Interval Type-2 Trapezoidal Fuzzy Numbers Research Articles

Comparative Ranking Preferences Decision Analysis through a Novel Fuzzy TOPSIS Technique for Vehicle Selection

Acquiring a vehicle or financing its purchase is often considered a luxury, particularly for middle-class households. In addition to their primary concern, consumers prioritize distinguishing elements such as vehicle type, size, capacity, engine power, fuel efficiency, safety features, and life-cycle costs. Furthermore, the choice of vehicle has multiple factors and is contingent upon the financial prosperity of the household, allowing for precise expression. The decision-making process is complex and entails selecting the most appropriate alternatives. This study proposes a novel fuzzy technique for order of preference by similarity to the ideal solution (FTOPSIS) method to solve vehicle selection multi-criteria decision-making (MCDM) problems. Decision-makers express their opinions on each alternative and criterion in linguistic terms, in terms of generalized interval type-2 trapezoidal fuzzy numbers (GIT2TrFNs). The FTOPSIS process involved utilizing the defuzzification of GIT2TrFNs to acquire the normalization matrix. Finally, the proposed approach prioritizes the options and chooses the best vehicle when faced with conflicting criteria, as illustrated through a numerical illustration.

Sustainable Urban Conveyance Selection through MCGDM Using a New Ranking on Generalized Interval Type-2 Trapezoidal Fuzzy Number

This article proposes a modified ranking technique for generalized interval type-2 trapezoidal fuzzy numbers. For demonstrating uncertainty and managing imprecision in decision-making information, interval type-2 fuzzy sets are beneficial. The proposed ranking methodology resolves the difficulty of multi-criteria group decision-making on sustainable urban conveyance. Additionally, the proposed ranking approach considers all crucial aspects of transportation sustainability, including the effectiveness of durable transportation systems from economic, social, and ecological perspectives in multi-criteria group decision-making scenarios. The new ranking methodology yields superior outcomes for choosing sustainable urban transportation options. In the numerical part, studies compared the proposed ranking approach to other methods currently used for various MCDM techniques.

Sustainable Supplier Selection and Evaluation for the Effective Supply Chain Management System

With increased environmental protection awareness, sustainability has been incorporated into supply chain management. Sustainable supplier selection and evaluation have become an acritical part of supply chain management. They can significantly improve the supply chain’s operational performance and enhance enterprises’ competitiveness. Based on trapezoidal interval type-2 fuzzy numbers (TIT2FNs) and cloud probability dominance relations (PDR), manufacturers can make more tangible and environmentally friendly decisions in the SSSE process. In this paper, a SSSE indicator system is first established using the necessary economic, environmental, and social factors. The importance of the indicators described in linguistic terms is transformed into TIT2FNs, and the weight of each indicator is calculated. In order to prevent candidate suppliers from promoting performance maliciously, different weights are given according to the impact of the enterprise’s historical performance on the present. Finally, the cloud PDR method is used to determine the optimal sustainable supplier. A case study and analysis are provided to show the feasibility and superiority of the proposed method.

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.

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.

The solution for type-2 fuzzy linear programming model based on the nearest interval approximation

Linear programming is an important branch of operations research. The model is mature in theory and widely used in real life. However, various complex realistic scenarios involve fuzzy information. In this paper, we consider a fuzzy linear programming (FLP) model in which all parameters are trapezoidal interval type-2 fuzzy numbers (IT2FNs) and propose a solution method based on the nearest interval approximation and the best-worst cases (BWC) method. We prove the nearest interval approximation interval of trapezoidal IT2FNs, then the trapezoidal IT2FNs in the model are transformed into interval numbers which both upper and lower limits are interval numbers. With the help of best-worst cases (BWC) method, the sub-models of the transformed interval linear programming model are proposed, and four sub-solutions with different specific meanings can be obtained by solving them respectively. Finally, an application example is presented to show the rationality and practical significance of the method.

Introducing a trapezoidal interval type-2 fuzzy regression model

The uncertainty is an important attribute about data that can arise from different sources including randomness and fuzziness, therefore in uncertain environments, especially, in modeling, planning, decision-making, and control under uncertainty, most data available contain some degree of fuzziness, randomness, or both, and at the same time, some of this data may be anomalous (outliers). In this regard, the new fuzzy regression approaches by creating a functional relationship between response and explanatory variables can provide efficient tools to explanation, prediction and possibly control of randomness, fuzziness, and outliers in the data obtained from uncertain environments. In the present study, we propose a new two-stage fuzzy linear regression model based on a new interval type-2 (IT2) fuzzy least absolute deviation (FLAD) method so that regression coefficients and dependent variables are trapezoidal IT2 fuzzy numbers and independent variables are crisp. In the first stage, to estimate the IT2 fuzzy regression coefficients and provide an initial model (by original dataset), we introduce two new distance measures for comparison of IT2 fuzzy numbers and propose a novel framework for solving fuzzy mathematical programming problems. In the second stage, we introduce a new procedure to determine the mild and extreme fuzzy outlier cutoffs and apply them to remove the outliers, and then provide the final model based on a clean dataset. Furthermore, to evaluate the performance of the proposed methodology, we introduce and employ suitable goodness of fit indices. Finally, to illustrate the theoretical results of the proposed method and explain how it can be used to derive the regression model with IT2 trapezoidal fuzzy data, as well as compare the performance of the proposed model with some well-known models using training data designed by Tanaka et al. [55], we provide two numerical examples.

An extended gained and lost dominance score method based risk prioritization for Fine-Kinney model with interval type-2 fuzzy information

The Fine-Kinney model is one of the most extensively adopted classical occupational risk analysis techniques which has been regarded as a helpful means for addressing the risk identification and evaluation problems in various fields. However, current extended Fine-Kinney models have limited capacity to cope with occupational risk evaluation and prioritization problems considering interactive relationships among multi-risk parameters under inter-uncertain and intra-uncertain environments. To overcome the limitations, this paper proposes a hybrid risk prioritization approach for the Fine-Kinney model by integrating GLDS (gained and lost dominance score) method, interval type-2 fuzzy sets (IT2FSs), and Maclaurin symmetric mean (MSM) operator. First, the trapezoidal interval type-2 fuzzy numbers (TrIT2FNs) are introduced to depict the inter-uncertain and intra-uncertain risk evaluation information. Then, an ordered weighted averaging (OWA) operator is constructed to aggregate the complex and uncertain risk evaluation information from heterogeneous decision-makers in which the similarity-measure-based weighting method is incorporated. Next, the GLDS method combined with the weighted MSM operator is developed to address the risk prioritization problem in the Fine-Kinney model by considering the inter-dependencies among multi-risk parameters. Finally, a numerical example of occupational risk evaluation for potential hazards in construction excavation is presented within IT2FSs to demonstrate the application and availability of the extended Fine-Kinney model. After that, the comparison and sensitivity analyses are conducted to further illustrate the superiority and rationality of the proposed approach.

The integrated PFMEA approach with interval type-2 fuzzy sets and FBWM: A case study in the automotive industry

The change of market’s demand could be predictable to a certain degree at stable conditions but it may vary due to disruptive events. This research contributes by establishing the improvement of PFMEA (Process Failure Mode and Effect Analysis) analysis in the domain of assessment and determining severity risk factor, as well as identifying of failure priority. According to the researchers’ and practitioners’ suggestions, severity needs to be considered from the multiple aspects. The risk factor severity is considered from the aspects of product importance, quality, and cost. These aspects have different relative importance, which is determined in an exact way. The relative importance of the aspects, as well as the values of the risk factors, was described by linguistic expressions that are modeled by using the Interval type-2 trapezoidal fuzzy numbers (IT2TrFNs). IT2FBWM was used to determine weight vectors of risk factors. The priority of failures is determined according to the Action priority model which proposed by AIAG & VDA (Automotive Industry Action Group and German Association of the Automotive Industry). The proposed methodology is tested in a Case study where the real-life data originated from a company from the Republic of Serbia that operates as a part of an automotive supply chain.

A Hybrid Methodology for Prioritizing of Store Plan Alternatives Produced with Rule-Based Design

With the widespread use of computers, in the design world, rule-based design methods, which can work in harmony with computer logic and can be easily adapted to the computer environment, have come to the fore. It is possible to analyze the logic of a design made with the rule-based design method. It is even possible to change the design which is placed on the rule base by removing the rules, in the computer environment, or creating new designs with the same design logic. In this paper, a new hybrid model is proposed based on Interval Type-2 Fuzzy Analytic Network Process (IT2 FANP) and Interval Type-2 Fuzzy TOPSIS (IT2 Fuzzy TOPSIS) for the evaluation of store plan alternatives produced with rule-based design method. The IT2 FANP method is used to determine the weight of criteria determined by experts in the selection of store plan alternatives. Then, the IT2 Fuzzy TOPSIS method is used to obtain the ranking of alternatives with Interval Type-2 trapezoidal fuzzy numbers. The originality of the paper comes from the first-time usage of a hybrid approach based on IT2 FANP and IT2 Fuzzy TOPSIS methodology in the prioritizing of store plan alternatives produced with rule-based design method.

Selection of solar tracking system using extended TOPSIS technique with interval type-2 pythagorean fuzzy numbers

The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is considered among the most frequently used techniques to deal with multi-criteria group decision-making (MCGDM) conflicts. In this article, we have presented an extended TOPSIS technique in the framework of interval type-2 trapezoidal Pythagorean fuzzy numbers (IT2TrPFN). We first projected a novel approach to evaluate the distance between them using ordered weighted averaging operator and (alpha ,beta )-cut. Subsequently, we widen the concept of TOPSIS method formed on the distance method with IT2TrPFNs and applied it on MCGDM dilemma by considering the attitudes and perspectives of the decision-makers. Lastly, an application of solar tracking system and numerous contrasts with the other existing techniques are presented to express the practicality and feasibility of our projected approach.

Ranking of interval type 2 fuzzy numbers using correlation coefficient and Mellin transform

Ranking of fuzzy numbers exhibits a significant role to solve the multiple attributes group decision making (MAGDM) problems. One of the commonly used indices for MAGDM problems is the correlation coefficient. Type-2 fuzzy numbers (T2FNs) are considered to be more effective than type-1 fuzzy numbers (T1FNs) to handle uncertainties in MAGDM problems. Moreover, T2FNs allow additional freedom to reflect uncertainty. In this paper, we propose a new approach to rank the interval type-2 fuzzy numbers (IT2FNs) using the correlation coefficient, where the correlation coefficient is obtained using the Mellin transform. Initially, we define the correlation coefficient for interval type-2 trapezoidal fuzzy numbers (IT2TrFNs) using Mellin transform and prove some of its major features. Then a new group decision-making method has been recommended using the proposed ranking concept. Eventually, three examples are given to demonstrate the usefulness of the suggested method. Finally, a comparative study is conducted to depict the feasibility of the developed ranking technique.

Multi-attribute decision making using grey relational projection method based on interval type-2 trapezoidal fuzzy numbers

Multi-attribute decision making using grey relational projection method based on interval type-2 trapezoidal fuzzy numbers

A new multiple attribute decision making method for selecting design schemes in sponge city construction with trapezoidal interval type-2 fuzzy information

Selecting the most suitable design scheme in sponge city construction can be seen as a multiple attribute decision-making (MADM) problem. To express the uncertain and fuzzy decision-making information, interval type-2 fuzzy sets (IT2FSs) are useful tools. The paper focuses on decision making with trapezoidal interval type-2 fuzzy numbers (TIT2FNs) and discusses the evaluation of municipal road design schemes in sponge city construction. To do these, several operations on TIT2FNs based on Hamacher t-norm and t-conorm are first defined, where both the operations on the membership degree and on eight non-negative real values are considered. Then, two (2-additive) generalized Shapley trapezoidal interval type-2 fuzzy Hamacher Choquet integral operators are presented, which globally reflect interactions among elements. Considering the case where the decision-making weighting information is incomplete known, Manhattan distance measure-based models for obtaining the optimal fuzzy measure and 2-additive measure are constructed, respectively. Furthermore, an approach for trapezoidal interval type-2 fuzzy MADM is developed. Finally, a practical example is provided to illustrate the utilization of the new method, and comparison analysis is provided.

A new soft computing approach for green supplier selection problem with interval type-2 trapezoidal fuzzy statistical group decision and avoidance of information loss

Green supplier selection problem (GSSP) is viewed as multiple attributes group decision-making (MAGDM) issue that includes the green growth and influential factors within subjective and objective natures. Because of the expanding uncertain conditions of social and economic environments, some assessment factors are not sufficiently described by numerical appraisals and classic fuzzy sets. Moreover, supply chain decision makers (DMs) may not provide complete rationality under numerous viable choice circumstances. In this research, a new MAGDM model is proposed by interval type-2 trapezoidal fuzzy numbers (IT2TrFNs) via some matrices of possibilistic mean and standard deviation statistical concepts. A new weighting method of experts within the group decision-making process is developed based on possibilistic statistical information. Also, a new ranking process based on relative-closeness coefficients is presented to rank all green supplier candidates under IT2TrF uncertainty. Finally, this research offers an illustrative example in supply chain networks to appraise green supplier candidates in terms of some factors by the proposed model along with the comparison to a recent decision method.

Some new signed distances and similarity measures of interval type-2 trapezoidal fuzzy numbers and comparative study

Some new signed distances and similarity measures of interval type-2 trapezoidal fuzzy numbers and comparative study

Trapezoidal interval type-2 fuzzy soft stochastic set and its application in stochastic multi-criteria decision-making

Trapezoidal interval type-2 fuzzy soft set (TrIT2FSS) (Zhang and Zhang, Appl Math Model 37:4948–4971, 2013) is a delicious generalization of soft set theory where the performance of the alternatives over some parameters is assigned by means of trapezoidal interval type-2 fuzzy numbers (TrIT2FNs). Zhang and Zhang (2013) proposed an approach to multi-criteria group decision-making (MCGDM) problems under trapezoidal interval type-2 fuzzy soft set. However, due to the increasing complexity of decision-making problems, the performance of the alternatives may be determined randomly with respect to some possible states related to the decision-making problems which are known as stochastic multi-criteria decision-making (SMCDM) problems. To handle such type of SMCDM problems based on trapezoidal interval type-2 fuzzy soft set, no research exists till now. To fill up this lacuna, here we have formulated a new generalization of TrIT2FSS to solve the MCDM problems under stochastic environment. First, we have introduced the notion of trapezoidal interval type-2 fuzzy soft stochastic set (TrIT2FSSS). Second, we deal with the obligatory definition of expected trapezoidal interval type-2 fuzzy soft set (ETrIT2FSS). Finally, we have proposed a methodology for handling the trapezoidal interval type-2 fuzzy soft stochastic set (TrIT2FSSS) based stochastic MCDM problems. Additionally, in this model we have assumed that the weights of each of the parameters are partially known. We have proposed a process to obtain the weights of the parameters using signed distance measurement. An application of our proposed approach regarding the selection of the best company for investment of a bank has also been given to describe the feasibility and effectiveness of our proposed approach.

Rankings and operations for interval type-2 fuzzy numbers: a review and some new methods

Interval type-2 fuzzy numbers (IT2FNs) are a particular kind of type-2 fuzzy numbers (T2FNs). In most scientific works, since arithmetic operations required IT2FNs are simpler than those of T2FNs, mathematical calculations on IT2FNs are used more frequently rather than the T2FNs. Hence, in recent decades, the study on IT2FNs have been intensified significantly. These numbers can be explained by trapezoidal and triangular forms. In this article, first, the concept of general interval type-2 trapezoidal fuzzy numbers (GIT2TrFNs) and then arithmetic operations among them are introduced. Next, three new ranking methods are suggested for GIT2TrFN. Finally, several examples are used to illustrate and compare new ranking methods with others.

A multi-item transportation problem with mode of transportation preference by MCDM method in interval type-2 fuzzy environment

In this paper, we employ all the parameters as trapezoidal interval type-2 fuzzy numbers to cope with ambiguity and vagueness problem. There are two issues being addressed in this paper. The first is the selection of the most convenient transportation mode. We present a method for solving multi-criteria decision-making problem to deal with evaluating and ranking alternatives from the best to the worst with respect to decision maker(s) preferences. This is applied to find the most preferred transportation mode among available modes concerning some evaluation criteria for a transportation problem. A possibility degree is used for comparisons between the overall values of alternatives to raise a possibility degree matrix. Based on that matrix, the alternatives are ranked according to the ranking vector derived from the matrix, and the best one is selected. The second is to construct a multi-item transportation problem using that preferred mode of transportation. To get the crisp model, a defuzzification approach is adopted. To convert multi-objective transportation problem into a single-objective problem, two different techniques (i) fuzzy goal programming method and (ii) convex combination method are used. Then the reduced single-objective problem is solved by generalized reduced gradient method (LINGO-14.0) and a set of optimal solutions are obtained and presented graphically.

Multi-criteria decision-making method based on type-2 fuzzy sets

Type-2 fuzzy sets (T2FSs) are the extension of type-1 fuzzy sets (T1FSs), which can convey more uncertainty information in solving multi-criteria decision-making (MCDM) problems. Motivated by the extension from interval numbers to triangular fuzzy numbers, three-trapezoidal-fuzzy-number-bounded type-2 fuzzy numbers (TT2FNs) are defined on the basis of interval type-2 trapezoidal fuzzy numbers (IT2TFNs), and they can convey more uncertainty information than T1FSs and IT2FSs. Moreover, the drawbacks of the existing computational models of generalized fuzzy numbers are analyzed, and a new computational model of fuzzy numbers is proposed, which is further extended to TT2FNs. Besides, a MCDM method is proposed to deal with the evaluation information given in the form of TT2FNs. Finally, an illustrative example and comparison analysis are provided to demonstrate the feasibility and validity of the proposed method.