposed divergence measure found much better results in comparison with the other existing methods. Conclusion: A new divergence measure for intuitionistic fuzzy sets is introduced with some of its properties. Applications of the proposed divergence measure to pattern recognition and MADM are illustrated through examples. The comparison of the proposed method with the existing methods shows the legacy of the results of the proposed method. It is concluded that the proposed divergence measure is effective for solving real-world problems related to MADM and pattern recognition.

Analysis of the Shortest Path in Spherical Fuzzy Networks Using the Novel Dijkstra Algorithm

The concept of fuzzy graph (FG) and its generalized forms has been developed to cope with several real-life problems having some sort of imprecision like networking problems, decision making, shortest path problems, and so on. This paper is based on some developments in generalization of FG theory to deal with situation where imprecision is characterized by four types of membership grades. A novel concept of T-spherical fuzzy graph (TSFG) is proposed as a common generalization of FG, intuitionistic fuzzy graph (IFG), and picture fuzzy graph (PFG) based on the recently introduced concept of T-spherical fuzzy set (TSFS). The significance and novelty of proposed concept is elaborated with the help of some examples, graphical analysis, and results. Some graph theoretic terms are defined and their properties are studied. Specially, the famous Dijkstra algorithm is proposed in the environment of TSFGs and is applied to solve a shortest path problem. The comparative analysis of the proposed concept and existing theory is made. In addition, the advantages of the proposed work are discussed over the existing tools.