Solving fully neutrosophic linear programming problem with application to stock portfolio selection

Neutrosophic set is considered as a generalized of crisp set, fuzzy set, and intuitionistic fuzzy set for representing the uncertainty, inconsistency, and incomplete knowledge about the real world problems. In this paper, a neutrosophic linear programming (NLP) problem with single-valued trapezoidal neutrosophic numbers is formulated and solved. A new method based on the so-called score function to find the neutrosophic optimal solution of fully neutrosophic linear programming (FNLP) problem is proposed. This method is more flexible than the linear programming (LP) problem, where it allows the decision maker to choose the preference he is willing to take. A stock portfolio problem is introduced as an application. Also, a numerical example is given to illustrate the utility and practically of the method

A method to solve two-player zero-sum matrix games in chaotic environment

This research article proposes a method for solving the two-player zero-sum matrix games in chaotic environment. In a fast growing world, the real life situations are characterized by their chaotic behaviors and chaotic processes. The chaos variables are defined to study such type of problems. Classical mathematics deals with the numbers as static and less value-added, while the chaos mathematics deals with it as dynamic evolutionary, and comparatively more value-added. In this research article, the payoff is characterized by chaos numbers. While the chaos payoff matrix converted into the corresponding static payoff matrix. An approach for determining the chaotic optimal strategy is developed. In the last, one solved example is provided to explain the utility, effectiveness and applicability of the approach for the problem.Abbreviations: DM= Decision Maker; MCDM = Multiple Criteria Decision Making; LPP = Linear Programming Problem; GAMS= General Algebraic Modeling System

On Characterizing Efficient and Properly Efficient Solutions for Multi- Objective Programming Problems in a Complex Space

In this paper, a complex non- linear programming problem with the two parts (real and imaginary) is considered. The efficient and proper efficient solutions in terms of optimal solutions of related appropriate scalar optimization problems are characterized. Also, the Kuhn-Tuckers' conditions for efficiency and proper efficiency are derived. This paper is divided into two independently parts: The first provides the relationships between the optimal solutions of a complex single-objective optimization problem and solutions of two related real programming problems. The second part is concerned with the theory of a multi-objective optimization in complex space

Characterizing edge-based doubly resolving sets within circulant networks Cn(1,2) C_n(1, 2)

The focus of this article lies on the notion of the edge version of doubly resolving sets (EVDRSs) in circulant networks. EVDRSs refer to unique edge subsets that are necessary for identifying individual edges in a network and distinguishing them based on their edge distances to the elements of the EVDRS. The main objectives were to define the minimal size of EVDRSs for circulant networks $C_n(1, 2)$ and to investigate their basic properties. The systematic research helped to achieve a new understanding of the existence, construction, and characterization of EVDRSs in circulant networks $C_n(1, 2)$. It is established that the EVDRSs in the circulant network $C_n(1, 2)$ are finite and are bounded by the order of the network. Among the numerous implications of these findings are those that refer to the design and optimization of distributed sensor networks, improving communication and network protocols, as well as tracking the spread of infectious diseases and epidemics over social networks. The application of the identified methodology helps improve the process of network optimization which contributes to the development of more effective and robust circulant-based structures

Dynamic bipolar fuzzy aggregation operators: A novel approach for emerging technology selection in enterprise integration

Emerging technology selection is crucial for enterprise integration, driving innovation, competitiveness, and streamlining operations across diverse sectors like finance and healthcare. However, the decision-making process for technology adoption is often complex and fraught with uncertainties. Bipolar fuzzy sets offer a nuanced representation of uncertainty, allowing for simultaneous positive and negative membership degrees, making them valuable in decision-making and expert systems. In this paper, we introduce dynamic averaging and dynamic geometric operators under bipolar fuzzy environment. We also establish some of the fundamental crucial features of these operators. Moreover, we present a step by step mechanism to solve MADM problem under bipolar fuzzy dynamic aggregation operators. In addition, these new techniques are successfully applied for the selection of the most promising emerging technology for enterprise integration. Finally, a comparative study is conducted to show the validity and practicability of the proposed techniques in comparison to existing methods

Multi-criteria decision-making based on Pythagorean cubic fuzzy Einstein aggregation operators for investment management

Pythagorean cubic fuzzy sets (PCFSs) are a more advanced version of interval-valued Pythagorean fuzzy sets where membership and non-membership are depicted using cubic sets. These sets offer a greater amount of data to handle uncertainties in the information. However, there has been no previous research on the use of Einstein operations for aggregating PCFSs. This study proposes two new aggregator operators, namely, Pythagorean cubic fuzzy Einstein weighted averaging (PCFEWA) and Pythagorean cubic fuzzy Einstein ordered weighted averaging (PCFEOWA), which extend the concept of Einstein operators to PCFSs. These operators offer a more effective and precise way of aggregating Pythagorean cubic fuzzy information, especially in decision-making scenarios involving multiple criteria and expert opinions. To illustrate the practical implementation of this approach, we apply an established MCDM model and conduct a case study aimed at identifying the optimal investment market. This case study enables the evaluation and validation of the established MCDM model's effectiveness and reliability, thus making a valuable contribution to the field of investment analysis and decision-making. The study systematically compares the proposed approach with existing methods and demonstrates its superiority in terms of validity, practicality and effectiveness. Ultimately, this paper contributes to the ongoing development of sophisticated techniques for modeling and analyzing complex systems, offering practical solutions to real-world decision-making problems

Goal programming approach for solving heptagonal fuzzy transportation problem under budgetry constraint

Transportation problem (TP) is a special type of linear programming problem (LPP) where the objective is to minimize the cost of distributing a product from several sources (or origins) to some destinations. This paper addresses a transportation problem in which the costs, supplies, and demands are represented as heptagonal fuzzy numbers. After converting the problem into the corresponding crisp TP using the ranking method, a goal programming (GP) approach is applied for obtaining the optimal solution. The advantage of GP for the decision-maker is easy to explain and implement in real life transportation. The stability set of the first kind corresponding to the optimal solution is determined. A numerical example is given to highlight the solution approach

A Novel Method for Neutrosophic Assignment Problem by using Interval-Valued Trapezoidal Neutrosophic Number

Assignment problem (AP) is well- studied and important area in optimization. In this research manuscript, an assignment problem in neutrosophic environment, called as neutrosophic assignment problem (NAP), is introduced. The problem is proposed by using the interval-valued trapezoidal neutrosophic numbers in the elements of cost matrix. As per the concept of score function, the interval-valued trapezoidal neutrosophic assignment problem (IVTNAP) is transformed to the corresponding an interval-valued AP. To optimize the objective function in interval form, we use the order relations. These relations are the representations of choices of decision maker. The maximization (or minimization) model with objective function in interval form is changed to multi- objective based on order relations introduced by the decision makers' preference in case of interval profits (or costs). In the last, we solve a numerical example to support the proposed solution methodology

On a Flow-Shop Scheduling Problem with Fuzzy Pentagonal Processing Time

Scheduling involves planning and arranging jobs across a coordinated set of events to satisfy the customer’s demands. In this article, we present a simple approach for the flow-shop (FS) scheduling problem under fuzzy environment in which processing time of jobs are represented by pentagonal fuzzy numbers. This study is intended to reduce the rental cost of the machine in compliance with the rental policy. The fuzzy FS scheduling problem is solved without converting the processing time into its equivalent crisp numbers using a robust ranking technique and a fuzzy arithmetic pentagonal fuzzy numbers. A numerical illustration indicates that the approach is workable, accurate, and relevant

On Solutions of Fully Fuzzy Linear Fractional Programming Problems Using Close Interval Approximation for Normalized Heptagonal Fuzzy Numbers

This paper attempts to solve the linear fractional programming problem with fully fuzzy normalized heptagonal fuzzy numbers using the close interval approximation of normalized heptagonal fuzzy number, which is one of the best interval approximations. The maximization (minimization) problem with interval objective function is converted into multi- objective based on order relations introduced by the decision makers’ preference between interval profits (costs). Finally, an example is presented to illustrate the proposed method