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Multi-attribute decision making is aimed at identifying the problem of ranking the finite alternatives or selecting the best alternatives within feasible alternatives. In this study, we investigate two new notions, namely q-rung orthopair multi-fuzzy set and q-rung orthopair multi-fuzzy soft set, which combine the benefits of both q-rung orthopair fuzzy set and multi-fuzzy soft set. The eminent characteristic of these two new notions is their ability to overcome the insufficiency of the q-rung orthopair fuzzy set and multi-fuzzy soft set. It is observed that the nature of the q-rung orthopair multi-fuzzy set and the q-rung orthopair multi-fuzzy soft set is more beneficial for expressing unclear and vague information. Some of their fundamental operations, namely complement, equality, subset, union and intersection operations, are defined. Next, the TOPSIS mechanism using the correlation coefficient has been presented to rank the best airlines to fly during the COVID-19 pandemic in a q-rung orthopair multi-fuzzy soft environment. Finally, a comparative analysis of the developed approach is given to ensure the supremacy of the proposed method in the existing literature. [ABSTRACT FROM AUTHOR]

A well-researched field is the development of Computer Aided Diagnosis (CADx) Systems for the benign-malignant classification of abnormalities detected by mammography. Due to the nature of the breast parenchyma, there are significant uncertainties about the shape and geometry of the abnormalities that may lead to an inaccurate diagnosis. These same uncertainties give mammograms a fuzzy character that is essential to the application of fuzzy processing. Fuzzy set theory considers uncertainty in the form of a membership function, and therefore fuzzy sets can process imperfect data if this imperfection originates from vagueness and ambiguity rather than randomness. Fuzzy contrast enhancement can improve edge detection and, by extension, the quality of related classification features. In this paper, classical (Linguistic hedges and fuzzy enhancement functions), advanced fuzzy sets (Intuitionistic fuzzy set (ΙFS), Pythagorean fuzzy set (PFS), and Fermatean fuzzy sets (FFS)), and a Genetic Algorithm optimizer are proposed to enhance the contrast of mammographic features. The advanced fuzzy sets provide better information on the uncertainty of the membership function. As a result, the intuitionistic method had the best overall performance, but most of the techniques could be used efficiently, depending on the problem that needed to be solved. Linguistic methods could provide a more manageable way of spreading the histogram, revealing more extreme values than the conventional methods. A fusion technique of the enhanced mammography images with Ordered Weighted Average operators (OWA) achieves a good-quality final image. [ABSTRACT FROM AUTHOR]

The selection of antivirus masks is an important problem in the context of the ongoing COVID-19 pandemic. Multiple attribute decision-making (MADM) algorithmic approaches can be used to evaluate and compare different masks based on multiple criteria, such as effectiveness, comfort, and cost. An aggregation of interval-valued multi-fuzzy hypersoft sets provides a flexible framework for handling uncertainty and imprecision in the MADM process. This approach allows for the integration of multiple sources of information such as expert opinions and empirical data, and considers the different levels of uncertainty and ambiguity associated with each criterion. By using the matrix-manipulated aggregation of interval-valued multi-fuzzy hypersoft sets like the induced fuzzy matrix, α -level matrix, threshold matrix, and mid-threshold matrix, an algorithm is proposed for the optimal selection of material for manufacturing antivirus masks. The robustness of the algorithm is maintained by following simple computation-based stages that enable a wide range of multidisciplinary readers to understand the idea vividly. By using this algorithm, it is possible to improve the accuracy and reliability of the decision-making process and to better balance the trade-offs between the different criteria, i.e., the computed results of the proposed algorithm and the structural aspects of the proposed approach are both compared with some relevant existing structures. Computation-based and structural comparisons are presented to assess the adaptability and reliability of the study. The first one is meant to check reliability, while the second is meant to check flexibility. In both cases, however, the presented approach yields the required standard. By comparing the prospective structure to the relevant developed model, the implications of the proposed framework are explored. [ABSTRACT FROM AUTHOR]

We develop a novel mathematical tool known as complex multi-fuzzy soft set (CMFSS) which has the ability to handle uncertainties, imprecision, and vagueness of information that are inherent in the data by considering the amplitude and phase terms of the complex numbers simultaneously. This CMFSS constitutes of a hybrid structure of multi-fuzzy set and soft set which are defined in a complex setting. The structure is flexible as it allows for a greater range of values for the membership function by extending them to the unit circle in a complex plane through modification of the multi-fuzzy soft set by the inclusion of an additional term called the phase term in order to take into account of the periodic nature of the data. Accordingly, the novelty of this paper lies in the complex multi-membership functions which consider more range of values while handling the uncertainty of the periodic data. In this paper, the concept of complex multi-fuzzy soft set is introduced. We then define its basic operations of complement, union and intersection and study some related properties, with supporting proofs. Subsequently, by means of level soft sets, we present an algorithm to solve a CMFSSs decision making problem, to illustrate the effectiveness and practicality of the proposed concept. Finally, we introduce axiomatic definitions of entropy and similarity measure for CMFSSs, and some formulas have also been put forward to calculate them. Numerical examples are given to demonstrate that the proposed entropy measure for CMFSSs is an important concept for measuring uncertainty in the information/data. Furthermore, some theorems are proposed showing how the entropy of CMFSS can be found from the similarity measure of CMFSS.

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.

In this paper, we generalize the definition of Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions.

The paper presents the concept of multi-fuzzy set and its operations. In addition some algebraic structures of multi-fuzzy set were introduced; in particular, the lattice structures, semigroups and groupoids of multi-fuzzy set were established. Some related results were also provided. [ABSTRACT FROM AUTHOR]

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainty. In this work, new soft model, called the generalised multi-fuzzy bipolar soft model is proposed, and an algorithm based on this notion is presented. Some basic properties of this concept are studied and the related results are investigated. Finally, an application based on generalised multi-fuzzy soft sets in decision making is analyzed. [ABSTRACT FROM AUTHOR]

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with vagueness and uncertainties. It is worth noting that the decision making theory has been proven a more effective tool in the real-world problems under imprecise environments. In this paper, we introduce a new fuzzy soft model, called the multi-fuzzy bipolar soft set model. Some operations of this notion are first investigated and some of the related properties are studied. Finally, an algorithm based on multi-fuzzy bipolar soft set is presented and an illustrative example is given to analyze the application of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Soft set theory has been evolved as a completely new mathematical tool for modeling vague concepts. Yong Yang et.al propounded the theory of Multi-fuzzy soft set and its application to decision making. In this paper, we instigated the concept of Modular and Distributive in lattice ordered multi-fuzzy soft set () and also obtain relevant results. [ABSTRACT FROM AUTHOR]

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.

We introduce the concept of complex multi-fuzzy soft expert set (CMFSES) for which the range of its membership functions are rep- resented in terms of complex numbers. CMFSES has the ability to realize more range of values while handling uncertainty of data that is captured by the amplitude terms and phase terms of the complex numbers, simultaneously. It also has a mechanism to incorporate the adequate parameterization capabilities and the opinions of all experts regarding the validity of the information at hand in one mode, thus making it quite appropriate for use in decision-making problems, whereas the time factor plays a key role in determining the final decision. Some operations related to this new concept have been defined, such as complement, union and intersection, AND and OR operations. We also investigate structural properties of these operations based on this concept. An algorithm is developed in complex multi-fuzzy expert soft set setting for a decision making method. Finally an illustrative example is employed to show that it can be successfully applied to problems that contain uncertainties. In addition, a comparison between CMFSES and other existing methods is made to reveal the dominance of our proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we first proposed the extension principles of neutrosophic multi-sets and cut sets which are a bridge between neutrosophic multi-sets and crisp sets. Then the representation theorem of neutrosophic multi-sets based on cut sets are studied. Finally, the addition, subtraction, multiplication and division operations over neutrosophic multi-sets are defined based on the extension principle. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the definition of Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to correct the assertions (3) and (4) of Theorem 3.23 proposed by Zhang and Shu [Journal of Intelligent and Fuzzy Systems 27 (2014) 2115-2125]. A counterexample illustrates the flaw of the assertions.We introduce the notion of generalized possibility multi-fuzzy soft sets and use it to correct the flawin those assertions. Finally we introduce two new definitions and five theorems to improve the work of Zhang and Shu, along with two examples. [ABSTRACT FROM AUTHOR]

Fuzzy membrane computing is a newly developed and promising research direction in the area of membrane computing that aims at exploring the complex interaction between membrane computing and fuzzy theory. This paper provides a comprehensive survey of theoretical developments and various applications of fuzzy membrane computing, and sketches future research lines. The theoretical developments are reviewed from the aspects of uncertainty processing in P systems, fuzzification of P systems and fuzzy knowledge representation and reasoning. The applications of fuzzy membrane computing are mainly focused on fuzzy knowledge representation and fault diagnosis. An overview of different types of fuzzy P systems, differences between spiking neural P systems and fuzzy reasoning spiking neural P systems and newly obtained results on these P systems are presented. [ABSTRACT FROM AUTHOR]

The soft set theory, proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. By introducing a generalization parameter which itself is multi-fuzzy, we define the concept of possibility multi-fuzzy soft sets. Some operations on a possibility multi-fuzzy soft set are investigated, such as complement operation, union and intersection operations, 'AND' and 'OR' operations. Then similarity measure between two possibility multi-fuzzy soft sets is discussed, and its application to medical diagnosis has been shown. Finally, a practical example is provided to illustrate the validity of possibility multi-fuzzy soft sets in decision making problem. [ABSTRACT FROM AUTHOR]

In this paper we propose a method to construct more general fuzzy sets using ordinary fuzzy sets as building blocks. We introduce the concept of multi-fuzzy sets in terms of ordered sequences of membership functions. The family of operations T, S, M of multi-fuzzy sets are introduced by coordinate wise t-norms, s-norms and aggregation operations. We define the notion of coordinate wise conjugation of multifuzzy sets, a method for obtaining Atanassov's intuitionistic fuzzy operations from multi-fuzzy sets. We show that various binary operations in Atanassov's intuitionistic fuzzy sets are equivalent to some operations in multi-fuzzy sets like M operations, 2-conjugates of the T and S operations. It is concluded that multi-fuzzy set theory is an extension of Zadeh's fuzzy set theory, Atanassov's intuitionsitic fuzzy set theory and L-fuzzy set theory. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 ( L M F S S ) has been applied in forecasting process. However, similarity measure is not used in this application. In our research, similarity measure of L M F S S is proposed to calculate the similarity between two L M F S S s . Moreover, some of its properties are introduced and proved. Finally, an application of L M F S S in decision making using similarity measure is analysed. [ABSTRACT FROM AUTHOR]