Trapezoidal Interval Research Articles

Two-level balancing multi-objective algorithm for trapezoidal type-2 fuzzy flexible job shop problems

Uncertainty remains a critical issue in realistic applications in many fields. However, there is little literature considering trapezoidal interval type-2 fuzzy set (TIT2FS) in scheduling problems. To fill this gap, we propose a two-level balancing multi-objective optimization algorithm for a distributed flexible job shop scheduling problem (DFJSP), wherein two typical constraints are considered: the TIT2FS processing time and the transportation resource limitation. Two objectives are to be minimized: the TIT2FS fuzzy makespan and energy consumption. A two-level evolution mechanism is employed. The first level comprises two populations to optimize the two respective objectives, while the second level is composed of two populations to perform the convergence and diversity balancing tasks. Next, an efficient problem-specific initialization method with several heuristics is presented. Subsequently, different types of mutation and crossover operators are proposed under the consideration of problem knowledge. To further improve the performance of exploration and exploitation abilities, we present a balancing enhanced local search method. Finally, we performed detailed comparisons with four efficient algorithms. The results show that the two-level optimization algorithm was efficient in both convergence and diversity abilities, indicating that our algorithm can efficiently achieve a balance between these abilities.

Sustainable-resilient-responsive supply chain with demand prediction: An interval type-2 robust programming approach

This study configures a novus multi-objective three-stage supply chain network that aims at optimizing sustainability, resilient and responsive measures, simultaneously. At first, a novel prediction model based on Markov chain, Dempster-Safer evidence theory and Shapely value is developed under trapezoidal interval type-2 fuzzy ambience to predict the demand of future scenarios. The prediction model prevents undesired loss occurred due to illogical demand consideration. To encounter interval type-2 fuzziness as well as risk in decision making, an unprecedented trapezoidal interval type-2 fuzzy robust possibilistic programming approach is introduced. The DEcision MAking Trial and Evaluation Laboratory method is suggested in the framework of trapezoidal interval type-2 fuzzy to prioritize the objective function by scrutinizing the interrelationship among different objective function components. As a result, the subjectiveness in the decision making framework is reduced. The generated configuration is then analysed using a blended approach that merges multi-choice reference goal programming with utility functions and particle swarm optimization. The integrated approach produces high-quality solution in lesser computational time. The insightful explorations are delivered based on a case study of hydrogen fuel supply chain in India. The outcomes show how resilient tactics are quite effective and can significantly enhance social, environmental, and economic aspects. It is determined that the best results for supply chain are obtained when the suggested sustainable, resilience and responsiveness tactics are used jointly. Moreover, the sensitivity analysis results suggest that the objective functions are substantially affected by the responsive level; therefore, managers ought to envisage the trade-off between responsiveness and other objective functions.

Optimal site selection for construction and demolition waste disposal using GIS-FAHP: a case study from Kafr El Sheikh City, Egypt.

The increasing number of building and demolition projects results in huge amounts of construction and demolition wastes (CDWs) that are illegally dumped. However, these wastes must be disposed of in appropriate legal sites to protect the environment and human health. After reviewing the literature, no prior research examined optimal site selection for dumping or recycling CDW in an Egyptian city. Furthermore, the absence of field surveys did not offer a holistic understanding of the specific criteria used in the model for this region, nor did it permit an assessment of the suitability of existing dumpsites, thereby revealing certain limitations in the final results. In this regard, this research aims to apply a multi-criteria geographic information system (GIS)-based framework to identify an optimal site for CDW disposal in Kafr El Sheikh City. The criteria affecting the site selection are identified and categorized from prior literature, which are further refined using field surveys and focus group to evaluate their applicability in the context of an Egyptian city. After conducting questionnaire surveys, the trapezoidal interval type II fuzzy analytic hierarchy process is applied to compute the weights of the identified criteria from the perspective of each group of experts. The entropy-based aggregation approach is employed to identify the compromise weights taking into account the preferences of different groups. GIS is a powerful tool for geoprocessing and analyzing spatial big data. The result is a scenario map for the optimal site locations with varying suitability scales (i.e., excellent, very good, good, average, poor, and very poor). The proposed methodology provides what-if scenarios based on a selected set of criteria. According to the results of the multi-criteria decision analysis models, the suitability varies based on the weights of the criteria. For the equal-weighted criteria model, the excellent category covers 5.96% of the study area, increasing to 6.48% for the weighted criteria model. These areas primarily lie in the northeast direction. Conversely, the majority of the study area, 41.80% under equal-weighted criteria and 32.39% under weighted criteria, falls within the average and poor suitability categories, respectively. In general, the most suitable areas are located on the outskirts of the city, and the suitability decreases near the central business district. To bridge the gap between research findings and practical applications, a land use analysis employing satellite imagery is conducted to pinpoint suitable locations for CDW disposal. Existing CDW dumpsites predominantly fall within the range of poor to very good for the equal-weighted criteria model, while the weighted criteria model categorizes them into the poor (16.66%) and average (83.33%) categories. The findings demonstrated the applicability of the proposed framework for CDW disposal management and planning.

A methodology for personnel selection in business development: An interval type 2-based fuzzy DEMATEL-ANP approach

The employee selection procedure holds significant importance for every company or organization involved in current economic activities. It is vital to underscore staff selection since it plays a crucial role in determining a firm's success. When a corporation selects a suitable applicant for a position and initiates the recruiting process, it might mark a critical point for the firm and substantially impact its functioning. In the present study, I utilized the trapezoidal interval type-2 (IT2) fuzzy Decision-Making Trial and Evaluation Laboratory (DEMATEL) - Analytic Network Process (ANP) methodology to conduct person selection. Additionally, statistically significant values for both the primary and secondary criteria related to staff recruitment were determined. The employment of square comparison matrices is essential for implementing the DEMATEL-ANP approach. The number of subcriteria for this application is equal to that of the alternative. The approach was successfully executed without facing any obstacles. The aim of this research was to investigate the viability of employing IT2 Fuzzy Systems to handle and control uncertainty efficiently. In addition, the implementation of sensitivity analysis plays a vital role in the context of multicriteria decision-making (MCDM) techniques.

A weighted centroids approach based trapezoidal interval type-2 fuzzy TOPSIS method for evaluating agricultural risk management tools

A weighted centroids approach based trapezoidal interval type-2 fuzzy TOPSIS method for evaluating agricultural risk management tools

Trapezoidal Interval Type-2 Fuzzy PIPRECIA-MARCOS Model for Management Efficiency of Traffic Flow on Observed Road Sections

Road infrastructure management is an extremely important task of traffic engineering. For the purpose of efficient management, it is necessary to determine the efficiency of the traffic flow through PAE 85%, AADT and other exploitation parameters on the one hand, and the number of different types of traffic accidents on the other. In this paper, a novel TrIT2F (trapezoidal interval type-2 fuzzy) PIPRECIA (pivot pairwise relative criteria importance assessment)-TrIT2F MARCOS (measurement of alternatives and ranking according to compromise solution) was developed in order to, in a defined set of 14 road segments, identify the most efficient one for data related to light goods vehicles. Through this the aims and contributions of the study can be manifested. The evaluation was carried out on the basis of seven criteria with weights obtained using the TrIT2F PIPRECIA, while the final results were presented through the TrIT2F MARCOS method. To average part of the input data, the Dombi and Bonferroni operators have been applied. The final results of the applied TrIT2F PIPRECIA-TrIT2F MARCOS model show the following ranking of road segments, according to which Vrhovi–Šešlije M-I-103 with a gradient of −1.00 represents the best solution: A5 > A8 > A2 > A1 > A4 > A3 > A6 > A12 > A13 = A14 > A11 > A7 > A9 > A10. In addition, the validation of the obtained results was conducted by changing the values of the four most important criteria and changing the size of the decision matrix. Tests have shown great stability of the developed TrIT2F PIPRECIA-TrIT2F MARCOS model.

Enhancing fuzzy evidential reasoning approach using dynamic adjustment mechanism and new rule-based transformation for engineering emergency response evaluation

With the frequent occurrence of various emergency events in engineering field, engineering emergency response (EER) evaluation plays an increasingly significant role in handling such situations and provides great challenges to research since the uncertain information and the urgent response time. Aiming at achieving timely and effective emergency response, an enhanced evidential reasoning (ER) approach based on the dynamic adjustment mechanism and new rule-based transformation is proposed. First, the linguistic terms to represent various preference information provided by experts are encoded into the trapezoidal interval type-2 fuzzy sets (TrIT2FSs) with different granularities. Second, for ensuring the validity of the information, based on the definition of the expert decision risk preference coefficients, a dynamic adjustment mechanism is constructed to identify and adjust the preference information. Meanwhile, combined with social network, the experts’ weights can be calculated and revised several times to obtain group information. Then, a new rule-based transformation and related optimization models are proposed to convert the TrIT2FSs into interval belief structures. Furthermore, considering the importance of attributes, the relative weights and interval belief structures are combined. Finally, according to integrated interval belief structures obtained by the analytical ER algorithm, a new ranking approach with the optimism degree and decision tendency degree is constructed to rank the interval expected utility and score utility of each alternative. To further show the effectiveness, superiorities, and stability of the proposed method, a case study on the EER evaluation is preformed and some comparisons and discussions are provided.

Fuzzy Hidden Markov Model Using Aggregation Operators

The Fuzzy Markov Model (FMM) is a fascinating domain for dealing with ambiguity in real-world scenarios. In type 2 fuzzy set (T2F), it has an uncertainty footprint, and the region circumscribed by the lower and upper interval membership functions is uncertain. In fuzzy sets, Triangular norms (t-norms) are a valuable tool for understanding the conjunction in fuzzy logic and, as a result, determining where fuzzy sets intersect. Norms and conforms in Triangular operations that generalize logical conjunction and disjunction. They also provide a natural explanation for the conjunction and disjunction in mathematical fuzzy logic semantics. Fuzzy Frank Triangular Norms have been used to verify this t-norm as there are many of them the aggregation qualities of Trapezoidal Interval Type-2 numbers (TpIT2FNs) because triangular norm meets the compatibility with Frank norms. Frank triangular norms provide more flexibility and robustness this requires more justification in the information fusion process than other triangular norms. Previous works on not concentrate on Frank’s norms. Other Aggregation works on norms that are not flexible to get the solution. Because of that, the Frank norms are used for the hidden Markov model. We've also used them in the Viterbi method with TpIT2FNs for Fuzzy Hidden Markov Model in the staff selection process.

An integrated interval type-2 fuzzy rough technique for emergency decision making

This paper aims to develop a hybrid emergency decision-making (EDM) method by combining best–worst method (BWM), multi-attributive border approximation area comparison (MABAC) and prospect theory (PT) in trapezoidal interval type-2 fuzzy rough (TrIT2FR) environment. In this hybrid method, the decision information is represented by trapezoidal interval type-2 fuzzy rough numbers (TrIT2FRNs). Firstly, this paper defines the TrIT2FRN and analyzes its desirable properties. Then, the TrIT2FR-BWM is developed to determine criteria weights. To develop the TrIT2FR-BWM, this paper completes the following three core issues: (i) propose an effective theorem to normalize the TrIT2FR weights; (ii) build a crisp programming model to transform the minmax objective of weight-determining model for the TrIT2FR-BWM; (iii) design a consistency ratio for the TrIT2FR-BWM to check the reliability of the determined criteria weights. Afterwards, this paper extends the classical MABAC into TrIT2FR environment to calculate the border approximation area (BAA). Subsequently, the PT is used to rank the alternatives, in which the calculated BAA is selected as the reference point. Lastly, the validity of the proposed method is certificated with a real site selection case of makeshift hospitals on COVID-19. Sensitivity analysis and comparative analyses are conducted to illustrate the robustness and superiorities of the proposed method. Some valuable results are summarized as follows: (i) the best alternative determined by the proposed method conforms with the actual selection result, (ii) the proposed models in the TrIT2FR-BWM have strong robustness, (iii) PT is helpful to improve the decision quality of EDM.

SELECTION OF TEAM LEADER USING AN INTEGRATED INTERVAL TYPE-2 FUZZY DEMATEL-ANP-TOPSIS METHOD

The selection of a team leader is a crucial process that significantly impacts the success of a business and its overall structure, particularly in the context of an increasingly competitive environment. Selecting a team leader from a group of individuals within an organization who consistently deliver superior outcomes, exhibit collaborative behavior, demonstrate cooperation, and share a commitment to a shared objective poses a challenging predicament for the enterprise to achieve. This issue can be approached as a Multiple Criteria Decision Making (MCDM) problem. The process of selecting a suitable candidate for the role of team leader and subsequently determining the duration of their promotion within the organization can have significant ramifications. The present study employed the integrated trapezoidal interval type-2 (IT2) fuzzy DEMATEL-ANP-TOPSIS technique to address the issue of team leader selection. This problem entails the consideration of four primary criteria, along with twenty sub-criteria and twenty alternatives. The IT2 fuzzy DEMATEL-ANP approach was employed to derive the weight degrees of the sub-criteria. Subsequently, the IT2 fuzzy TOPSIS method was incorporated into the model to assign weights to the alternatives. The final phase of the study involved the utilization of sensitivity analysis to evaluate the robustness of the constructed model.

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.

Knowledge-based prognostics and health management of a pumping system under the linguistic decision-making context

The process industry implements important maintenance strategies on the basis of the health status of system operation to reduce engineering maintenance cost and concurrently ensure reliability and safety. This study presents an architecture for knowledge-based prognostics and health management (K-PHM) by applying the trapezoidal interval type-2 fuzzy linguistic term sets. The proposed K-PHM methodology successfully provides operational information for diagnostics, prognostics, and subsequent actionable knowledge for health management in subjective decision making. It emphasizes knowledge-driven maintenance strategies to increase system reliability and safety within linguistic decision making. The main objective of this study is to focus on the uncertainty within the knowledge formation derived from data and subsequent information expressed with linguistic terms generated from domain experts in the K-PHM methodology. Fuzzy sets and fuzzy logic reasoning techniques are used in conjunction to enhance the capability of handling uncertainty throughout the PHM process. The effectiveness of the proposed K-PHM is verified with the authentic case study for the predictive maintenance of a chemical pumping system against abnormal vibration.

Trapezoidal interval type-2 fuzzy analytical hierarchy process technique for biophilic element/design selection in lodging industry

Recently, hoteliers focussed shifts on green practices because of sustainable goals. Also, guests are more health-conscious nowadays. Hence, biophilic elements and designs attract hoteliers and guests, and selecting the best biophilic elements/designs is one of the most important decision-making problems in the lodging industry. This study investigates the various biophilic elements/designs as main criteria and sub-criteria and evaluates them through the trapezoidal interval type-2 fuzzy analytic hierarchy process technique. Once the main biophilic elements and sub-biophilic elements for hotel selection are identified, the hierarchy structure has been designed. Then the weights are calculated using the interval type-2 fuzzy analytic hierarchy process technique. Finally, the biophilic element/design with the highest priority weight is selected as the most preferred by the guests. The robustness of the results is checked by comparing them with the results of the crisp analytic hierarchy process and sensitivity analysis. The findings of the study will help the decision-makers of the lodging industry in making more efficient and effective strategies.

RECOGNIZING LEAN SIX SIGMA SOFTWARE PROJECT MANAGER BY FUZZY METHODOLOGY IN SOFTWARE INDUSTRY

The main objective of this research is to design a structure for Identifying Lean Six Sigma Software Manager among software professionals by Fuzzy Sets. Researchers investigated that the software management of six sigma software projects and software management’s dedication are important for the deterrence of failure of them. Because the problem of identification of lean six sigma manager has several and differing conditions, this is MCDM (Multiple criteria Decision Making) software problem. Geometric structure of trapezoidal interval FAHP (Fuzzy Analytical Hierarchy Process) technology. This is several times used techniques, is applied for software company manager identification, membership functions of fuzzy sets. It provides additional degrees of freedom that make it possible to directly model uncertainties. There is no study about the selection of lean six sigma software manager in suitable literature. Software Company is one of the most important sectors for jobs all over the world. Some software companies are contacted and studied their software processes carefully. In Lean Six Sigma Software manager identification process, there are multiple criteria to consider and many candidates. In order to put those software development criteria in numerical presentation and ranking, Fuzzy Analytical Hierarchy Process (FAHP) is a widely used Multi Criteria Decision Making (MCDM) tool. In this article, the planned criteria are Software Project Development Team Leadership-PC1, Software Project Development Sectoral Expertise-PC2, Personal and Software Project Development Environmental Analysis Capability- PC3,Software Training andEducation-PC4. Key Words: Software Manager Selection; Fuzzy Analytical Hierarchy Process; Lean six sigma; Multi criteria Decision Making ; Software Development Processes

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.

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.

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.

Site selection decision framework for photovoltaic hydrogen production project using BWM-CRITIC-MABAC: A case study in Zhangjiakou

Hydrogen production by photovoltaic power generation can not only effectively alleviate the problem of high cost of electrolysis water by making full use of light resources, but also is an efficient, clean and carbon-reducing way to produce hydrogen. The purpose of this paper is to provide a practical model for site selection decision of photovoltaic hydrogen production project (PVHPP) based on multi-criteria decision-making (MCDM) method, and take Zhangjiakou City, Hebei Province as an example for analysis. Firstly, a set of evaluation criteria system including natural factors, economic factors, technical factors, social factors and environmental factors is constructed. Secondly, probabilistic hesitation fuzzy linguistic term set (PHFLTS) and trapezoidal interval type-2 fuzzy set (TIT2FS) are combined to describe the information of qualitative criteria. Then, the subjective and objective weights are calculated by using best-worst method (BWM) and criteria importance through intercriteria correlation (CRITIC), and the comprehensive weights are obtained by using the idea of game theory. The multi-attribute boundary approximation regional comparison (MABAC) method is then used to sort the alternative plant sites. The ranking results show that A2 (Chongli District) performs the best, and A1 (Qiaodong District) is the second best. Finally, taking Zhangjiakou as an example, sensitivity analysis and comparative analysis are carried out to verify the validity and reliability of the model.

An Adoptable Multi-Criteria Decision-Making Analysis to Select a Best Hair Mask Product-Extended Weighted Aggregated Sum Product Assessment Method

Hair masks (HMs) act as one of the solutions for most of the hair problems like dandruff, frizziness, breakage, premature- greying and so on. Due to its various benefits, HM products are acquiring more popularity among the individuals. As there are different varieties of HM products available in the market, the confusion arises in choosing a HM which suits the individual’s hair profile and causes less side effects. Here, we have employed multi-criteria decision-making (MCDM) combined with fuzzy set theory to obtain better results. We used the extended Weighted Aggregated Sum Product Assessment (WASPAS) method based on trapezoidal interval type-2 fuzzy set (TIT2FS) in this research paper to handle vagueness and complexity in real-world problems. For determining the objective weights of the criteria, we used the entropy method of weight finding. An example of selecting a hair mask product (HMP) among four alternatives based on five criteria is provided to illustrate the applicability of the proposed method. In comparison to other MCDM methods, the approach yielded more practical results. By doing a sensitive study, the method’s stability is also assessed.

An interval type-2 fuzzy TOPSIS for MAGDM applied to solar power systems

This article proposes a new version of the technique of order preference by similarity to an ideal solution (TOPSIS) to solve fuzzy multi-attribute group decision making (MAGDM) problems using trapezoidal interval type-2 fuzzy sets (IT2FSs). The traditional TOPSIS ranks the alternatives according to their relative degree of closeness to the ideal solutions. On the other hand, TOPSIS based on similarity measure ranks the alternatives according to their total degree of similarity to the ideal solutions. This study extends TOPSIS using similarity measure using map distance to IT2FSs. First, the similarity measure based on map distance for interval-valued fuzzy sets (IVFSs) is extended to encompass IT2FSs due to the deficiency in IT2FSs similarity measures. Then, TOPSIS using similarity measure is applied. Hence, fuzzy MAGDM problems can be handled in a more flexible intelligent manner and avoiding defuzzification with its drawbacks. An illustrative example is given to explain the approach. Then, a practical problem in assessing thermal energy storage technologies in solar power systems is solved, where the weights of the attributes and the performance of the qualitative attributes are linguistic variables modeled by IT2FSs. The reliability of two normalization techniques is examined and the impact of the theoretical and empirical reference points on the solution is investigated.