Journal of Fuzzy Extension and Applications
Volume:5 Issue: 3, Summer 2024

Group decision-making in capital investment involves a collaborative process where multiple stakeholders contribute their perspectives, insights, and expertise to evaluate investment opportunities and make informed decisions. This process's practical and methodological aims can vary depending on the organization's goals, industry, and market conditions. Researching capital investment group decision-making is motivated by several factors, such as optimizing investment decisions, enhancing performance, managing risk, adapting to changing conditions, and building knowledge and expertise. The investment decision relates to the distribution of financial resources. Investors select the most appropriate investment opportunities based on risk profiles, investment aims, and expected returns. Fuzzy multicriteria group decision-making in capital investment extends the traditional decision-making process to accommodate multiple criteria that are often uncertain, vague, or subjective in nature. This paper aims to suggest a technique known as the Fuzzy Technique for Order Preference by Similarity to Ideal Solution (fuzzy TOPSIS) for group decision-making about investment in the respective vehicle. The fuzzy TOPSIS technique represents a decision for experts, which is multicriteria and includes an aggregated decision-making process. This paper shows the application of this method when choosing the best alternative, considering the choice of vehicle.

Predicting the exact outcome of a real-life problem, which may occur in various fields like the industrial or healthcare sector, is challenging. Due to high information uncertainty and complicated factors influencing the industrial sector, traditional data-driven prediction approaches can hardly reflect real changes in practical situations. Fuzzy programming is a powerful prediction reasoning and risk assessment model for uncertain environments. This article mainly explores and applies a modified form of fuzzy programming, namely the Fuzzy Linear Fractional Programming Problem (FLFPP), having the coefficients of the objectives and constraints as Triangular Fuzzy Numbers (TFNs). The FLFPP is converted into an equivalent crisp Multi-Objective Linear Fractional Programming Problem (MOLFPP) and solved individually to associate an aspiration level. Then, by applying the Fuzzy Goal Programming (FGP) technique, the maximum degree of each membership goal is obtained by minimizing the negative deviational variables. We carry out two industrial application simulations in a hypothetical industrial scenario. Our study shows that the proposed model is practical and applicable to the uncertain practical environment to realize the prediction, and the results obtained are compared with those of the existing methods.

In this work, we investigate the existence, uniqueness, and different stability types, focusing on Ulam-Hyers stability, of a solution to a nonlinear fuzzy fractional differential equation with Caputo generalized Hukuhara differentiability of order ℘ ∈ (n − 1, n). We establish explicit criteria to guarantee both the existence and uniqueness of the solution, employing the Banach fixed point theorem. Additionally, we present two examples to enhance the illustration of our findings.

This research delves into the exploration of Pythagorean fuzzy sublattices and Pythagorean fuzzy ideals within the context of lattice theory. Through a rigorous analysis of structural theorems concerning these concepts derived from Pythagorean fuzzy sets, we uncover significant parallels with classical theory. Additionally, we investigate the behavior of Pythagorean fuzzy ideals under lattice homomorphisms. Our findings shed light on the applicability and utility of Pythagorean fuzzy theory in lattice-based structures, offering insights into their properties and relationships.

Tourism is a worthy catalyst for development in emerging economies and supports growth in most developing countries. Consequently, countries continuously strive to enhance tourism competitiveness to magnetize worldwide tourists. However, due to significant environmental changes and intense competition, tourism organizations are compelled to adopt new strategies. A literature review demonstrates a broad spectrum of possible and available strategies for countries to choose from, necessitating the prioritization of strategies appropriate to the host country's situation and conditions. In this study, we implemented the Antifragility Analysis Algorithm (AAA) to address the research problem (identifying and prioritizing tourism strategies in the western region of Mazandaran province, Iran). We also collected experts' verbal judgments using Neutrosophic Sets (NSs), which can effectively address ambiguity and uncertainty. Initially, with the help of experts in the field, we identified eleven available strategies. Then, we identified five influential environmental indicators and possible states for each, defining thirteen alternative scenarios (one current scenario and twelve future scenarios). Subsequently, the performance of strategies in each indicator state was estimated using NSs. Then, considering the future scenarios, the antifragility scores of the strategies were determined. The results indicate all listed strategies are antifragile, meaning that adopting and implementing each could yield more significant benefits than the current situation. According to the findings, market research, infrastructure development, community engagement, diversification, and monitoring strategies should be implemented in the initial stage. Following them, destination branding, halal tourism, and crisis management strategies should be implemented in the next stage, and the remaining strategies can be executed in the final stage.

This article successfully attempts to introduce the notion of Inverse Neutrosophic Mixed Graphs (INMG) together with its applications. This novel approach highlights the network modeling of real physical situations with indeterminacy. Here, INMG are developed with both directed and undirected relationships between nodes that express the circumstances where the truth membership degrees of the edges are superior or equivalent to the least of the truth membership degrees of the associated vertices and where false membership and indeterminacy values of the edges are inferior or equivalent to the maximum of false membership and indeterminacy values of the corresponding vertices. Furthermore, some fundamental functions and algebraic characteristics of INMG are examined to attain a profound insight into the properties and applications. To illustrate the application of INMG, the article provides a numerical example centered around social networks. By employing INMG in this context, the article demonstrates how the model can effectively capture and represent the complex relationships within social networks, taking into account the inherent uncertainties and indeterminacies present in such systems.

A multiple set is an extended version of a fuzzy set that simultaneously addresses an element’s multiplicity and uncertainty. In this paper, we define the approximate equality of multiple sets and study some relevant properties associated with it. We then apply the notion of approximation equality of multiple sets to solve a pattern recognition problem. A novel class of similarity measures involving implication operators is introduced and the characteristics of approximate equality corresponding to these similarity measures are discussed. Further, we propose the concepts of σ-entropy, σ-distance measure, and σ-similarity measure of multiple sets and illustrate these with some examples. Finally, we define the theory of similarity measures between elements in multiple sets.