Trapezoidal Fuzzy Research Articles

A Solution Approach for Multi-Level Multi-Objective Quadratic Fractional Programming with Trapezoidal Fuzzy Numbers using Rouben Ranking Function

The paper proposed a methodology for obtaining a set of efficient solutions for a model which is multi-level multiobjective quadratic with fractional objectives and constraints having trapezoidal fuzzy number (MLMOQFP-TrFN) as coefficients. The model consists of r-levels with several objectives involved to be solved under a set of quadratic constraints. The proposed approach starts with the solution process of the top level and other levels are solved in succession but depending on the solution of the previous levels. The solution process of each level comprises mainly three stages. In the beginning, the Rouben Ranking Function is used to convert the rth-level of fuzzy model into a deterministic or crisp one. After that, the crisp form is reconstructed to get a non-fractional model with the help of an iterative parametric approach. Further, in the last, non-fractional model which is still having multiple objectivesis reconstructed to form a model having only one objective with ɛ -constraint method and is lastly solved by following the solution of (r-1)th- level to get a desired set of efficient solution. Such programming models are very useful in day to day life such as in economic planning, industrial activities, waste management, neural networking, unmanned aerial and underwater vehicle management, agricultural yield improvement, transportation problems with maximizing profits and minimizing wastage of material and cost and so on. An algorithm depicting all the steps of solution approach is also presented to reflect a clear idea for the approach. In addition, a numerical regarding the presentation of complete approach that is studied is given in the end.

Solution of linear programming problem with trapezoidal fuzzy coefficients using score functions

Solution of linear programming problem with trapezoidal fuzzy coefficients using score functions

An Extended MULTIMOORA Based on Trapezoidal Fuzzy Neutrosophic Sets and Objective Weighting Method in Group Decision-Making

Multi-objective optimization based on ratio analysis plus full multiplicative form (MULTIMOORA) is an efficient decision-making method for solving multi-criteria group decision-making (MCGDM) processes. It uses three strategies to examine different alternatives and to determine their evaluation values. These strategies include ratio system approach (RSA), reference point approach (RPA), and full multiplicative form (FMF). However, this method presents some challenges in the examination model, such as the ability to aggregate and determine the final result according to these strategies without considering value differences, the complexity of calculating the aggregation and multi-time comparisons, and the probability of distinguishing circular reasoning rules in dominance theory. In addition, determining an appropriate instrument for handling uncertainty, inconsistency, and incompleteness of information and a suitable weight for each criterion and decision-maker for reducing human interventions are also considered and will be a complex MCGDM process. To overcome these weaknesses, we propose an extended MULTIMOORA based on trapezoidal fuzzy neutrosophic numbers (TraFNNs) for MCGDM. We integrated it with ordinal priority approach (OPA) method to decide the initial weights for decision-makers and criteria without human subjective assessment. In addition, we used correlation coefficient and standard deviation (CCSD) technique to statistically compute the relationship between these strategies in resolving unique weights to obtain realistic results and eliminate the above issues. Finally, sensitivity and comparative analyses demonstrate the capability and effectivity of the extended method.

Flood Risk Assessment of Metro System Using Improved Trapezoidal Fuzzy AHP: A Case Study of Guangzhou

Metro systems have become high-risk entities due to the increased frequency and severity of urban flooding. Therefore, understanding the flood risk of metro systems is a prerequisite for mega-cities’ flood protection and risk management. This study proposes a method for accurately assessing the flood risk of metro systems based on an improved trapezoidal fuzzy analytic hierarchy process (AHP). We applied this method to assess the flood risk of 14 lines and 268 stations of the Guangzhou Metro. The risk results validation showed that the accuracy of the improved trapezoidal fuzzy AHP (90% match) outperformed the traditional trapezoidal AHP (70% match). The distribution of different flood risk levels in Guangzhou metro lines exhibited a polarization signature. About 69% (155 km2) of very high and high risk zones were concentrated in central urban areas (Yuexiu, Liwan, Tianhe, and Haizhu); the three metro lines with the highest overall risk level were lines 3, 6, and 5; and the metro stations at very high risk were mainly located on metro lines 6, 3, 5, 1, and 2. Based on fieldwork, we suggest raising exits, installing watertight doors, and using early warning strategies to resist metro floods. This study can provide scientific data for decision-makers to reasonably allocate flood prevention resources, which is significant in reducing flood losses and promoting Guangzhou’s sustainable development.

An efficiency-based interval type-2 fuzzy multi-criteria group decision making for makeshift hospital selection

Since makeshift hospitals have strong ability in blocking the spread of the virus, how to design some methods to select the reasonable sites of makeshift hospitals is vitally important for containing COVID-19. This paper investigates an efficiency-based multi-criteria group decision making (MCGDM) method by combining the best-worst method (BWM) and data envelopment analysis (DEA) in trapezoidal interval type-2 fuzzy (TrIT2F) environment. This MCGDM method is called TrIT2F-BWM-DEA, where the TrIT2F-BWM is used to determine the weights of criteria and decision-makers, and the TrIT2F-DEA is employed to rank alternatives by measuring their overall efficiencies. Based on cut set theory, the expectation and average expectation (AE) of TrIT2FSs are successively defined. To solve three key issues in the development of the TrIT2F-BWM, this paper proposes a flexible ranking relation of TrIT2FSs to transform the TrIT2F constraints, initiates an efficient theorem to normalize the TrIT2F weights, and designs an input-based consistency ratio to check the reliability of the determined weights. A fully TrIT2F-DEA model is originally built to measure the TrIT2F efficiencies of alternatives. The alternatives are finally ranked according to the AEs of alternatives’ TrIT2F efficiencies. A site selection case of Fangcang hospitals and some comparative analyses are provided to confirm the validity and merits of the proposed TrIT2F-BWM-DEA.

A Modified TODIM Based on Compromise Distance for MAGDM with q-Rung Orthopair Trapezoidal Fuzzy Numbers

The q-rung orthopair fuzzy number (q-ROFN) has been recently developed by Yager and has been widely applied in handling real-life decision-making problems. To enhance its usefulness in dealing with complex practical issues, this paper first proposes the new concept of q-rung orthopair trapezoidal fuzzy numbers (q-ROTrFNs) which is a new and useful extension of q-ROFNs. Then, we investigate the operation of q-ROTrFNs and develop a new ranking method for q-ROTrFNs. We also propose a new q-rung orthopair trapezoidal fuzzy Hamming distance measure. More important, we develop a useful q-rung orthopair trapezoidal fuzzy modified TODIM group decision-making method. In this method, a new q-rung orthopair trapezoidal fuzzy weighted aggregating (q-ROTrFWA) operator is developed to integrate individual decision matrices into the collective decision matrix, and a q-rung orthopair trapezoidal fuzzy distance measure-based compromise approach is proposed to determine the relative dominance degree of alternatives. It is worth to mention that the modified TODIM method not only expands the freedom of decision makers but also allows decision makers to choose the appropriate risk preference parameter. Finally, a case study on health management of hypertensive patients is conducted to demonstrate the feasibility of the modified TODIM group decision-making method, and the developed method is further verified by comparison analysis with the existing methods and sensitive analysis of different parameters.

Computer-Based Fuzzy Numerical Method for Solving Engineering and Real-World Applications

The nonlinear equation is a fundamentally important area of study in mathematics, and the numerical solutions of the nonlinear equations are also an important part of it. Fuzzy sets introduced by Zedeh are an extension of classical sets, which have several applications in engineering, medicine, economics, finance, artificial intelligence, decision-making, and so on. The most special types of fuzzy sets are fuzzy numbers. The important fuzzy numbers are trapezoidal fuzzy and triangular fuzzy numbers, which have several applications. In this research article, we propose an efficient numerical iterative method for estimating roots of fuzzy nonlinear equations, which are based on the special type of fuzzy number called triangular fuzzy number. Convergence analysis proves that the order of convergence of the numerical method is three. Some real-life applications are considered as numerical test problems from engineering, which contain fuzzy quantities in the parametric form. Engineering models include fractional conversion of nitrogen-hydrogen feed into ammonia and Van der Waal’s equation for calculating the volume and pressure of a gas and motion of the object under constant force of gravity. Numerical illustrations are given to show the dominance efficiency of the newly constructed iterative schemes as compared to existing methods in the literature.

Analysis of Water Distribution System under Uncertainty Based on Genetic Algorithm and Trapezoid Fuzzy Membership

AbstractIn most studies of hydraulic simulation of water distribution systems (WDS), the uncertain input parameters such as nodal demands, pipe roughness coefficients, pipe diameters, water levels ...

A fuzzy leakage inventory model with shortage using triangular and trapezoidal fuzzy numbers

Inventory refers to any kind of economically valued resources that are in various stages of being made ready for sale. With the development of the Economic Order Quantity (EOQ) model by Ford Harris, many models under different conditions and assumptions are proposed. Leakage is a common phenomenon whose occurrence will reduce the profitability of the firm by increasing the minimum operational cost. In majority of real-life inventory problems we face many uncertainties in the key parameters of the corresponding model. These impreciseness and uncertainties in crisp model are improved by using fuzzy set theory. So, in this context, a fuzzy leakage inventory order level is developed by taking holding cost and shortage cost as Triangular as well as Trapezoidal Fuzzy Numbers. Defuzzification is done using Signed Distance Method. A relevant numerical example is illustrated along with sensitivity analysis to justify the proposed notion that the optimal values are improved in fuzzy environment as compared to that of in crisp environment.

Research on the consistency of additive trapezoidal fuzzy preference relations

Trapezoidal fuzzy numbers offer a suitable and flexible way to express vague judgments of decision makers. This paper studies decision making with additive trapezoidal fuzzy preference relations. It first analyzes the issues encountered in previous consistency concepts for additive trapezoidal fuzzy preference relations. Then, two new consistency concepts, namely, an additive consistency concept and a multiplicative consistency concept, are introduced. To verify the rationality, several of their properties are discussed. To efficiently assess the consistency of additive trapezoidal fuzzy preference relations, several corresponding optimization models are formed. When the objective function values of the built models are zero, the associated additive trapezoidal fuzzy preference relations are consistent. Considering the case where additive trapezoidal fuzzy preference relations are incomplete, optimization models based on the consistency analysis are built, by which identified unknown judgments have the highest consistency level with the known ones. In general, additive trapezoidal fuzzy preference relations are unacceptably consistent. To rank objects from additive trapezoidal fuzzy preference relations, several optimization models for improving the consistency level are built, which consider the self-confidence of the decision makers, the total adjustment and the number of adjusted elements. According to the above discussion, two frameworks for ranking objects from additive trapezoidal fuzzy preference relations are provided that are based on the additive and multiplicative consistency analysis, respectively. Finally, numerical examples are provided to highlight the concrete application and to deliver the comparative analysis.

The Integration of Fuzzy-ISM, Fuzzy-AHP, and Fuzzy-MICMAC Approach under Trapezoid Fuzzy Linguistic to Analyze Enablers of The Logistics Outsourcing Relationship: Mekong Delta, Vietnam Rice Supply Chain Context

The purpose of this paper is to analyze the effects of the factors and determine the importance of these factors to the LO relationship with the desire to improve the efficiency in logistics activities of the supply chain. An integrated approach including Fuzzy Interpretation Structure Model (FISM), Fuzzy Cross-Impact Matrix Multiplication Applied to Classification (FMICMAC) analysis, Fuzzy Analytic Hierarchy Process (FAHP) is structured in reaching this purpose. Specifically, the impact of factors on the LO relationship will be determined through the FISM-FMICMAC method, then FAHP will use the results from this FISM-FMICMAC analysis step to perform the determination of the level of importance of contributing factors to the LO relationship. The fuzzy number formats of this paper are all in trapezoidal format. To evaluate the proposed framework, a typical example of logistics activity in the Mekong Delta Rice Supply Chain (SuC) was selected. The results have shown the impact level of 14 factors on the LO relationship under 4 clusters (Dependent, Linkage, Independent Autonomous). Finally, only the 10 most outstanding of the 14 factors were used to conduct FAHP analysis to find the global weightages which contribute to the LO relationship by each factor.

Decision-Making Problem Based on Confidence Intuitionistic Trapezoidal Fuzzy Einstein Aggregation Operators and Their Application

Confidence level plays an important role in decision making in daily life. Therefore, the focus of our paper is to develop the idea of confidence level. With the help of confidence level in this paper, we explore some new operators, namely confidence intuitionistic trapezoidal fuzzy Einstein weighted averaging (abbreviated as CITFEWA) operator, confidence intuitionistic trapezoidal fuzzy Einstein ordered weighted averaging (abbreviated as CITFEOWA) operator, confidence intuitionistic trapezoidal fuzzy Einstein hybrid averaging (abbreviated as CITFEHA) operator, confidence intuitionistic trapezoidal fuzzy Einstein weighted geometric (abbreviated as CITFEWG) operator, confidence intuitionistic trapezoidal fuzzy Einstein ordered weighted geometric (abbreviated as CITFEOWG) operator and confidence intuitionistic trapezoidal fuzzy Einstein hybrid geometric (abbreviated as CITFEHG) operator. The benefit of the confidence approaches is that these techniques not only deliver evidence of the problems to the experts, but these operators and methods also develop the grades of the decision makers of that these experts are familiar with the option for the selection. To develop the proposed operators, we investigate and study some of their basic properties. To show the importance and efficiency of the new methods, these methods are applied to decision making. Lastly, an example is given for the confirmation of the viability and availability of the proposed approaches and methods.

A framework for group decision making with multiplicative trapezoidal fuzzy preference relations

Trapezoidal fuzzy numbers are efficient to represent the quantitative vagueness and ambiguity of decision makers (DMs). Preference relations are powerful to express pairwise judgments of DMs with respect to alternatives. Combining their advantages, this paper focuses on group decision making (GDM) with multiplicative trapezoidal fuzzy preference relations (MTrFPRs) and proposes a new consistency-consensus based GDM method. To achieve this goal, a new consistency concept for MTrFPRs is proposed by analyzing the drawbacks of the previous ones. By utilizing this concept, optimal models for judging the consistency of MTrFPRs are built. Meanwhile, a consistency index is proposed to measure the consistency level of any given MTrFPR. After that, an algorithm for ranking alternatives from acceptable consistent MTrFPRs is proposed. For GDM, a central-derivation model for determining the fuzzy measure on a set of DMs is proposed. Furthermore, an optimal model for reaching the consensus threshold is constructed. Finally, a GDM method with MTrFPRs is proposed and an application example is utilized to show the efficiency of the proposed GDM method and to compare with the existing GDM methods. The proposed GDM method outperforms the existing GDM methods. It provides us with a very useful way for GDM based on MTrFPRs.

Selection of projects for automotive assembly structures using a hybrid method composed of the group-input compatible, best-worst method for criteria weighting and TrBF-TOPSIS

The constant search for the optimal outcome, and its associated decision-making schemes within automotive assembly projects, can be greatly enhanced by utilizing informed decision methods that access relevant information. When simulated project alternatives are developed and benchmarks established, decision makers must select the appropriate project. When differences in opinion arise between decision makers, or when selection criteria are numerous, it can be difficult to be sure the correct choice was made. This highlights the need for a method that assists decision makers, when presented with such circumstances, so that they can be sure their choice is informed and optimal. Therefore, this paper proposes the use of a hybrid best-worst method (BWM) for weighting group decision making; and a Trapezoidal Bipolar Fuzzy TOPSIS (TrBF-TOPSIS) decision making strategy. The proposed method is used in ranking twenty-one design alternatives for automotive door assembly structures. The observed results indicate that the proposed method can be a relevant tool for variable selection in automotive assembly projects that involve multiple criteria and alternative designs.

The New Fuzzy Analytical Hierarchy Process with Interval Type-2 Trapezoidal Fuzzy Sets and Its Application

The degree of type-1 fuzzy sets membership function cannot express the linguistic variable of a complex problem. The type-2 fuzzy sets as a problem solver such that more fuzziness for constructing membership functions can be handled. Recently, many multi-criteria decision making (MCDM) methods have been expanded using type-2 fuzzy sets. Analytical Hierarchy Process (AHP) is one of the well-known MCDM that can take into account multiple and conflicting criteria at the same time. Our goal is to develop an interval type-2 trapezoidal fuzzy AHP through the new proposed ranking i.e. the modified total integral value. Based on the illustrative examples for trapezoidal type-2 fuzzy sets, the new proposed ranking has a well-performance in ranking. Furthermore, we apply the new trapezoidal type-2 fuzzy AHP to a supplier selection problem. Based on the results of the application, the new fuzzy AHP has the same ranking results as the existing fuzzy AHP.

An Area Similarity Measure for Trapezoidal Interval Type-2 Fuzzy Sets and Its Application to Service Quality Evaluation

An Area Similarity Measure for Trapezoidal Interval Type-2 Fuzzy Sets and Its Application to Service Quality Evaluation

An Extension of EDAS Method Equipped with Trapezoidal Bipolar Fuzzy Information: An Application from Healthcare System

An Extension of EDAS Method Equipped with Trapezoidal Bipolar Fuzzy Information: An Application from Healthcare System

A Proposed Technique to Resolve Transportation Problem by Trapezoidal Fuzzy Numbers

Objectives: To find the best optimal solution of transportation problem in fuzzy environment Method: We proposed a new method to find the optimal solution. Findings: This study introduces a Median method. By applying the same we transform the fuzzy transportation problem to an exquisite valued one and subsequently into a new proposed process to uncover the fuzzy realistic solution. Also, we find a minimum transportation cost. Novelty: The numerical illustration demonstrates that the new projected method for managing the transportation problems on fuzzy algorithms. AMS Mathematics Subject Classification (2010): 90C08, 90C90 Keywords Median, Median of Trapezoidal Fuzzy Numbers, Median of Triangular Fuzzy Numbers, Trapezoidal Fuzzy Numbers, Transportation Problem, and Fuzzy Transportation Problem

Comparative Analysis of Hybrid Fuzzy MCGDM Methodologies for Optimal Robot Selection Process

The generalized interval-valued trapezoidal fuzzy best-worst method (GITrF-BWM) provides more reliable and more consistent criteria weights for multiple criteria group decision making (MCGDM) problems. In this study, GITrF-BWM is integrated with the extended TOPSIS (technique for order preference by similarity to the ideal solution) and extended VIKOR (visekriterijumska optimizacija i kompromisno resenje) methods for the selection of the optimal industrial robot using fuzzy information. For a criteria-based selection process, assigning weights play a vital role and significantly affect the decision. Assigning weights based on direct opinions of decision makers can be biased, so weight deriving models, such as GITrF-BWM, overcome this discrepancy. In previous studies, generalized interval-valued trapezoidal fuzzy weights were not derived by using any MCGDM method for the robot selection process. For this study, both subjective and objective criteria are considered. The preferences of decision makers are provided with the help of linguistic terms that are then converted into fuzzy information. The stability and reliability of the methods were tested by performing sensitivity analysis, which showed that the ranking results of both the methodologies are not symmetrical, and the integration of GITrF-BWM with the extended TOPSIS method provides stable and reliable results as compared to the integration of GITrF-BWM with the extended VIKOR method. Hence, the proposed methodology provides robust optimal industrial robot selection.

Development of a multi-period multi-attribute group decision-making method using type- 2 fuzzy set of linguistic variables

Recently, fuzzy linguistic variables have gained a great deal of attention from researchers in many decision-making problems. In this problems, type-2 fuzzy sets have been used to better cover linguistic data uncertainty. However, many of research works in this regard have been performed in type-2 fuzzy domain and in static mode. Since the decision making problems in the real world usually fluctuate over time, so it need to use decision making models in multi period of time. In the present research, a Multi-Period (Dynamic) Multi-Attribute Group Decision-Making (MPMADM) method is presented based on type-2 fuzzy sets where decision-making attributes are first expressed in linguistic terms and then incorporated, as interval type-2 fuzzy numbers, into problem solving where a new integrating operator called Multi-Period Trapezoidal Interval Type-2 Fuzzy Number Weighted Arithmetic averaging (MPTIT2FNWA) is defined on type-2 interval fuzzy numbers to integrate decision-making information in multiple periods of time. Once finished with explaining the proposed method, a numerical example is given to evaluate the proposed method in terms of effectiveness and applicability, with the results compared to those of other methods.