Trapezoidal Fuzzy Numbers Research Articles

Optimization of the vendor's inventory model with multisupplier and multiretailer using fuzzy parameters

This paper explores the multi-item vendor's inventory (VI) model in which the vendor replenishes the products from various suppliers and satisfies the retailers' demand. Different types of products scrutinize this model under two cases. The first case considers the products are replenished in bulk and packed in small quantities by the vendor and sent to the retailers. The second case presumes that the vendor replenishes the packed items from the supplier and sent to retailers without the packaging process. The wastage of products during the packaging process occurs in the first case and the deterioration of items occurs in both cases. The unpredictable parameters such as the proportion of wastage products and the proportion of deteriorated products lead the model under fuzzy logic. The VI model and the Vendor's fuzzy inventory (VFI) are framed. VFI model is formulated by assuming the wastage rate and the deterioration rate as triangular fuzzy numbers (TFN) as well as trapezoidal fuzzy numbers. The defuzzification method of TFN and trapezoidal fuzzy numbers by the combination of Beta distribution and a uniform distribution is utilized in this paper. For both cases, the optimal ordering and purchasing period, the optimal retailer's replenishment period, and the optimal packaging period for case (i) is computed which minimizes the vendor's total cost. The computational example and sensitivity analysis are performed to flourish the study more effectively.

A Supply Chain Model Based on Data-Driven Demand Uncertainty under the Influence of Carbon Tax Policy

The era of digital economy has spawned new factors of production represented by big data. Data-driven sustainable growth and innovative development is the main line of enterprise digital transformation. In view of the uncertainty of supply chain demand, the optimization of supply chain management under the influence of carbon tax policy is studied from the low-carbon perspective. By introducing the fuzzy theory and a membership function to describe the need for uncertainty, a supply chain optimization model considering the influence of carbon emissions is constructed. Carbon tax policy is regarded as the constraint condition of external production. In the case of fuzzy cost changes, the optimization decision of enterprise supply chain management under carbon tax policy is explored. A trapezoidal fuzzy number is used to determine model fuzziness, and the trapezoidal fuzzy number combined with a genetic algorithm is used to solve the model. Furthermore, taking a certain enterprise as an example, the validity of the model is verified by the mathematical programming model method, considering the data driven and taking the data as the means of production.

Using an Integrated Consistent Fuzzy Preference Relations and Interval Type-2 Fuzzy Topsis Methodology for Personnel Selection and Promotion

Promotion is an organizational procedure. Education, experience, and personal qualities are crucial requirements for individuals to be promoted. Their characteristics determine the promotion-eligible employee's approach to the job and compatibility with coworkers. This research employs an integrated Consistent Fuzzy Preference Relations (CFPR) - Interval Type-2 (IT2) Fuzzy TOPSIS methodology to identify the most competent individuals for promotion. Using this methodology, the ranking of individuals for a case study in Turkey is calculated. The CFPR technique calculates the weight of the criteria stated by experts in our most recent research [1]. Then, the IT2 Fuzzy TOPSIS method is used to determine the order of options using IT2 trapezoidal fuzzy numbers. Thus, the best competent candidate for promotion is selected. Thus, managers and human resources departments may assess and promote employees rapidly.

Mehar approach to solve fuzzy linear fractional minimal cost flow problems

To the best of author’s knowledge, only one approach is proposed in the literature to solve fuzzy linear fractional minimal cost flow problems (minimal cost flow problems in which each known arc cost is represented either by a triangular fuzzy number or a trapezoidal fuzzy number). In this paper, the mathematical incorrect assumptions, considered in the existing approach to solve fuzzy linear fractional minimal cost flow problems, are pointed out. Also, by generalizing an existing approach for solving fuzzy linear fractional programming problems, an approach (named as Mehar approach) is proposed to solve fuzzy linear fractional minimal cost flow problems. Furthermore, two numerical examples are solved to illustrate the proposed Mehar approach.

Bipolar fuzzy information‐based PROMETHEE‐based outranking scheme for mitigating vampire attack in wireless sensor networks

AbstractThe sensor nodes comprising sensing devices, small processing units, and battery, cooperate in wireless sensor networks (WSNs) for gathering potential factors that aids in achieving significant decision‐making processes in deployed applications. WSNs are vulnerable to security threats due to their open nature, availability characteristics, and lack of energy, resulting in a diversified number of security attacks. Among the security attacks, vampire attack is the serious threat as they drain the energy of nodes, which in turn crumbles the network lifetime and energy stability in WSNs. In this article, Bi‐Polar Information‐Based Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE)‐based outranking scheme is proposed for detecting and isolating vampire attacks to improve throughput with minimized energy consumptions and delay for prolonging lifetime. This proposed BPFI‐POR scheme used bipolar information that facilitates an asymmetrical association between two decision making factors that influences the discrimination and selection of genuine nodes from vampire nodes during the routing process. It aids in characterizing precise and vague information through bipolar fuzzy linguistic terms that has the maximized probability of being represented as trapezoidal bipolar fuzzy numbers. It estimated the cooperation of intermediate sensor nodes' based on trapezoidal bipolar fuzzy numbers for determining their preference or selection using criteria that could be influenced during the routing process. It also used the ranking function for accessing the alternatives through crisp real preferences with entropy weighting information responsible for attributes weight computation. The simulation results of the BPFI‐POR scheme confirmed better throughput, detection time with minimized energy consumptions and latency on par with the competitive algorithms.

An Extended ORESTE Approach for Evaluating Rockburst Risk under Uncertain Environments

Rockburst is a severe geological disaster accompanied with the violent ejection of rock debris, which greatly threatens the safety of underground workers and equipment. This study aims to propose a novel multi-criteria decision-making (MCDM) approach for evaluating rockburst risk under uncertain environments. First, considering the heterogeneity of rock mass and complexity of geological environments, trapezoidal fuzzy numbers (TrFNs) are adopted to express initial indicator information. Thereafter, the superiority linguistic ratings of experts and a modified entropy weights model with TrFNs are used to calculate the subjective and objective weights, respectively. Then, comprehensive weights can be determined by integrating subjective and objective weights based on game theory. After that, the organísation, rangement et synthèse de données relarionnelles (ORESTE) approach is extended to obtain evaluation results in a trapezoidal fuzzy circumstance. Finally, the proposed approach is applied to assess rockburst risk in the Kaiyang phosphate mine. In addition, the evaluation results are compared with empirical methods and other trapezoidal fuzzy MCDM approaches. Results show that the proposed extended ORESTE approach is reliable for evaluating rockburst risk, and provides an effective reference for the design of prevention techniques.

Multiple Attribute Decision Making Based on Interval-Valued Neutrosophic Trapezoidal Fuzzy Numbers and its Application in the Diagnosis of Viral Flu

Decision-making technique (DMT) is mostly used in artificial intelligence and cognitive sciences to elaborate individual and social perception. So, one of the most important strategies in DMT evolved in medical diagnosis scrutiny regarding the connection of symptoms and diagnosis of diseases due to uncertainty and fuzziness in the relevant information. The focus of this article is to develop a diagnostic decision making strategy for the diagnosis of Viral diseases with close related symptoms using the Interval-valued trapezoidal neutrosophic fuzzy Numbers (IVTrNFN) w.r.t multiple attribute decision making (MADM) strategy where, the attribute value is evolved to Interval-valued trapezoidal neutrosophic fuzzy number and the attribute weight is unknown and can be related to the GRA (Grey relational analysis projection) technique. In this research several operational laws are developed as well as the expected value and the hamming distance between two IVTrFNs are introduced. Moreover, the information entropy method is used to determine the attributes weights and the grey relational analysis as well as the projection method are involved too in the proposed framework. The ranks of the alternative decisions are evaluated by their relative closeness to PIS (Positive Ideal Solutions), which combine the grey relational projection values from positive and negative ideal solutions associated with each alternative. Finally, a Viral disease example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

The decision making method of financial institutions in industrial cluster upgrading based on interval-valued intuitionistic trapezoidal fuzzy number game matrix

The decision problem of financial institutions supporting the upgrading of industrial clusters is ambiguous, and it is difficult to satisfy the basic feature of uncertainty by the payment function constructed by precise values. To cope with the fuzziness and uncertainty of game matrix, this paper firstly proposes a basic theory of interval-valued intuitionistic trapezoidal fuzzy number (IITFN) based on score function and accuracy function to construct an IITFN fuzzy matrix game (FMG) model. Next, expected utility theory is used to offer the acquisition of mixed strategy optimal solution of IITFN-FMG. Finally, it is applied to analyze the conditions and strategies of financial institutions to support the upgrading of industrial clusters. The main innovations of this paper are: The introduction of interval-valued intuitionistic trapezoidal fuzzy number to characterize the fuzzy features in the decision-making process of financial institutions and cluster enterprises, the proposed construction of a game matrix based on IITFN, and the corresponding solution method to obtain the conditions and strategies for financial institutions to support the upgrading of industrial clusters, and the proposed method and countermeasures to break the “prisoner’s dilemma” in the cooperation between financial institutions and cluster enterprises.

Approximation of 3D trapezoidal fuzzy data using radial basis functions

We present a new methodology to approximate a trapezoidal fuzzy numbers set by using smoothing radial basis functions (RBFs). The methodology uses different error and similarity indices to determine and compare the accuracy of the approximation of the given trapezoidal fuzzy data. For the proposed approximation method a fuzzy radial basis functions type are defined, called fuzzy smoothing radial basis functions under tension. The computation of one of these approximation functions from a given trapezoidal fuzzy data set is described and some convergence results are proved. Finally, some examples in two-dimensions are given to compare the behavior of the presented method by using the proposed error and similarity indices for different configurations of the fuzzy smoothing radial basis functions under tension.

An Improved EDAS Method for the Multi-Attribute Decision Making Based on the Dynamic Expectation Level of Decision Makers

The improved evaluation based on the distance from average solution (EDAS) of the interval-valued intuitionistic trapezoidal fuzzy set is proposed. At first, we propose a new distance between interval-valued intuitionistic trapezoidal fuzzy numbers according to their interval endpoints and centroid point, and its properties are also discussed. Furthermore, we apply the proposed distance measure to calculate the expectation level of the emergency plan, and the optimal dynamic expectation level of the emergency plan is obtained by solving the programming model. Then, we improve the EDAS method based on the dynamic expectation level of the decision makers and apply it to calculate the optimal emergency plan. Finally, a numerical example about flood disaster rescue is given to verify the feasibility and effectiveness of the proposed method, which is also compared with the existing methods.

Modified Hungarian Method for Solving Balanced Fuzzy Transportation Problems

This paper discusses how to solve balanced transportation problems, with transportation costs in the form of trapezoidal fuzzy numbers. Fuzzy costs are transformed into crisp costs using the Robust’s method as a ranking function. A new approach of modified Hungarian method has been applied to solve the problem of fuzzy transportation. This approach solves the fuzzy transportation problem in one stage of optimization and yields the same results as other methods that solve the problem in two stages.

Effect of LR-type trapezoidal fuzzy numbers on profit analysis of gas turbine system

Effect of LR-type trapezoidal fuzzy numbers on profit analysis of gas turbine system

Modified Ranking Function to Compute Fuzzy Matrix Games

Game theory problems (GTP) frequently occur in Economy, Business Studies, Sociology, Political Science, Military Activities, and so on are some of the subjects covered. To tackle the uncertainty in Games, the analysis of games in which the payoffs are represented by fuzzy numbers (FN) will benefit from fuzzy set theory (FST). The purpose of this paper is to develop an efficient technique for solving constraint matrix games (MG) with payoff trapezoidal fuzzy numbers (TFN). The description of the new ranking method is introduced for a constrained matrix with TFN and values. Stock market forecasting has been one of the most important research areas for decades. Stock market values are volatile, non-linear, complicated and chaotic. Based on a ranking function (RF), we used a new algorithm to solve the fuzzy game problem (FGP) employing TFN and also to try to get a desirable gain. Centered on the latest proposed ranking algorithm, the Fuzzy decision method is designed to analyze possible stock opportunists. The paper considers a zero-sum game for two persons in which TFN are fuzzy payoffs. A ranking method (RM) is proposed to convert TFN into crisp numbers (CN) and it is used to solve FGP. The fuzzy game (FG) issue with concept strategies pure minimax maximin is presented. This problem is converted into the crisp problem by a new RF and then solved using the arithmetic (oddment) method. With the help of numerical examples, the suggested technique is explained. This paper finalizes the conclusion and includes an outlook for future study in this direction

A STUDY ON OPTIMAL STRATEGY N-POLICY FUZZY VACATION QUEUEING SYSTEM WITH SERVER START UP AND TIME OUT USING L-R METHOD

In this study, the process of finding performance measures of N* is the optimal threshold , L is the expected system length and T(N*) is the minimum expected cost for an optimal strategy analysis of N-policy FM / FM / 1 Vacation Queueing system with server Start-up and Time-out, in which the arrival rate and service rate triangular and trapezoidal fuzzy numbers are proposed. By using L-R method the L-R method is smaller and more convenient differentiate to alpha-cuts method. The cogency of the model is study by numerical example.

Blockchain technology in construction organizations: risk assessment using trapezoidal fuzzy ordinal priority approach

PurposeIn the digital transformation era, the construction industry is not immune to unintended consequences and disruptions of distributed ledger technologies like blockchain. At the micro-level, construction organizations need an in-depth understanding of blockchain risks to take proactive strategies for being on the safe side. This study seeks to answer “What are the risks associated with blockchain technology from the firm-level perspective? And how can this disruptive technology overshadow the business objectives and impact organizational criteria?”Design/methodology/approachThe current research proposes a novel model for risk assessment based on the trapezoidal fuzzy ordinal priority approach (OPA-F) in the multi-criteria decision-making (MCDM) context. The proposed model handles uncertainties of experts' judgment around three primary parameters: the importance of organizational criteria, the impact of blockchain risks on criteria and the probability of risk occurrence.FindingsThe case study shows that organizational “communication and information” is exposed to the most blockchain risk. On the contrary, blockchain has less to do with an organization's “corporate social responsibility.” Furthermore, effective blockchain risk management can bring about cost efficiency, quality and improved customer experience for this case study. In the end, the authors develop a conceptual blockchain risk management framework based on findings.Research limitations/implicationsThis study will broaden researchers' horizons regarding “blockchain in construction context” and “blockchain risk management.”Practical implicationsFurthermore, executives looking for blockchain-based solutions can benefit from research findings and lessons learned from this case study before decision-making. Lastly, the risk assessment model based on trapezoidal OPA-F can be used both for research purposes and industrial decision problems.Originality/valueTo the best of the authors’ knowledge, it is for the first time that the OPA-F is employed in a risk assessment model. Also, the original OPA-F is extended to trapezoidal OPA-F using trapezoidal fuzzy numbers, and it is the first attempt to evaluate blockchain risks facing construction organizations and develop a blockchain risk management framework accordingly.

Fuzzy preference ranking organization method for enrichment evaluation‐based node cooperation technique for improving QoS in MANETs

SummaryCooperation between mobile nodes is the predominant factor required for achieving reliable data dissemination in mobile ad hoc networks (MANETs), since non‐cooperative nodes crumbles the routing process and degrades network performance. The degree of non‐cooperation rendered by mobile nodes need to be accurately identified by exploring feasible and comprehensive number of criteria to achieve maximized cooperation in uncertain MANET. In this paper, fuzzy preference ranking organization method for enrichment evaluation (FPROMETHEE)‐based node cooperation technique is proposed with the merits of trapezoidal fuzzy interval numbers that aids in the selection of high trustworthy mobile nodes for attaining maximized data delivery. This FPROMETHEE technique utilizes complex and multiple criteria for potential ranking in the presence of finite number of mobile nodes. It prevented the bias of information that is more common during the judgmental process associated with the cooperation estimation of mobile nodes. It includes information about the relative weights of criteria and decision maker's preferences for estimating the trust of mobile nodes to include or isolate them from the routing path. It is also useful in handling the degree of uncertainly involved in the process of routing without compromising Quality of Service (QoS) level in the network. The simulation experiments of the proposed FPROMETHEE technique conducted using ns‐2 simulator confirmed its predominance in enhancing the packet dissemination rate, throughput, energy consumptions, total overhead, and packet loss rate for different number of mobile nodes, malicious nodes, and pairs of source and destination nodes.

A multi-objective optimization approach for clean treatment of food waste from an economic-environmental-social perspective: A case study from China

The combination of anaerobic digestion and transesterification technologies to treat food waste avoids the environmental problems associated with other treatment methods and effectively utilizes food waste to produce valuable products for society. However, as the anaerobic mono-digestion of food waste is not as efficient as anaerobic co-digestion of food waste with other substrates, this needs to be considered in food waste treatment system planning. Few studies on the mixed treatment of food waste with other substrates have considered the system from the economic, environmental, and social perspectives. Therefore, this paper comprehensively considered the economic, environmental, and social objectives of food waste treatment systems and developed a multi-objective optimization model to investigate the optimal systems operational strategy for food waste mixed treatment with other substrates by anaerobic co-digestion and transesterification. Uncertainties regarding the source quantities of food waste and substrates are solved in the proposed model using trapezoidal fuzzy numbers, and a case study in China is given to assess the validity and practicality of the proposed model. It was found that different substrate types and different mixing proportions affected the optimal system decisions, environmental and economic objectives were mutually constraining, and there was a positive relationship between the social objectives and the economic and environmental objectives.

The novel approach for ranking generalized interval type-2 trapezoidal fuzzy numbers based on integral value

Interval type 2 fuzzy sets (IT2FS) give us with additional value of membership function to represent the uncertainty and the fuzziness of the real word than type 1 fuzzy sets (T1FS). In real problem, the ranking of interval type 2 fuzzy numbers is an important component in the fuzzy decision making system. The existing ranking approaches i.e. centroid is cited by many researchers and has wide application, and then integral value also often developed by researchers both in the form of T1FS and newly in the form IT2FS. However, the existing ranking approaches still have shortcomings of the ranking function. In this paper, the concepts of left and right of interval type-2 trapezoidal fuzzy numbers (IT2TrFN) i.e the novel total integral value with index of optimistic is proposed to overcome the shortcomings of the existing ranking approaches. By using several examples, the new total integral value is capable to cover the shortcomings of the existing approaches and has well-consistency in ranking IT2TrFN with equal and different hight value.

On solving multi-objective fully quadratic fractional optimisation model with interactive FGP approach

PurposeThe main motive behind framing this paper is to provide a compromised solution for trapezoidal fuzzy number–multi-objective fully quadratic fractional optimisation model (TrFN-MOFQFOM) by avoiding ambiguities and confusion of decision-makers (DMs). Many researchers have used Taylor's series and parametric approach to transform fractional objective function into non-fractional ones, but Taylor's series expansion is valid only up to a neighbourhood. To avoid these extra efforts, this article suggests a methodology in which numerator of objective function is optimised under the condition of optimising denominator.Design/methodology/approachThis paper suggests an efficient procedure to search for compromised solution of MOFQFOM with fuzzy coefficients using α-level set and FGP approach. Incomplete data in model is dealt with α-level set. Then after defuzzification, non-fractional models are built from fractional model to get optimal solution of every objective. Finally, the linear weighted sum of negative deviational variables is minimised to satisfy all objective functions up to maximum possible extent.FindingsOn applying suggested approach to the example given in end, the authors arrived at compromised solution having and . The applied procedure requires less computational efforts and provides the preferred compromised solution.Originality/valueThis work has not been done previously by anyone. The idea being developed here of constructing non-fractional model by dealing numerators and denominators separately is completely new. 10; In the end, an algorithm, flowchart and numerical are also given to clarify the applicability of the suggested approach.

Fuzzy linear programming problem with α-cut and roubast ranking methods

In this paper we are going to solve fuzzy linear programming problem with Triangular and Trapezoidal fuzzy numbers. Here we are using ranking method technique with -Cut to get optimal solution for solving fuzzy linear programming problem with trapezoidal and triangular fuzzy numbers and also compare the existing methods. To illustrate the method numerical examples is solved and the obtained results are discussed.