Complex-Fuzzy Adaptive Image Restoration – An Artificial-Bee-Colony-Based Learning Approach

Self-learning complex neuro-fuzzy system with complex fuzzy sets and its application to adaptive image noise canceling

The innovative concept of Complex Fuzzy Set is introduced. The objective of the this paper to investigate the concept of Complex Fuzzy set in constraint to a traditional Fuzzy set , where the membership function ranges from [0, 1], but in the Complex fuzzy set extended to a unit circle in a complex plane, where the member ship function in the form of complex number. The Compressive study of mathematical operation of Complex Fuzzy set is presented. The basic operation like addition, subtraction, multiplication and division are described here. The Novel idea of this paper to measure the similarity between two fuzzy relations by evaluating δ -equality. Here also we introduce the probabilistic interpretation of the complex fuzzy set where we attempted to clarify the distinction between Fuzzy logic and probability. KEY WORD Complex fuzzy set, Complex fuzzy relation, complement of complex fuzzy relation, δ -equality, probability.

In recent days researchers have tried to handle the maximum information and use those techniques and methods in which there is no chance of data loss or loss of information is minimum. The structure like fuzzy set and complex fussy set cannot discuss the upper and lower approximations. Moreover, we can observe that a fuzzy rough set cannot discuss the second dimension and in this case, there is a chance of data loss. To cover all these issues in previous ideas, the notion of a complex fuzzy rough set in Cartesian form is the demand of the day because this structure can discuss the second dimension as well as upper and lower approximations. For this purpose, in this manuscript, we have developed the theory of complex fuzzy relation and complex fuzzy rough set in Cartesian form. Moreover, we have initiated the fundamental laws for complex fuzzy rough numbers based on Frank t-norm and t-conorm. The fundamental tools that can convert the overall input into a single output are called aggregation operators (AOs). So based on the characteristics of AOs, we have defined the notion of complex fuzzy rough Frank average and complex fuzzy rough Frank geometric AOs. The utilization of the developed theory is necessary to show the importance and validity of the delivered approach. So based on developed notions, we have defined an algorithm for this purpose along with an illustrative example. We have utilized the introduced structure for the classification of AI tools for civil engineering. Moreover, the comparative analysis of the delivered approach shows the advancement of the introduced structure as compared to existing notions.

Mushrooms are food ingredient that is currently favored by the public. Seeing the large demand for mushrooms, many mushroom businesses have developed. The high level of demand for mushrooms by consumers in different locations results in the high time and costs spent in distributing mushrooms. In addition, determining distribution routes in mushroom marketing is still done manually based on the sender's knowledge, therefore reduces the effectiveness and efficiency of mushroom marketing because the distribution routes used are not optimal. To overcome these problems, it is necessary to determine an effective and efficient distribution route to reduce distribution costs and speed up distribution time. Based on these problems, this research uses the Artificial Bee Colony (ABC) method in determining the distribution route of mushroom harvest. The purpose of this study was to apply the ABC method in determining the distribution routes of mushroom harvest. The result of this research is a visualization of mushroom distribution routes using the ABC method, so it can help to distribute mushroom harvest effectively and efficiently. The research method consists of defining the problem, collecting data, analyzing systems and implementing methods, designing systems, building systems, and drawing conclusions.

In this manuscript we demonstrate interval-valued bipolar complex fuzzy set (IVBCFS) and then interval-valued bipolar complex fuzzy soft set (IVBCFSS), as a generalization of fuzzy set, interval-valued fuzzy set, bipolar fuzzy set, complex fuzzy set and soft set. We also initiate operational laws and basic results and properties for IVBCFS and IVBCFSS. Further explanation is given for the basic algebraic operations like complement, extended union, extended intersection, restricted union, and restricted intersection, AND product and OR product for IVBCFSS. Moreover, we demonstrate some fundamental aggregation operators like IVBCFS average aggregation, IVBCFS geometric and as well as their properties. To emphasize the usefulness and application of the system, we also develop the decision-making method and joint instances of the IVBCFSS (set-ups 1 and 2). In order to describe the effectiveness and influence of the approaching novel work, this study uses a comparative analysis of the new creating concept with prevailing ideas.

The interval‐valued q‐rung orthopair fuzzy set (IVq‐ROFS) and complex fuzzy set (CFS) are two generalizations of the fuzzy set (FS) to cope with uncertain information in real decision making problems. The aim of the present work is to develop the concept of complex interval‐valued q‐rung orthopair fuzzy set (CIVq‐ROFS) as a generalization of interval‐valued complex fuzzy set (IVCFS) and q‐rung orthopair fuzzy set (q‐ROFS), which can better express the time‐periodic problems and two‐dimensional information in a single set. In this article not only basic properties of CIVq‐ROFSs are discussed but also averaging aggregation operator (AAO) and geometric aggregation operator (GAO) with some desirable properties and operations on CIVq‐ROFSs are discussed. The proposed operations are the extension of the operations of IVq‐ROFS, q‐ROFS, interval‐valued Pythagorean fuzzy, Pythagorean fuzzy (PF), interval‐valued intuitionistic fuzzy, intuitionistic fuzzy, complex q‐ROFS, complex PF, and complex intuitionistic fuzzy theories. Further, the Analytic hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) method are also examine based on CIVq‐ROFS to explore the reliability and proficiency of the work. Moreover, we discussed the advantages of CIVq‐ROFS and showed that the concepts of IVCFS and q‐ROFS are the special cases of CIVq‐ROFS. Moreover, the flexibility of proposed averaging aggregation operator and geometric aggregation operator in a multi‐attribute decision making (MADM) problem are also discussed. Finally, a comparative study of CIVq‐ROFSs with pre‐existing work is discussed in detail.

Capacitor Banks provide reactive power to improve voltage levels and will minimize power losses in the electric power system. In the South Sulawesi electric power system there are variations of buses so that the capacitor installed really needs to optimize the location and capacity of the capacitor. The Artificial Bee Colony (ABC) method is used in determining the location and magnitude of the compensator (capacitor bank) on the 150 kV high voltage transmission system in South Sulawesi. The purpose of this use is to determine the ability of ABC as a solution to the optimization method for improving voltage levels and minimizing power losses in high voltage transmissions. There are 7 scenarios carried out in this research, scenarios 2, 3, and 4 using conventional methods, scenarios 5 to 7 applying the ABC method. The results of these 6 scenarios are an increase in the voltage on the bus and the minimization of power losses in the South Sulawesi system. And the ABC method optimizes the operation of the electric power system.

Complex fuzzy set (CFS), as a generalization of fuzzy set (FS), is characterized by complex-valued membership degrees. By considering the complex-valued membership degree as a vector in the complex unit disk, we introduce the cosine similarity measures between CFSs. Then, we investigate some invariance properties of the cosine similarity measure. Finally, the cosine similarity measure is applied to measure the robustness of complex fuzzy connectives and complex fuzzy inference.

Recently, complex fuzzy sets have become a powerful tool for expanding the range of fuzzy sets that are located in a unit disk within complex plane. In this article, the complex fuzzy numbers are discussed and implemented to handle complex fractional fuzzy partial differential equation involving complex time-fractional fuzzy heat equation in sense of Hukuhara differentiability. After that, an explicit finite difference scheme known as the forward time center space are implemented to solve complex time-fractional fuzzy heat equations. The uncertainty present in our problem appears in the boundary and initial conditions as well as coefficients in both amplitude and phase terms simultaneously where the Convex normalized triangular fuzzy numbers are extended to unit disk in the complex plane. The properties and benefits of complex fuzzy set theory have been employed in the proposed numerical methods. A numerical experiment is used to showcase the efficiency and practicality of the presented method. The obtained outcomes are found to be consistent with the exact solution and related theoretical concepts.

Contemporary research has refined systems with complex fuzzy sets in order to improve the design and model of real-life applications. Symmetry and antisymmetry are basic characteristics of binary relations used when modeling the decision maker’s preferences. A recent focus has been the analysis of a complex data set using the properties of fuzzy concept lattice and the complex soft set. We will introduce a new concept to represent the information which utilizes the time factor, called fuzzy parameterized complex multi-fuzzy soft expert set ( F P - CMFSES ), and investigate part of its fundamental properties. This F P - CMFSES model allows us to validate the information provided by an expert, at a given phase of time, using the properties of complex fuzzy sets. We then construct an algorithm based on this concept by converting it from the complex state to the real state. Eventually, we implement it to a decision-making problem to demonstrate the applicability of the suggested method. A comparison among F P - CMFSES and other existing methods is made to expose the dominance of the suggested method. Apart from that, we also propose the weighted fuzzy parameterized complex multi-fuzzy soft expert set and investigate its application to decision-making.

A complex fuzzy set (CFS) is described by a complex-valued truth membership function, which is a combination of a standard true membership function plus a phase term. In this paper, we extend the idea of a fuzzy graph (FG) to a complex fuzzy graph (CFG). The CFS complexity arises from the variety of values that its membership function can attain. In contrast to a standard fuzzy membership function, its range is expanded to the complex plane’s unit circle rather than [0,1]. As a result, the CFS provides a mathematical structure for representing membership in a set in terms of complex numbers. In recent times, a mathematical technique has been a popular way to combine several features. Using the preceding mathematical technique, we introduce strong approaches that are properties of CFG. We define the order and size of CFG. We discuss the degree of vertex and the total degree of vertex of CFG. We describe basic operations, including union, join, and the complement of CFG. We show new maximal product and symmetric difference operations on CFG, along with examples and theorems that go along with them. Lastly, at the base of a complex fuzzy graph, we show the application that would be important for measuring the symmetry or asymmetry of acquaintanceship levels of social disease: COVID-19.

As a generalization of complex fuzzy set (CFS), complex hesitation fuzzy set (CHFS) is a powerful tool to express two-dimensional fuzzy information, but it ignores the randomness that exists widely in real life. Considering the randomness and ambiguity often simultaneously occur in real-world problems, we come up with an innovative fuzzy set called complex probabilistic hesitant fuzzy set (CPHFS) in this article, which is a joint extension of CFS and probabilistic hesitant fuzzy set (PHFS). Moreover, we establish four basic operations for complex probabilistic hesitant fuzzy element(CPHFE) and a series of useful operational laws are also developed. Secondly, several aggregation operators including complex probabilistic hesitant fuzzy weighted averaging operator(CPHFWA), complex probabilistic hesitant fuzzy weighted geometric operator(CPHFWG), complex probabilistic hesitant fuzzy Heronian Mean operator(CPHFHM) and complex probabilistic hesitant fuzzy Geometric Heronian Mean operator(CPHFGHM) as well as their weighted forms that can reflect the interrelationship among all decision attributes are proposed, which is of great use in multi-attribute decision making(MADM) or in multi-attribute group decision making(MAGDM) issues when we want to synthesize multiple evaluation values into one. Besides, we also present a number of valuable properties of these provided aggregation operators. Thirdly, a MADM process is built in the CPHF environment step by step based on the aggregation operators we have just established. Furthermore, we provide an example about purchasing a most suitable car to demonstrate the effectiveness and practicability of the proposed decision process. Finally, we point out the superiorities of MADM in working under the CPHF environment through comparing it with the existing method and also offer some possible prospects for further research. The method displayed in this work can effectively solve the MADM problems where the decision-making information is described by CPHFEs and the attributes are interactive.

Complex fuzzy sets (CFS) generalize traditional fuzzy sets (FS) since the membership functions of CFS reduces to the membership functions of FS. FS values are always at [0, 1], unlike CFS which has values in the unit disk of C. This paper merges notion and concept in group theory and presents the notion of a complex fuzzy subgroup of a group. This proposed idea represents a more general and better optional mathematical tool as one of the approaches in the fuzzy group. However, this research defines the notion of complex fuzzy subgroupiod, complex fuzzy normal subgroup, and complex fuzzy left(right) ideal. Therefore, the lattice, homomorphic preimage, and image of complex fuzzy subgroupiod and ideal are introduced and studied its properties. Finally, complex fuzzy subgroups and their properties are presented and investigated

<p>Complex spherical fuzzy sets (CSFSs) are a theory that addresses confusing and unreliable information in real-life decision-making contexts by integrating elements of two theories: spherical fuzzy sets (SFSs) and complex fuzzy sets (CFSs). CSFSs are classified into three categories, represented by polar coordinates: membership, nonmember, and abstention. These grades are located on a complex plane within a unit disc. It is necessary for the total squares representing the real components of the grades for abstinence, membership, and non-membership to not surpass a certain interval. Several aspects of CSFS and the corresponding operational laws were examined in this work. The key components of this article were based on CSFs, including complex spherical fuzzy Schweizer-Sklar prioritized aggregation (CSFSSPA), complex spherical fuzzy Schweizer-Sklar weighted prioritized aggregation (CSFSSWPA), complex spherical fuzzy Schweizer-Sklar prioritized geometry (CSFSSPG), and complex spherical fuzzy Schweizer-Sklar prioritized weighted geometry (CSFSSWPG). Additionally, the suggested operators' specific instances were examined. The main outcome of this work includes new aggregation techniques for CSFS information, based on t-conorm and t-norm from Schweizer-Sklar (SS). The basic characteristics of the operators were established by this study. We looked at a numerical example centered on efficient mobile e-tourism selection to show the effectiveness and viability of the recommended approaches. Additionally, we carried out a thorough comparative analysis to assess the outcomes of the suggested aggregation approaches in comparison to the current methods. Last, we offer an overview of the planned study and talk about potential directions for the future.</p>

<abstract> <p>A complex intuitionistic fuzzy set is a generalization framework to characterize several applications in decision making, pattern recognition, engineering, and other fields. This set is considered more fitting and coverable to Intuitionistic Fuzzy Sets (IDS) and complex fuzzy sets. In this paper, the abstraction of (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$) complex intuitionistic fuzzy sets and (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroups were introduced regarding to the concept of complex intuitionistic fuzzy sets. Besides, we show that (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroup is a general form of every complex intuitionistic fuzzy subgroup. Also, each of (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy normal subgroups and cosets are defined and studied their relationship in the sense of the commutator of groups and the conjugate classes of group, respectively. Furthermore, some theorems connected the (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroup of the classical quotient group and the set of all (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy cosets were studied and proved. Additionally, we expand the index and Lagrange's theorem to be suitable under (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroups.</p> </abstract>