Journal of Fuzzy Extension and Applications
Volume:4 Issue: 4, Autumn 2023

In this present study, the tumor growth model using the Gompertz equation with the Allee effect is developed under a fuzzy environment using the Generalized Hukuhara Derivative  (GHD) approach. To capture the tumor growth patterns with the Allee threshold, the parameters present in the model vary from time to time, and in real life, it is very difficult to estimate the exact cell count. In this vague situation, the initial condition, coefficient, and both together are taken as the fuzzy number. In this paper, the  GHD  approach is used to solve the fuzzy tumor growth model in which four different cases are considered with respect to (i)-gH differentiability and (ii)-gH differentiability concept. The main objective of this study is to present a significant reduction in uncertainty while modeling the tumor growth in a fuzzy environment with the Allee effect. Finally, the proposed model and technique are illustrated by numerical simulation and analysis of tumor growth is conducted.

This study introduces an approach for Multiple Attribute Decision-Making (MADM) that deals with the complexity of Single-Valued Neutrosophic Uncertain Linguistic Variables (SVNULVs). This method is engineered to grasp the interconnectedness of multiple inputs and to meet the diverse requirements for semantic transformations. Due to the shortcomings of existing operational rules in terms of closeness and flexibility, this paper proposes a novel set of operational rules and a ranking process for SVNULVs, integrating the concept of a Linguistic Scale Function (LSF). We propose an innovative operator along with its weighted counterpart to amalgamate SVNULVs, thereby characterizing the dynamics among various inputs through these new operations. Concurrently, we scrutinize and discuss the unique cases and favorable properties of these proposed operators. Building upon this new operator, the paper also unveils a fresh MADM methodology leveraging SVNULVs. To validate the effectiveness of this proposed methodology, an illustrative example is employed, demonstrating the precision of the method and its advantages over existing MADM techniques.

In this paper, the (α,β)-level sets where α and β are elements in the interval [0,1] is introduced. Several related properties for (α,β)-cut of intuitionistic fuzzy normed ideals in a normed ring (NR) will be studied and proven. Further, for any two normed rings NR,NR^' with a mapping f:NR → NR^', a relation between the intuitionistic fuzzy normed ideal I of NR and the intuitionistic fuzzy normed ideal f(I) (the image of I) of NR^' will been obtained with the support of their (α,β)-level subsets.

DEMATEL serves as a tool for addressing multi-criteria decision-making problems, primarily by identifying critical factors that exert the most significant influence on a specific system. To enhance its capabilities in handling contextual decision problems, DEMATEL has been further developed through integration with various other MCDM methods. The inherent reliance on direct input from experts for initial decision information in DEMATEL raises concerns about the potential limitations imposed by experts' domain knowledge and bounded rationalities. The effectiveness of decision-making can be compromised if the initial information provided by experts is deemed unreliable, leading to debatable outcomes. To address these challenges, this study proposes the incorporation of a Bonferroni mean aggregation operator within a Pythagorean neutrosophic environment, illustrated through a numerical example applied to DEMATEL. This integration is intended to fortify decision accuracy by introducing a more enhanced decision framework by developing a new normalized weighted Bonferroni mean operator for Pythagorean neutrosophic set aggregation (PN-NWBM). By integrating this operator, this study aims to alleviate the impact of unreliable initial information and enhance the overall reliability of decision outcomes thereby contributing to its improvement in decision making. Through the implementation of the Bonferroni mean aggregation operator, the study anticipates achieving a more comprehensive and accurate representation of decision factors as illustrated in the numerical example. This research includes a comparative and sensitivity analysis to thoroughly examine the implications and effectiveness of the proposed integration.

The Intuitionistic Fuzzy Sets (IFSs) are generalizations of Zadeh’s fuzzy sets, in which the elements of the universe have apart from Zadeh’s membership and the degree of non-membership in [0, 1]. This paper studies applications of intuitionistic Fuzzy Sets (FS) to assessment and multi-criteria decision making, which are very useful when uncertainty characterizes the grades or parameters respectively assigned to the elements of the universal set. Applications to everyday life situations are also presented illustrating our results.

Different frameworks can be chosen to solve Multi-Criteria Decision-Making (MCDM) problems emerging in business, cyber environment, economy, health care, engineering and other areas. Uncertainty, vagueness and non-rigid boundaries of the initial information are frequently noticed when dealing with the practicalities of the MCDM tasks. Single-valued neutrosophic sets are considered as the effective tool to express uncertainty of the information, however in some cases it lacks the desirable generality and flexibility. The Q-single-valued neutrosophic sets were recently proposed to deal with this situation. Then, we develop a VIKOR method based on the Q-single-valued neutrosophic sets for novel MCDM method. In the decision-making framework, the proposed method is not only a way to solve the problem of MCDM, but also contains an important mathematical idea as a different solution approach. By applying this method to the real-life problem of cyber warfare, demonstrated the flexibility, effectiveness and feasibility of the proposed VIKOR method and compare the obtained results with the results of other existing methods.

In this paper, we present a novel method for solving Fractional Transportation Problems (FTPs) with fuzzy numbers using a ranking function. The proposed method introduces a transformation technique that converts an FTP with fuzzy numbers into an FTP with crisp numbers by employing the robust ranking technique. Subsequently, we formulate two transportation problems, one for maximization and another for minimization, based on the given FTP. The optimal solution for the original FTP is then derived by leveraging the solutions obtained for the formulated transportation problems. By optimizing these single-objective transport problems, our method provides decision-makers with the ability to make satisfactory managerial decisions and evaluate economic operations when confronted with logistic problems involving fractional transportation. To demonstrate the effectiveness of the proposed approach, we present several illustrative examples that showcase its practical application and efficiency.