Interval-valued Trapezoidal Fuzzy Numbers Research Articles

Risk Assessment of Constructing Deep Foundation Pits for Metro Stations Based on Fuzzy Evidence Reasoning and Two-tuple Linguistic Analytic Network Process

Accidents occur frequently while constructing deep foundation pits for metro stations, thereby risking substantial economic losses and casualties. To subject the construction of such pits to scientific and rational risk assessment and overcome the limitations of existing risk evaluation models and risk fusion problems, proposed here is a risk-assessment model for such pits based on fuzzy evidential reasoning and the two-tuple linguistic analytic network process (TL-ANP). First, the risk loss indicators are optimized, the weights of different risk events and of each risk loss indicator in the metro-station deep-foundation-pit construction project are calculated using TL-ANP, and trapezoidal fuzzy numbers are used to describe the occurrence probability of each risk event and loss. Second, relying on a table of expert weight indices, the best–worst method based on generalized interval-valued trapezoidal fuzzy numbers is used to determine the weights of experts. Finally, the overall risk grade of the construction project is evaluated by aggregating the risk levels of all risk events through an evidence-reasoning algorithm. The analysis results for a deep foundation pit for a station on Line 5 of Nanning Metro show that the model provides a quantitative basis for determining expert weights and risk loss weights reasonably and improving the reliability of the evaluation system. Also, not only does applying the method show that such a construction project can be judged as having a certain risk grade, but more importantly it can identify the key factors and loss indicators affecting the overall risk grade of the pit, whereupon risk control measures can be adopted in a targeted manner. In comparison with traditional methods, the proposed method is shown to be practical and effective, providing a reference basis for analyzing the risks of similar projects in the future and guaranteeing construction safety.

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.

A novel approach for solving all-pairs shortest path problem in an interval-valued fuzzy network: Suggested modifications

Enayattabr et al. (Journal of Intelligent and Fuzzy Systems 37 (2019) 6865– 6877) claimed that till now no one has proposed an approach to solve interval-valued trapezoidal fuzzy all-pairs shortest path problems (all-pairs shortest path problems in which distance between every two nodes is represented by an interval-valued trapezoidal fuzzy number). Also, to fill this gap, Enayattabr et al. proposed an approach to solve interval-valued trapezoidal fuzzy all-pairs shortest path problems. In this paper, an interval-valued trapezoidal fuzzy shortest path problem is considered to point out that Enayattabr et al.’s approach fails to find correct shortest distance between two fixed nodes. Hence, it is inappropriate to use Enayattabr et al.’s approach in its present from. Also, the required modifications are suggested to resolve this inappropriateness of Enayattabr et al.’s approach.

A Multistage Dynamic Emergency Decision-Making Method considering the Satisfaction under Uncertainty Information

Emergency decision-making (EDM) is of paramount importance, especially when the emergency occurs. The evolution nature of the emergency, such as multistage, uncertainty, dynamic, and information updating, has been playing a key role in the dynamic emergency decision-making process. However, most existing studies ignored the aforementioned nature. Our approach accounts for the dynamics inherent to a real emergency decision-making process and presents a multistage dynamic emergency decision-making (MSDEDM) procedure of a dynamic programming model based on decision-makers’ psychological reference satisfactory degree. Firstly, interval-valued trapezoidal intuitionistic fuzzy numbers (IVTrIFNs) are used to depict the relevant fuzziness and uncertainty of information. Secondly, by considering the dynamic evolution process of emergency and the decision-makers’ psychological reference expectation effect, the principle of MSDEDM approach is presented. Based on the analysis, the dynamic model on the new psychological reference satisfactory parameter formula is presented to obtain the optimal satisfaction and weight of each stage. Then, the value utility function based on the DMs’ risk attitude is proposed to obtain the comprehensive value of each emergency alternative for each stage and achieve the ranking results of each stage. Furthermore, a case study involving the transportation emergency decision-making problem demonstrates that the proposed method can achieve selection of the optimal alternatives for each stage, as well as adjustment of the alternatives for neighbouring stages. Finally, the comparative analysis and sensitivity analysis for the results are used to further verify the feasibility and practicability of the proposed method.

Fuzzy best-worst method based on generalized interval-valued trapezoidal fuzzy numbers for multi-criteria decision-making

This paper proposes a fuzzy best-worst method (BWM), called the GITrF BWM, based on generalized interval-valued trapezoidal fuzzy (GITrF) numbers (GITrFNs) for multi-criteria decision-making (MCDM). The reference comparisons between criteria are represented by GITrFNs and the weights of criteria are also taken the form of GITrFNs. The concept of normalized GITrF weight vector is proposed and a new graded mean integration representation (GMIR) of GITrFN is given. A goal programming model is built to obtain the optimal normalized GITrF weights of criteria. Furthermore, the GITrF consistency index and the GITrF consistency ratio are proposed. The GMIR of the GITrF consistency ratio is calculated to measure the acceptable consistency of all the reference comparisons between criteria. For the unacceptable consistent reference comparisons, we propose an approach to improve the consistency of reference comparisons between criteria. Finally, a GITrF BWM is proposed for MCDM. Three real examples are analyzed to illustrate the proposed GITrF BWM. The comparison analyses show that the proposed GITrF BWM outperforms the existing methods for MCDM in GITrF environments.

An Investigation Tool for Mounting Sustainable Practice

Smart mobile devices of the present era offer many services i.e. SMS, gaming, a camera, navigation, the Internet, television, etc., and their utilization has significantly risen during the last decades. Today, individuals are addicted to mobiles and cannot think of living without using them. Conversely, these mobiles become obsolete due to certain shortcomings and are eventually replaced with new ones and thus create e-waste, which are alarmed as threat to the society. In this work, the authors describe mobiles and e-waste in a closed loop structure for supporting green issues. The work has rooted generalized interval-valued trapezoidal fuzzy numbers (GIVTFNs) with a degree of similarity measure approach to model the rationale and to furnish decision results. The authors developed a decision support system to prevent e-waste by defining significant inadequacy liable for the larger alteration of working mobiles. The present study demonstrates the technical model under an Indian context to verify its applicability, but it can be used it under any regional or worldwide scenario.

A method for solving linear programming with interval-valued trapezoidal fuzzy variables

An efficient method to handle the uncertain parameters of a linear programming (LP) problem is to express the uncertain parameters by fuzzy numbers which are more realistic, and create a conceptual and theoretical framework for dealing with imprecision and vagueness. The fuzzy LP (FLP) models in the literature generally either incorporate the imprecisions related to the coefficients of the objective function, the values of the right-hand side, and/or the elements of the coefficient matrix. The aim of this article is to introduce a formulation of FLP problems involving interval-valued trapezoidal fuzzy numbers for the decision variables and the right-hand-side of the constraints. We propose a new method for solving this kind of FLP problems based on comparison of interval-valued fuzzy numbers by the help of signed distance ranking. To do this, we first define an auxiliary problem, having only interval-valued trapezoidal fuzzy cost coefficients, and then study the relationships between these problems leading to a solution for the primary problem. It is demonstrated that study of LP problems with interval-valued trapezoidal fuzzy variables gives rise to the same expected results as those obtained for LP with trapezoidal fuzzy variables.

Fuzzy shortest path in an interval-valued fuzzy hypergraph using similarity measures

In this paper, a new approach is introduced to find the shortest path between two given vertices on interval-valued fuzzy hypergraphs. When only crisp numbers are not sufficient to measure a real world parameter, fuzzy numbers are considered. But, there are many types of fuzzy numbers available in literature. Most useful fuzzy number is trapezoidal fuzzy numbers. Throughout this paper the interval-valued trapezoidal fuzzy number is used as the arc length of the interval-valued fuzzy hypergraph. We have measured similarity between two interval-valued fuzzy numbers to find the shortest path. An algorithm is also designed to find all possible hyperpaths in a hypergraph and calculated its time complexity

Non-Linear Arithmetic Operations on Interval Valued Trapezoidal Fuzzy Numbers

Fuzzy numbers have been introduced by Zadeh in order to deal with imprecise numerical quantities in a practical way. In this paper, some types of interval valued trapezoidal fuzzy numbers (IVTrFNs) and some non-linear arithmetic operations on interval valued trapezoidal fuzzy numbers have been proposed. Also relevant numerical illustrations are included to justify the above said notions.

Fuzzy risk analysis in familial breast cancer using a similarity measure of interval-valued fuzzy numbers

In this work, a new similarity measure was proposed based on the heights and areas of interval-valued trapezoidal fuzzy numbers. Some properties corresponding to the proposed similarity measure were illustrated. A comparison with the different existing similarity-measurement techniques demonstrated that the proposed method gave better results, overcoming the drawbacks of the existing methods. The proposed similarity-measurement technique was applied to the prediction of risk in the burning problem of Familial Breast Cancer (FBC). Finally, a numerical illustration for FBC was given using interval-valued trapezoidal fuzzy numbers.

Fuzzy linear programming approach for solving transportation problems with interval-valued trapezoidal fuzzy numbers

Transportation problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order to satisfy demands at destinations using available supplies at origins in a crisp environment. In real life situations, the decision maker may not be sure about the precise values of the coefficients belonging to the transportation problem. The aim of this paper is to introduce a formulation of TP involving interval-valued trapezoidal fuzzy numbers for the transportation costs and values of supplies and demands. We propose a fuzzy linear programming approach for solving interval-valued trapezoidal fuzzy numbers transportation problem based on comparison of interval-valued fuzzy numbers by the help of signed distance ranking. To illustrate the proposed approach an application example is solved. It is demonstrated that study of interval-valued trapezoidal fuzzy numbers transportation problem gives rise to the same expected results as those obtained for TP with trapezoidal fuzzy numbers.

Application of modified MULTI-MOORA for CNC machine tool evaluation in IVGTFNS environment: an empirical study

In this reporting, an aforesaid CNC machine tool evaluation appraisement module (index) has been conceptualised from the resource of existing literature to evaluation and ranking order of preferred candidate CNC machine tool. In this reporting, generalised interval-valued trapezoidal fuzzy numbers ordered weighted geometric average (GITFNOWGA) operator has been fruitfully and effectively applied for deliver important weights against measures based on set the expert panel subjective preference assessment (rating) in ascending order and then aggregate appropriate rating with following generalised interval-valued trapezoidal fuzzy numbers rule. Finally, multi objective optimisation by ratio analysis (MULTI-MOORA) based on different parts of MULTI-MOORA, namely: ratio system, reference point, and full multification form has been explored coupled with aggregated interval valued trapezoidal fuzzy number set in perceptive to evaluating and benchmarking the CNC machine tool from preferred options/alternatives. Finally, a case study is shown to highlight the proposed procedure.

Reprint of “Green decision-making model in reverse logistics using FUZZY-VIKOR method”

Due to the increasing global environmental consciousness and sustainability concerns, different industries that deal with Reverse Logistics (RL) are seeking methods to measure and analyze the impacts of their RL activities on the environment. However, making the greenest decision in the vague and complex area of RL makes this process somewhat difficult. Hence, to address these issues and provide a more meticulous and closer approach to the real world situations, a FUZZY-VIKOR method using interval-valued trapezoidal fuzzy numbers is proposed in the current research. As the further discussions explain, first, the significant factors in environmental sound practices together with the main processes and recovery options in RL are identified. Second, the influences of each green environmental factor on each RL recovery option are analyzed and ranked. To obtain concise results, the elicitation of experts is sought from among academicians and industry. The final results illustrate that, intriguingly, disposing of the returns has the lowest negative impact on the environment; thereby the best recovery option, while reselling of the returns was perceived as the worst recovery option. This research also suggests new directions for future research. From the managerial point of view, it would be interesting to study a sustainable reverse logistics through the proposed model. We only considered the impacts of environmental factors on RL, while the final decision will be more exact if the economic and societal aspects of RL are also analyzed. In addition, to reflect the technical views of all the stakeholders in RL towards the best recovery option and also take into account their concerns, we suggest designing a group decision making model across the RL using the Fuzzy-MADM methods.

Green decision-making model in reverse logistics using FUZZY-VIKOR method

Due to the increasing global environmental consciousness and sustainability concerns, different industries that deal with Reverse Logistics (RL) are seeking methods to measure and analyze the impacts of their RL activities on the environment. However, making the greenest decision in the vague and complex area of RL makes this process somewhat difficult. Hence, to address these issues and provide a more meticulous and closer approach to the real world situations, a FUZZY-VIKOR method using interval-valued trapezoidal fuzzy numbers is proposed in the current research. As the further discussions explain, first, the significant factors in environmental sound practices together with the main processes and recovery options in RL are identified. Second, the influences of each green environmental factor on each RL recovery option are analyzed and ranked. To obtain concise results, the elicitation of experts is sought from among academicians and industry. The final results illustrate that, intriguingly, disposing of the returns has the lowest negative impact on the environment; thereby the best recovery option, while reselling of the returns was perceived as the worst recovery option. This research also suggests new directions for future research. From the managerial point of view, it would be interesting to study a sustainable reverse logistics through the proposed model. We only considered the impacts of environmental factors on RL, while the final decision will be more exact if the economic and societal aspects of RL are also analyzed. In addition, to reflect the technical views of all the stakeholders in RL towards the best recovery option and also take into account their concerns, we suggest designing a group decision making model across the RL using the Fuzzy-MADM methods.

A geometric aggregation operator for decision making

We proposed an aggregation operator which is used to aggregate decision makers’ opinions in group decision making process. First, a Choquet integral-based distance between generalized interval-valued trapezoidal fuzzy numbers is defined. Then combining the generalized interval-valued trapezoidal fuzzy number aggregation operator with Choquet integral-based distance, an extension of technique for order preference by similarity to ideal solution method is developed to deal with a multi-criteria generalized interval-valued trapezoidal fuzzy number group decision making problems, where inter-dependent or interactive characteristics among criteria preference of decision makers are also considered. Finally, an illustrative example is provided to elaborate the proposed method.

A multi-attribute large group emergency decision making method based on group preference consistency of generalized interval-valued trapezoidal fuzzy numbers

In this paper, a new decision making approach is proposed for the multi-attribute large group emergency decision-making problem that attribute weights are unknown and expert preference information is expressed by generalized interval-valued trapezoidal fuzzy numbers (GITFNs). Firstly, a degree of similarity formula between GITFNs is presented. Secondly, expert preference information on different alternatives is clustered into several aggregations via the fuzzy clustering method. As the clustering proceeds, an index of group preference consistency is introduced to ensure the clustering effect, and then the group preference information on different alternatives is obtained. Thirdly, the TOPSIS method is used to rank the alternatives. Finally, an example is taken to show the feasibility and effectiveness of this approach. These method can ensure the consistency degree of group preference, thus decision efficiency of emergency response activities can be improved.

Dynamic Multi-Attribute Group Decision Making Model Based on Generalized Interval-Valued Trapezoidal Fuzzy Numbers

Abstract In this paper we investigate the dynamic multi-attribute group decision making problems, in which all the attribute values are provided by multiple decision makers at different periods. In order to increase the level of overall satisfaction for the final decision and deal with uncertainty, the attribute values are enhanced with generalized interval-valued trapezoidal fuzzy numbers to cope with the vagueness and indeterminacy. We first define the Dynamic Generalized Interval-valued Trapezoidal Fuzzy Numbers Weighted Geometric Aggregation (DGITFNWGA) operator and give an approach to determine the weights of periods, using the probability density function of Gamma distribution, and then a dynamic multi-attribute group decision making method is developed. The method proposed employs the Generalized Interval-valued Trapezoidal Fuzzy Numbers Hybrid Geometric Aggregation (GITFNHGA) operator to aggregate all individual decision information into the collective attribute values corresponding to each alternative at the same time period, and then utilizes the DGITFNWGA operator to aggregate the collective attribute values at different periods into the overall attribute values corresponding to each alternative and obtains the alternatives ranking, by which the optimal alternative can be determined. Finally, an illustrative example is given to verify the approach developed.

Robot selection by using generalized interval-valued fuzzy numbers with TOPSIS

The aim of this paper is to propose a method to aggregate the opinion of several decision makers on different criteria, regarding a set of alternatives, where the judgment of the decision makers are represented by generalized interval-valued trapezoidal fuzzy numbers. A generalized interval valued trapezoidal fuzzy number based technique for order preference by similarity to ideal solution is proposed that can reflect subjective judgment and objective information in real life. The weights of criteria and performance rating values of criteria are linguistic variables expressed as generalized interval-valued trapezoidal fuzzy numbers. Finally, an illustrative example is provided to elaborate the proposed method for the selection of a suitable robot according to our requirements.

Leanness estimation procedural hierarchy using interval-valued fuzzy sets (IVFS)

Purpose– Lean manufacturing is an operational strategy oriented toward achieving the shortest possible cycle time by eliminating waste. It is derived from the Toyota Production System and its key thrust is to increase the value-added work by eliminating waste and reducing incidental work. In today's competitive global marketplace, the concept of lean manufacturing has gained vital consciousness to all manufacturing sectors, their supply chains, and hence a logical measurement index system is indeed required in implementing leanness in practice. Such leanness estimation can help the enterprises to assess their existing leanness level and can compare different industries who are adapting this lean concept. The paper aims to discuss these issues.Design/methodology/approach– The present work exhibits an efficient fuzzy-based leanness assessment system using generalized interval-valued (IV) trapezoidal fuzzy numbers set. The concept of “degree of similarity” between two IV fuzzy numbers has been explored here to identify ill-performing areas towards lean achievement.Findings– The methodology described here has been found fruitful while applying for a particular industry, in India, as a case study. Apart from estimating overall lean performance metric, the model presented here can identify ill-performing areas towards lean achievement.Originality/value– The major contributions of this work have been summarized as follows: development and implementation of an efficient decision-making procedural hierarchy to support leanness extent evaluation. An overall lean performance index evaluation platform has been introduced. Concept of generalized IV trapezoidal fuzzy numbers has been efficiently explored to facilitate this decision-making. The appraisement index system has been extended with the capability to search ill-performing areas which require future progress.

The Interval-Valued Trapezoidal Approximation of Interval-Valued Fuzzy Numbers and Its Application in Fuzzy Risk Analysis

Taking into account that interval-valued fuzzy numbers can provide more flexibility to represent the imprecise information and interval-valued trapezoidal fuzzy numbers are widely used in practice, this paper devotes to seek an approximation operator that produces an interval-valued trapezoidal fuzzy number which is the nearest one to the given interval-valued fuzzy number, and the approximation operator preserves the core of the original interval-valued fuzzy number with respect to the weighted distance. As an application, we use the interval-valued trapezoidal approximation to handle fuzzy risk analysis problems, which overcome the drawback of existing fuzzy risk analysis methods.