Linguistic single‐valued neutrosophic soft sets with applications in game theory

The neutrosophic soft set emerges as a highly valuable and efficient adaptation of soft sets, specifically addressing parameterized values of alternatives. However, numerous decision-making algorithms rooted in neutrosophic soft sets often neglect the external factors impacting their effectiveness. This paper introduces the innovative concept of an effective neutrosophic soft expert set, meticulously crafted to encapsulate external influences on both neutrosophic soft sets and expert opinions within a unified model. This eliminates the necessity for additional operations. Notably, our groundbreaking approach seamlessly amalgamates the strengths of the neutrosophic soft expert set and the effective set, resulting in heightened efficiency and realism in this domain. The article comprehensively explores the fundamental operations of an effective neutrosophic soft expert set, elucidating these processes through apt examples. Finally, the paper showcases the practical application of this concept in decision-making problems, providing algorithms and illustrative examples to underscore its efficacy.

In this chapter, some basic definitions and operations on the concepts of fuzzy set, fuzzy number, intuitionistic fuzzy set, single-valued neutrosophic set, single-valued neutrosophic number (SVN-number) are presented. Secondly, two centroid point are called 1. and 2. centroid point for single-valued trapezoidal neutrosophic number (SVTN-number) and single-valued triangular neutrosophic number (SVTrN-number) are presented. Then, some desired properties of 1. and 2. centroid point of SVTN-numbers and SVTrN-numbers studied. Also, based on concept of 1. and 2. centroid point of SVTrN-numbers, a new single-valued neutrosophic multiple-attribute decision-making method is proposed. Moreover, a numerical example is introduced to illustrate the availability and practicability of the proposed method. Finally, since centroid points of normalized SNTN-numbers or SNTrN-numbers are fuzzy values, all definitions and properties of fuzzy graph theory can applied to SNTN-numbers or SNTrN-numbers. For example, definition of fuzzy graph theory based on centroid points of normalized SVTN-numbers and SVTrN-numbers is given.

Waste management is a key to sustainable development and environmental safety, particularly in the environment of the fast evolving smart cities. This study proposes a new decision-making model that will assist in the process of choosing effective sustainable methods in waste management for smart cities. It compares the four methods of waste management in relation to seven factors. Two Multi-Criteria Decision Making (MCDM) are used i) Analytical Hierarchy Process (AHP) and ii) Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) in a Neutrosophic Soft Set (NSS) environment. NSS have a more adaptive structure on dealing with the uncertainty and incapacity to be precise in the decision-making on waste management. In this methodology, AHP determines the weights of decision criteria, while TOPSIS ranks the effective waste management strategies for final selection. Ten professionals in the universities, industry, and government sector were used. This assessment was done by way of structured questionnaires of subjective opinions. As a result, the alternatives were ranked based on their closeness coefficient values as follows: A2 (0.632) > A1 (0.509) > A4 (0.352) > A3 (0.261). The given ranking shows that A2 is more effective than A1, A4, and A3.

The Analytical Hierarchy Process (AHP) approach and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method are two methods that are commonly used to handle multicriteria problems. The AHP technique uses a matrix of pairwise comparisons and a hierarchical approach to criteria in order to obtain the final criteria weights. In contrast, the TOPSIS approach incorporates the concepts of proximity to the ideal solution and preference. Next, TOPSIS uses the previously established criterion weights to compute each option's relative closeness score to the ideal answer. In order to determine how effectively the AHP and TOPSIS methodologies complement one another, this study aims to assess the protocols and underlying assumptions of the two approaches. When decision makers are aware of the benefits and drawbacks of each approach, they may choose the best course of action from a mix of the two. The results of the study indicate that the process may be streamlined, subjectivity can be reduced, and criterion weights can be stabilized by combining the AHP and TOPSIS approaches.The Analytical Hierarchy Process (AHP) approach and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method are two methods that are commonly used to handle multicriteria problems. The AHP technique uses a matrix of pairwise comparisons and a hierarchical approach to criteria in order to obtain the final criteria weights. In contrast, the TOPSIS approach incorporates the concepts of proximity to the ideal solution and preference. Next, TOPSIS uses the previously established criterion weights to compute each option's relative closeness score to the ideal answer. In order to determine how effectively the AHP and TOPSIS methodologies complement one another, this study aims to assess the protocols and underlying assumptions of the two approaches. When decision makers are aware of the benefits and drawbacks of each approach, they may choose the best course of action from a mix of the two. The results of the study indicate that the process may be streamlined, subjectivity can be reduced, and criterion weights can be stabilized by combining the AHP and TOPSIS approaches.

The single‐valued neutrosophic set (SVNS) is a more common platform for representing the degree of truth, indeterminacy, and falsity memberships. Indeterminacy is an important aspect of SVNS, and the score function (SF) is important in ranking alternatives in decision‐making scenarios. When the score and accuracy values for different SVNNs were equal, existing SFs were unable to rank the alternatives. To address the limitations, this paper introduces the perfect score function (PSF) as a solution for ranking single‐valued neutrosophic numbers (SVNNs) without any errors and presents the concepts of strong and weak SVNSs. This article has emphasized the drawbacks of the existing SF in SVNNs. Additionally, we propose an optimized weighted geometric operator (OWGO) for SVNNs, and its properties such as idempotency, boundedness, monotonicity, and commutativity are explored. Furthermore, the decision‐making approach has been depicted based on the proposed score function and OWGO to select the finest faculty for a university.

Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The neutrosophic soft rough set (NSRS) model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. In this research paper, we introduce the idea of neutrosophic soft rough graphs (NSRGs) and describe different methods of their construction. We consider the application of NSRG in decision-making problems. In particular, we develop efficient algorithms to solve decision-making problems.

Purpose - The purpose of this study, Borsa Istanbul 100 (BIST100) of the financial performance of energy companies traded multi-criteria decision making methods, TOPSIS (Technique for order preference by Similarity to ideal solution) method is measured. Methodology - For this purpose, 5 energy companies traded in BIST in 2021 and whose data are regularly accessed have been included in the scope of the study. The annual balance sheet and income statements of the companies were used in the study. The balance sheets and income statements of the companies within the scope of the research for the year 2021 were taken from the official website of the Public Lighting Platform (KAP). During the period when the application part of this study was conducted, the data of the year 2022 could not be used due to the fact that the data of the year 2022 has not yet been published. The obtained data were measured by TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method, which is one of the multi-criteria Decisionmaking methods, and the performance of the companies were analyzed and compared among themselves. Findings - Ipek Natural Energy Resources Research and Production A. One of the companies included in the study as a result of the analyzes performed by the TOPSIS method.Sh. ((IPEK) was found to be the company with the best data in terms of financial performance in the analyzes carried out in accordance with the criteria included in the evaluation. After this company, the second best company in terms of financial performance is Koza Anadolu Metal Madencilik Işletmeleri A.Sh. He appeared as a (COCOON). Conclusion - In the light of the analyzes carried out in the study; IPEKE company ranked first as the best company in terms of financial performance. Ardın KOZAA of IPEKE company ranked second, ASELS company ranked third, AKSEN company ranked fourth and VESTL company ranked last in terms of financial performance among the 5 companies included in the study. Dec. Apart from these data, it can be said that changing the December period to be based on different studies, using different financial ratios, the degree of importance given to criteria, using other multi-criteria decision-making methods (MSCS) such as MOORA other than TOPSIS may give results that may change the performance ranking. Keywords: BIST-100, TOPSIS, financial performance, energy, MCDMM JEL Codes: C61, M41, M49

Initial water rights allocation is a complex decision problem, and it is difficult for traditional methods to determine weights and solve the decision problem. In this study, an improved TOPSIS (Technique for order preference by similarity to ideal solution) method is proposed using vertical distance instead of Euclidean distance to calculate the closeness degree of schemes to the ideal solution, which overcomes the shortage of traditional TOPSIS method. In order to determine the weights of evaluation indexes reasonably, the improved method adopts game theory to harmonize and conjugate the subjective weight and the objective weight. On this basis, a comprehensive weight which eliminates the unilateral result can be obtained, and a model of initial water rights allocation in the watershed is established by the improved TOPSIS method. Finally, the proposed model is applied in the study of initial water rights allocation in Fuhuan River in Hubei Province, which shows rationality and validity when comparing with other models like traditional TOPSIS method, analytic hierarchy process and projection pursuit model.

PurposeThis paper aims to optimize the process parameters of the fused deposition modelling (FDM) process using the Grey-based Taguchi method and the results to be verified based on a technique for order preference by similarity to ideal solution (TOPSIS) and analytical hierarchy process (AHP) calculation.Design/methodology/approachThe optimization of process parameters is gaining a potential role to develop robust products. In this context, this paper presents the parametric optimization of the FDM process using Grey-based Taguchi, TOPSIS and AHP method. The effect of slice height (SH), part fill style (PFS) and build orientation (BO) are investigated with the response parameters machining time, surface roughness and hardness (HD). Multiple objective optimizations were performed with weights of w1 = 60%, w2 = 20% and w3 = 20%. The significance of the process parameters over response parameters is identified through analysis of variance (ANOVA). Comparisons are made in terms of rank order with respect to grey relation grade (GRG), relative closeness and AHP index values. Response table, percentage contributions of process parameters for both GRG and TOPSIS evaluation are done.FindingsThe optimum factor levels are identified using GRG via the Grey Taguchi method and TOPSIS via relative closeness values. The optimized factor levels are SH (0.013 in), PFS (solid) and BO (45°) using GRG and SH (0.013 in), PFS (sparse-low density) and BO (45°) using TOPSIS relative closeness value. SH has higher significance in both Grey relational analysis and TOPSIS which were analysed using ANOVA.Research limitations/implicationsIn this research, the multiple objective optimizations were done on an automotive component using GRG, TOPSIS and AHP which showed a 27% similarity in their ranking order among the experiments. In the future, other advanced optimization techniques will be applied to further improve the similarity in ranking order.Practical implicationsThe study presents the case of an automotive component, which illustrates practical relevance.Originality/valueIn several research studies, optimization was done on the standard test specimens but not on a real-time component. Here, the multiple objective optimizations were applied to a case automotive component using Grey-based Taguchi and verified with TOPSIS. Hence, an effort has been taken to find optimum process parameters on FDM, for achieving smooth, hardened automotive components with enhanced printing time. The component can be explored as a replacement for the existing product.

Nowadays, games exist everywhere in people's daily life, and game theory methods should not be just formulas and words in books, but also brought into people's daily life, helping people to solve many practical problems in life. This paper selects the most common problem in the life of postgraduate students - the choice of thesis direction between postgraduate students and their supervisors, takes Nash equilibrium as the theoretical support point, analyses the "prisoner's dilemma" model in game theory, combines with the payment matrix, and finds the solution to the problem. The solution to the problem is the application of game theory in daily life, which demonstrates the close connection between games and life.

A famous multi-criteria decision-making(MCDM) method called technique for order preference by similarity to ideal solution(TOPSIS) was often fuzzy generalized into fuzzy multi-criteria decision-making(fuzzy MCDM). In generalizing TOPSIS, fuzzy preference relation on interval-valued fuzzy numbers(IVFNs) is to find the ideal solution and anti-ideal solution for reserving lots of information. Usually, the work is complicated on computation. Practically, IVFNs is more difficult than others. In order to resolve the above tie for the decision-making problem about airport performance evaluation, we utilize TOPSIS and relative preference relation(RPR) in fuzzy MCDM. By combining RPR with TOPSIS, the performance evaluating problem of airports could be easily solved.

This study aims to objectively analyze the feasibility of prospective recipients of the Smart Indonesia Card Scholarship (KIP-K) by integrating the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method. The research dataset consists of 287 data on prospective scholarship recipients with 11 main attributes that reflect the socio-economic and academic conditions of students. The research process includes data collection, pre-processing, transformation of categorical attributes into numerical values using a linear weighting scheme, cluster analysis using DBSCAN, and candidate ranking using TOPSIS. DBSCAN is used to identify cluster patterns and detect anomalies in the data of potential recipients, while TOPSIS is used to rank candidates based on proximity to the ideal solution. The results of the grouping produced 10 clusters and one noise cluster that showed a variety of socio-economic characteristics of prospective scholarship recipients. The results of the ranking show that some of the candidates with the highest TOPSIS scores come from clusters with higher levels of economic vulnerability. In addition, some of the high-scoring candidates also came from the noise cluster, indicating that even though they did not belong to a particular group, they still met the eligibility criteria based on a multi-criteria evaluation. These findings show that the combination of DBSCAN and TOPSIS has the potential to support the process of analyzing the eligibility of scholarship recipients in a more systematic and data-driven manner.

This article describes how Smarandache defined neutrosophic sets to handle problems involving incomplete, indeterminacy and awareness of inconsistency knowledge, and is further developed to neutrosophic soft expert sets by Sahin et al. Adam and Hassan defined multi Q-fuzzy soft sets as an extension to fuzzy soft sets and gave its applications. This article will extend this further by presenting a novel concept of Q-neutrosophic soft expert sets, and define the associated related concepts and basic operations of complement, subset, union, intersection, AND and OR. This novel concept enables the single dimensionality of soft expert sets to be extended to two dimensions. Then, this article constructs an algorithm based on this concept. The following will illustrate the feasibility of the new method by an example. Finally, a comparison of the proposed method to existing methods is furnished to verify the effectiveness of the novel concept.

This research aims to improve project quality at PT ABC by integrating the Fuzzy Analytical Hierarchy Process (F-AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) within the Lean Six Sigma framework. This method assesses and selects quality improvement projects by considering uncertainty and complexity in decision-making. The Fuzzy AHP approach is used to flexibly assign criteria weights, while TOPSIS is used to rank projects based on performance scores relative to the ideal solution. This research aims to select the most suitable Lean Six Sigma project using the MCDM fuzzy AHP and TOPSIS approaches at PT ABC. There are three alternative quality improvement projects and three assessment criteria. The data processing results using Fuzzy AHP and TOPSIS showed that the most influential criterion was the impact criterion, with a value of 0.665. Overall, the order of influencing criteria is cost (0.260) and time (0.075). Based on a review of all criteria, the project to increase the drive plate production line (A) capacity was ranked first with a value of 0.772. Second place is the project to increase capacity and consolidate rear axle assemblies A and B with a value of 0.5529. Finally, the third is the process innovation and integrated manufacturing project to strengthen the business with a value of 0.4053.

"Coal-to-electricity" project can effectively reduce the air pollution in the northern China, and their benefits evaluation can reasonably reflect the effect of the projects. According to the present situation of the "coal-to-electricity" projects in a northern city, the evaluation index system is put forward to estimate the benefits of the projects with the aspects of economic benefits, social benefits and operation status of the distribution networks. A statistic method - TOPSIS (technique for order preference by similarity to ideal solution) is used to evaluation and analysis. In this method, the index system is weighted by the combination of analytic hierarchy process (AHP) and entropy weighting method. In the evaluation system of "coal-to-electricity" project, combination weighting - TOPSIS method can sort the different projects based on the distance between their comprehensive benefits and the positive and negative ideal solution. After the analysis of "coal-to-electricity" region with poor benefits, some recommendations can be given. Three actual project examples are applied for the evaluation system, and then the evaluation result of the examples is compared. Finally, the result is analyzed, while some improvement measures are put forward in these examples, which can give the reference and the guidance for the further implementation of the projects.