Breast cancer is a leading cause of death in women worldwide, and early detection is crucial for successful treatment. Computer-aided diagnosis (CAD) systems have been developed to assist doctors in identifying breast cancer on ultrasound images. In this paper, we propose a novel fuzzy relative-position-coding (FRPC) Transformer to classify breast ultrasound (BUS) images for breast cancer diagnosis. The proposed FRPC Transformer utilizes the self-attention mechanism of Transformer networks combined with fuzzy relative-position-coding to capture global and local features of the BUS images. The performance of the proposed method is evaluated on one benchmark dataset and compared with those obtained by existing Transformer approaches using various metrics. The experimental outcomes distinctly establish the superiority of the proposed method in achieving elevated levels of accuracy, sensitivity, specificity, and F1 score (all at 90.52%), as well as a heightened area under the receiver operating characteristic (ROC) curve (0.91), surpassing those attained by the original Transformer model (at 89.54%, 89.54%, 89.54%, and 0.89, respectively). Overall, the proposed FRPC Transformer is a promising approach for breast cancer diagnosis. It has potential applications in clinical practice and can contribute to the early detection of breast cancer.
This article introduces the structure of the (t,s)-regulated interval-valued neutrosophic soft set (abbr. (t,s)-INSS). The structure of (t,s)-INSS is shown to be capable of handling the sheer heterogeneity and complexity of real-life situations, i.e. multiple inputs with various natures (hence neutrosophic), uncertainties over the input strength (hence interval-valued), the existence of different opinions (hence soft), and the perception at different strictness levels (hence (t,s)-regulated). Besides, a novel distance measure for the (t,s)-INSS model is proposed, which is truthful to the nature of each of the three membership (truth, indeterminacy, falsity) values present in a neutrosophic system. Finally, a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and a Viekriterijumsko Kompromisno Rangiranje (VIKOR) algorithm that works on the (t,s)-INSS are introduced. The design of the proposed algorithms consists of TOPSIS and VIKOR frameworks that deploy a novel distance measure truthful to its intuitive meaning. The conventional method of TOPSIS and VIKOR will be generalized for the structure of (t,s)-INSS. The parameters t and s in the (t,s)-INSS model take the role of strictness in accepting a collection of data subject to the amount of mutually contradicting information present in that collection of data. The proposed algorithm will then be subjected to rigorous testing to justify its consistency with human intuition, using numerous examples which are specifically made to tally with the various human intuitions. Both the proposed algorithms are shown to be consistent with human intuitions through all the tests that were conducted. In comparison, all other works in the previous literature failed to comply with all the tests for consistency with human intuition. The (t,s)-INSS model is designed to be a conclusive generalization of Pythagorean fuzzy sets, interval neutrosophic sets, and fuzzy soft sets. This combines the advantages of all the three previously established structures, as well as having user-customizable parameters t and s, thereby enabling the (t,s)-INSS model to handle data of an unprecedentedly heterogeneous nature. The distance measure is a significant improvement over the current disputable distance measures, which handles the three types of membership values in a neutrosophic system as independent components, as if from a Euclidean vector. Lastly, the proposed algorithms were applied to data relevant to the ongoing COVID-19 pandemic which proves indispensable for the practical implementation of artificial intelligence.
It is imperative to comprehensively evaluate the function, cost, performance and other indices when purchasing a hypertension follow-up (HFU) system for community hospitals. To select the best software product from multiple alternatives, in this paper, we develop a novel integrated group decision-making (GDM) method for the quality evaluation of the system under the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs). The design of our evaluation indices is based on the characteristics of the HFU system, which in turn represents the evaluation requirements of typical software applications and reflects the particularity of the system. A similarity is extended to measure the IVq-ROFNs, and a new score function is devised for distinguishing IVq-ROFNs to figure out the best IVq-ROFN. The weighted fairly aggregation (WFA) operator is then extended to the interval-valued q-rung orthopair WFA weighted average operator (IVq-ROFWFAWA) for aggregating information. The attribute weights are derived using the LINMAP model based on the similarity of IVq-ROFNs. We design a new expert weight deriving strategy, which makes each alternative have its own expert weight, and use the ARAS method to select the best alternative based on these weights. With these actions, a GDM algorithm that integrates the similarity, score function, IVq-ROFWFAWA operator, attribute weights, expert weights and ARAS is proposed. The applicability of the proposed method is demonstrated through a case study. Its effectiveness and feasibility are verified by comparing it to other state-of-the-art methods and operators.
The health organizations around the world are currently facing one of the greatest challenges, to overcome the current global pandemic, COVID-19. It erupted in December 2019, in Wuhan City, China. It spreads rapidly throughout the world within couple of months. In this paper, the data of the COVID-19 have been collected, organized, analyzed and interpreted using the discrete-time model of SIR epidemic model. Moreover, results for several countries from different regions of the world have been obtained. Furthermore, comparative study has been carried out for the countries under consideration. The comparison was performed for the data of different countries on same dates of each month. However, the calculations are carried out for thirteen consecutive weeks, to investigate the rate of spread and the control of the disease in these countries. This guides us to some important concepts like factors favoring the spread of virus and those resisting the spread. Different regions are studied and their data have been evaluated to know which regions are the most effected. This study helps to know the important factors about the behavior of the coronavirus in different environments, such as lockdowns, temperatures, humidity and other restrictions. The proposed concepts and equations can be used to project the upcoming behavior of the pandemic.
Traffic management methods aim to increase the infrastructure's capacity to lower congestion levels. Using vehicle-to-vehicle (V2V), vehicle-to-infrastructure (V2I), and vehicle-to-everything (V2X) connectivity technologies, connected autonomous vehicles (CAVs) have the potential to operate as actuators for traffic control. In this study, a CAV-based alternative approach for traffic management is proposed (SWSCAV), and its performance is compared to that of lane control signals (LCS) and variable speed limits (VSL), which are also traffic management systems. When a shockwave is detected due to an incident, the CAVs on the road slow until they reach the speed of the observed shockwave (SWS), according to this proposed procedure. Thus, the incoming traffic flow towards the incident is slowed, preventing the queue behind from extending. In a simulation of the urban mobility (SUMO) environment, the suggested method is evaluated for 4800 scenarios on a three-lane highway by varying the market penetration rate of CAVs in traffic flow, the control distances, the incident lane, and the duration. The proposed method reduces the incidence of density values of over 38 veh/km/lane and 28 veh/km/lane in the vicinity of the incident region by 12.68 and 8.15 percent, respectively. Even at low CAV market penetration rates, the suggested method reduces traffic density throughout the network and in the location of the incident site by twice as much as the LCS system application.
The major objective of the current investigation is to build an integrated multiple criteria group decision-making (MCGDM) methodology based on combined compromise solution (CoCoSo) and spherical fuzzy set for determining the optimal solar power station. To begin with, an innovative spherical fuzzy score function is brought forward to strengthen the efficiency of the comparison for spherical fuzzy number (SFN). Secondly, several newly operational laws for SFN are defined and some novel aggregation operation based on them are propounded. The corresponding excellent properties of the novel operators are also explored at length. Further, the spherical fuzzy method on the removal effects of criteria (MEREC) technique is presented by the proposed score function to work out the importance of the criteria. Lastly, an MCGDM approach is propounded based on improved spherical fuzzy CoCoSo to obtain the ranking of the solar power station locations. The feasibility and practicability of the proposed SF-MEREC-CoCoSo method are investigated through the comparison study with the extant methods. The sensibility analysis is also executed to discuss the robustness and stability of the propounded methodology.
This paper intends to introduce mathematical tools for aggregation of the generalized hesitant fuzzy numbers in order to increase the use of them in the real world. The proposed operators, are based on general form of t-norm and t-conorm functions, enable us to do some mathematical computations and aggregate the given generalized hesitant fuzzy numbers. At first, some famous Archimedean t-norms and t-conorms, i.e., Algebraic, Einstein, Hamacher, and Frank t-norms and t-conorms, and their properties, have been developed to be employed with generalized hesitant fuzzy numbers. Then, several averaging and geometric-based aggregation operators for generalized hesitant fuzzy numbers have been proposed. Later on, a decision-making algorithm has been defined based on such operators to address the problems. The necessity and application of the proposed concepts have been explained by some numerical examples.
Friction stir spot welding (FSSW) is one of the most popular fusion joining processes. The process is a solid-state welding process that allows welding of weldable as well as non-weldable materials. As a part of this investigation, weld samples of Al6061-T6 were reinforced with silicon carbide (SiC) powder with an average particle size of 45 µm. Initially, a Taguchi L9 orthogonal array was developed with three factors, i.e., rotational speed of the tool, pre-dwelling time, and diameter of the hole that was filled with SiC before welding. The effects of the SiC particles and process parameters were investigated as tensile-shear load and micro-hardness. The optimisation of parameters in order to maximise the output responses-i.e., strength and hardness of the welded joints-was performed using a hybrid WASPAS-Taguchi method. The optimised process parameters obtained were a 3.5 mm guiding hole diameter, 1700 rpm tool rotation speed, and 14 s of pre-dwelling time.
The main objective of this paper is to present an improved neural network algorithm (INNA) for solving the reliability-redundancy allocation problem (RRAP) with nonlinear resource constraints. In this RRAP, both the component reliability and the redundancy allocation are to be considered simultaneously. Neural network algorithm (NNA) is one of the newest and efficient swarm optimization algorithms having a strong global search ability that is very adequate in solving different kinds of complex optimization problems. Despite its efficiency, NNA experiences poor exploitation, which causes slow convergence and also restricts its practical application of solving optimization problems. Considering this deficiency and to obtain a better balance between exploration and exploitation, searching procedure for NNA is reconstructed by implementing a new logarithmic spiral search operator and the searching strategy of the learner phase of teaching-learning-based optimization (TLBO) and an improved NNA has been developed in this paper. To demonstrate the performance of INNA, it is evaluated against seven well-known reliability optimization problems and finally compared with other existing meta-heuristics algorithms. Additionally, the INNA results are statistically investigated with the Wilcoxon sign-rank test and Multiple comparison test to show the significance of the results. Experimental results reveal that the proposed algorithm is highly competitive and performs better than previously developed algorithms in the literature.
COVID-19 is a respiratory infection caused by a coronavirus that spreads from person to person. In the present situation, the COVID-19 pandemic is a swiftly rising phase. Now the time is the second wave ending phase of coronavirus and the third wave coming phase of coronavirus in India. The pandemic situation is moving forward all over India. Nowadays, the worldwide COVID-19 pandemic structure is a very hazardous situation. The COVID-19 vaccine can suppress this situation and gain preventive measures against coronavirus. In producing the COVID-19 vaccine, the Indian medical board plays a significant role. The COVID-19 vaccines have exhibited 90%-95% efficacy in preventing symptomatic COVID-19 infections. Against COVID-19, for emergency purposes, the Indian medical board has approved three vaccines: Covishield, Covaxin, and Sputnik V. Generally, the Indian people are embarrassed about the vaccination of COVID-19. All people are thinking about which vaccine is best for them. This labyrinth can be evaluated effectively using the multi-criteria decision-making (MCDM) technique. Therefore, we have proposed a novel MCDM technique for selecting COVID-19 vaccines. The main aim of this paper is to develop an MCDM technique based on a λ -weighted ranking interpreter ( R λ + , R λ - ). The first time, we have defined positive and negative λ -weighted rank interpreter for the ranking of single-valued bipolar neutrosophic (SVbN) number. Additionally, positive and negative λ -weighted values and positive and negative λ -weighted ambiguity of an SVbN-number are formulated here. Some important, valuable theorems and corollary of SVbN-number are formulated. To show the applicability of the proposed MCDM technique, we have considered a real decision-making problem where ratings of the alternatives are with SVbN-numbers.
The Fermatean fuzzy set (FFS) is a momentous generalization of a intuitionistic fuzzy set and a Pythagorean fuzzy set that can more accurately portray the complex vague information of elements and has stronger expert flexibility during decision analysis. The Combined Compromise Solution (CoCoSo) approach is a powerful decision-making technique to choose the ideal objective by fusing three aggregation strategies. In this paper, an integrated, multi-criteria group-decision-making (MCGDM) approach based on CoCoSo and FFS is used to assess green suppliers. To begin, several innovative operations of Fermatean fuzzy numbers based on Schweizer-Sklar norms are presented, and four aggregation operators utilizing the proposed operations are also developed. Several worthwhile properties of the advanced operations and operators are explored in detail. Next, a new Fermatean fuzzy entropy measure is propounded to determine the combined weight of criteria, in which the subjective and objective weights are computed by an improved best-and-worst method (BWM) and entropy weight approach, respectively. Furthermore, MCGDM based on CoCoSo and BWM-Entropy is brought forward and employed to sort diverse green suppliers. Lastly, the usefulness and effectiveness of the presented methodology is validated by comparison, and the stability of the developed MCGDM approach is shown by sensitivity analysis. The results shows that the introduced method is more stable during ranking of green suppliers, and the comparative results expound that the proposed method has higher universality and credibility than prior Fermatean fuzzy approaches.
The objective of this paper is to present a novel idea about the continuous possibilistic cooperative static game (Poss-CCSTG). The proposed Poss-CCSTG is a continuous cooperative static game (CCSTG) in which parameter associated with the cost functions of the players involves the possibility measures. The considered Poss-CCSTG is converted into the crisp α-CCSTG problem by using the α-cuts and hence into the multiple objective nonlinear programming problem. To solve the formulated α-CCSTG problem, an interactive approach is presented in the study with the use of the reference direction method. Further, the Lexicographic weighted Tchebycheff model is derived to obtain the weights. Also, a parametric study corresponding to the α-possibly optimal solution is defined and determined. Finally, a decision-maker can compare their desired solution with the attainable reference point and the weak efficient solution. The presented model is illustrated with a numerical example and its advantages are stated.
Algorithms
Fuzzy hybrid models are strong mathematical tools to address vague and uncertain information in real-life circumstances. The aim of this article is to introduce a new fuzzy hybrid model named as of q-rung orthopair m-polar fuzzy soft set (q-RO-m-PFSS) as a robust fusion of soft set (SS), m-polar fuzzy set (m-PFS) and q-rung orthopair fuzzy set (q-ROFS). A q-RO-m-PFSS is a new approach towards modelling uncertainties in the multi-criteria decision making (MCDM) problems. Some fundamental operations on q-RO-m-PFSSs, their key properties, and related significant results are introduced. Additionally, the complexity of logistics and supply chain management during COVID-19 is analysed using TOPSIS (technique for ordering preference through the ideal solution) and GRA (grey relational analysis) with the help of q-RO-m-PFS information. The linguistic terms are used to express q-RO-m-PFS information in terms of numeric values. The proposed approaches are worthy efficient in the selection of ventilator's manufacturers for the patients suffering from epidemic disease named as COVID-19. A practical application of proposed MCDM techniques is demonstrated by respective numerical examples. The comparison analysis of the final ranking computed by proposed techniques is also given to justify the feasibility, applicability and reliability of these techniques.
The assessment of investment risk for the countries along the route in Belt and Road (B&R) can be deemed as a multiple criteria group decision making (MCGDM) issue since multiple investment options based on diverse criterions are assessment by experts. Pondering that the complexity and uncertainty of the assessment setting and the cognition fuzziness and psychological behavior of experts bring challenges to risk assessment, this paper designed an integrated MCGDM risk investment evaluation framework by synthesizing MABAC method and prospect theory under Fermatean fuzzy setting. Firstly, a Fermatean fuzzy interactive distance measure is presented to ascertain the weight of evaluation experts and criterions. Next, some Fermatean fuzzy Frank aggregation operators based upon the proposed Frank operations are developed to fuse Fermatean fuzzy information efficiently. In addition, an innovative evaluation framework for risk investment is designed based on improved prospect theory MABAC and CRITIC approaches. Conclusively, an empirical concerning risk investment issues in B&R is employed to confirm the applicability and feasibility of the constructed evaluation framework, involving the simulation experiments on sensitivity analysis and contrast studies. The assessment information provided by investors using the linguistic assessment terms based upon their cognition ability of them. These outcomes obtained by the propounded method and comparison analysis further emphasize the validity and salient merits of the propounded framework and provide several auxiliary suggestions for investors.
This study aims to model a workforce-planning problem of pilot roles which include captain and first officer in an airline company and to make an efficient plan having maximal utilization of minimum workforce requirements. To tackle this problem, a mixed integer programming based a new mathematical model is proposed. The model considers different conditions such as employing pilots with different skill types, resignations, retirements, holidays of pilots, transitions between different skills regarding needs of the demands during the planning horizon. The application of the proposed approach is investigated using a case study with real-world data from an airline company in Turkey. The results show that a company can use transitions instead of new employment and this is a more suitable medium-term production and human resource planning decision.
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The paper aims to present the concept of power aggregation operators for the T-spherical fuzzy sets (T-SFSs). T-SFS is a powerful concept, with four membership functions denoting membership, abstinence, non-membership and refusal degree, to deal with the uncertain information as compared to other existing fuzzy sets. On the other hand, the relationship between the different pairs of the attributes are well recorded in terms of power operators. Thus, keeping these advantages of T-SFSs and power operator, the objective of this work is to define several weighted averaging and geometric power aggregation operators. The stated operators named as T-spherical fuzzy weighted, ordered weighted, hybrid averaging and geometric operators for the collection of the T-SFSs. The various properties and the special cases of them are also derived. Further, the consequences of proposed new power aggregation operators are studied in view of some constraints. Finally, a multiple attribute decision making algorithm, based on the proposed operators, is established to solve the problems with uncertain information and illustrate with numerical examples. A comparative study, superiority analysis and discussion of the proposed approach are furnished to confirm the approach.
In this study, a typical supply chain network design problem consisting of plants, distribution centers, and customers is considered with the assumptions of multi-mode demand and multi-mode transportation. In it, the parameters of the problem are considered as a trapezoidal intuitionistic fuzzy value to handle the vagueness in the information. Based on it, a hybrid approach is proposed where the fuzzy objective function is converted to a set of crisp objective functions and the fuzzy constraints are crisped using their credibility measure. Finally, the crisp multi-objective formulation is obtained and solved it with different approaches. To evaluate the formulations and solution approaches, a case study from healthcare sector and several test problems are used. The results of computational experiments are used to compare the solution approaches, where the behavior of the proposed crisp formulation is fully discovered.
With the rapid outbreak of COVID-19, most people are facing antivirus mask shortages. Therefore, it is necessary to reasonably select antivirus masks and optimize the use of them for everyone. However, the uncertainty of the effects of COVID-19 and limits of human cognition add to the difficulty for decision makers to perfectly realize the purpose. To maximize the utility of the antivirus mask, we proposed a decision support algorithm based on the novel concept of the spherical normal fuzzy (SpNoF) set. In it, firstly, we analyzed the new score and accuracy function, improved operational rules, and their properties. Then, in line with these operations, we developed the SpNoF Bonferroni mean operator and the weighted Bonferroni mean operator, some properties of which are also examined. Furthermore, we established a multi-criteria decision-making method, based on the proposed operators, with SpNoF information. Finally, a numerical example on antivirus mask selection over the COVID-19 pandemic was given to verify the practicability of the proposed method, which the sensitive and comparative analysis was based on and was conducted to demonstrate the availability and superiority of our method.
Coronavirus Infections/prevention & control , Decision Making , Disease Outbreaks/prevention & control , Pandemics/prevention & control , Personal Protective Equipment , Pneumonia, Viral/prevention & control , Algorithms , Betacoronavirus , COVID-19 , Cognition , Coronavirus , Coronavirus Infections/epidemiology , Fuzzy Logic , Humans , Mathematical Concepts , Pneumonia, Viral/epidemiology , SARS-CoV-2 , Uncertainty
This paper aims to give deeper insights into decision making problem based on interval-valued fuzzy soft set (IVFSS). Firstly, a new score function for interval-valued fuzzy number is proposed for tackling the comparison problem. Subsequently, the formulae of information measures (distance measure, similarity measure and entropy) are introduced and their transformation relations are pioneered. Then, the objective weights of various parameters are determined via new entropy method, meanwhile, we develop the combined weights, which can show both the subjective information and the objective information. Moreover, we propose three algorithms to solve interval-valued fuzzy soft decision making problem by Weighted Distance Based Approximation (WDBA), COmbinative Distance-based ASsessment (CODAS) and similarity measure. Finally, the effectiveness and feasibility of approaches are demonstrated by a mine emergency decision making problem. The salient features of the proposed methods, compared to the existing interval-valued fuzzy soft decision making methods, are (1) it can obtain the optimal alternative without counterintuitive phenomena; (2) it has a great power in distinguishing the optimal alternative; and (3) it can avoid the parameter selection problems.
