Fuzzy Interval Research Articles

Multi criteria decision-making for distributed energy system based on multi-source heterogeneous data

The distributed energy system (DES) has been regarded as a socio-technical innovation that can improve energy efficiency and reduce carbon emission. Based on the construction and planning of a DES project in Henan Province, this paper aims to develop a comprehensive decision-making framework for selecting the most appropriate DES composition schemes with multi-source heterogeneous data. Thus, a new multi-criteria decision-making method based on fuzzy preference relations and improved Choquet integral is generated. Firstly, an evaluation criteria system is established from economic, technical, environmental and social dimensions, and 10 secondary criteria are presented. Secondly, based on the interval fuzzy preference relations of criteria given by experts, the iteration of weights of criteria is continued until the group consistency degree reaches the threshold. Thirdly, the deviation degree is used to transform the initial data, which include crisp values, interval numbers and linguistic terms to isomorphism data. Thereafter, the fuzzy measures are calculated using Mobius transformation coefficients and the final scores of the alternatives are obtained by means of Choquet integral, which can eliminate the overlap information between criteria. Finally, a real case is given to illustrate the effectiveness of the proposed evaluation criteria and technique. The result shows the multi energy complementary system as the most appropriate alternative for the project, followed by the solar-air source heat pump system, fuel cell system, natural gas system, internal combustion engine system and traditional system. Conclusively, the discussion, comparative analysis and some policy implications to promote the development of distributed energy industry are given. This study not only can assist stakeholders to obtain greater benefits of the DES, but also can serve as a reference for the government towards the development of more robust regulations and policies.

(2010-6244) An identifi cation model for a fuzzy time based stationary discrete process

A new approach of fuzzy processes, the source of which are expert knowledge reflections on the states on Stationary Discrete Extremal Fuzzy Dynamic System (SDEFDS) in extremal fuzzy time intervals, are considered. A fuzzy-integral representation of a stationary discrete extremal fuzzy process is given. A method and an algorithm for identifying the transition operator of SDEFDS are developed. The SDEFDS transition operator is restored by means of expert knowledge reflections on the states of SDEFDS. The regularization condition for obtaining of the quasi-optimal estimatorof the transition operator is represented by the theorem. The corresponding calculating algorithm is provided. The results obtained are illustrated by an example in the case of a finite set of SDEFDS states.

Solving Discounting Problem Using Piece-Wise Quadratic Fuzzy Numbers

The discounting problem is one of the important aspects in investment, portfolio selection, purchasing with credit, and many other financial operations. In this paper, a discounting problem using piecewise quadratic fuzzy numbers is proposed. The implementation of piecewise quadratic fuzzy numbers is described based on such operations. Fuzzy arithmetic and interval number arithmetic are used for computation. The close interval approximation of piecewise quadratic fuzzy numbers is used for solving the proposed discounting problem. This research article addresses the discounted investment for Year 1, Year 2, and Year 3. Additionally, the authors determine the cumulative discounted investment for different values of the parameter α ranging from 0 to 1. A discounting problem using piecewise quadratic fuzzy numbers is solved as a numerical example to illustrate the proposed procedure.

Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Sets and its Application on Multi-Attribute Decision-Making by Using Aggregation Operator Method

Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Sets (IVBNHFS) can express complex multi-attribute decision-making (MADM) problems with its interval valued, bipolar, neutrosophic, and hesitant fuzzy elements simultaneously. The two weighted operators, average and geometric, are accustomed aggregation operator method for handling MADM problems. However, we give the Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Weighted Average (IVBNHFWA) and Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Weighted Geometric (IVBNHFWG) operators to aggregate the IVBNHFS and their properties are also discussed in detail. Occasionally, we predestined a MADM method based on the IVBNHFWA and IVBNHFWG operators. Finally, this paper provides an illustrative numerical example of a case study of MADM to authenticate the application and effectiveness of the proposed approaches. Also, we give a comparative study with the existing methods.

Picture fuzzy tolerance graphs with application

In this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy phi -tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking phi as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy phi -tolerance chaingraphs which is the picture fuzzy phi -tolerance graphs of a nested family of picture fuzzy intervals are presented. A real-life application in sports competition is modeled using picture fuzzy min-tolerance graph. Also a comparison is given between picture fuzzy tolerance graphs and intuitionistic fuzzy tolerance graphs.

Risks of water and wastewater PPP projects: an investors’ perspective

PurposeWater and wastewater (WW) projects are gaining attention in Iran because of shortages of water resources. However, these projects are lengthy and they are accompanied by numerous risks, such as lack of sufficient financial resources. Public–private partnerships (PPPs) are taken into account as a constructive approach to deal with the problem of insufficient government funds and they are increasingly being implemented to construct the required infrastructures in different countries. Although WW projects in PPPs can reduce the government’s debt, investors are still uncertain about this approach. Hence, this study aims to identify and evaluate the risk of all parties involved in WW-PPP projects, from the viewpoint of investor.Design/methodology/approachFirst, the risk factors which are involved in WW projects are identified by interviewing experts and reviewing the literature by means of fault tree analysis (FTA) tool. Second, the probability and effects of the risky factors which are related to specific event are evaluated and analyzed by hybridization of interval fuzzy Type-2 sets (IT2FS) and risk score formulation. Finally, some solutions are proposed to deal with the most challenging risks.FindingsSix gate events, namely, risks which are related to investors such as investor’s consultant-related risks, risky conditions from engineering, procurement, and construction (EPC) contractors’ point of view, risk factors which public sector takes into account, public sector’s consultant-related risks which public sector’s consultant consider challenging and external factors were defined according to the literature. From FTA tool and by interviewing the experts, 94 basic events were identified. Finally, from hybridization of IT2FSs and risk score formulation, top five risks are determined as “Difficulty of injecting financial resources into the project,” “Fluctuation in inflation rate,” “Poor decision-making process” in public sector, “Difficulty of importing the equipment which are required for the project (such as pumps, grain catchers, garbage collectors, etc.) from other countries” and “Impact of risky conditions in other projects on operation of PPP project.”Originality/valueIn the absence of a constructive approach for risk identification and a reliable model for evaluating the identified risks in PPP projects, this research project is one of the first research studies which used FTA for identifying risks and hybridization of IT2FSs and risk score formulation for evaluating the risks.

A Rudimentary Approach to Develop Context for Convexity cum Concavity on Soft Expert Set with Some Generalized Results

Soft set theory is considered as the preeminent tool to tackle the problems involving vagueness by controlling all complexities of optimization theory, fuzzy set theory and interval theory. Some models have been developed to solve problems in decision making and medical diagnosis with one expert by using this theory. This causes a problem with those who use questionnaires in their research. Soft expert set overcomes this problem and facilitates the user to know the opinion of all experts in one model. The concept of convexity plays a key role to deal optimization, pattern recognition-classification and many other related topics in operation research, numerical analysis and other disciplines of mathematical sciences. In this study, a mathematical cum abstract technique is employed to develop basic concept of convex and concave soft expert sets to deal with their important applications. Some classical results on convexity cum concavity are modified under uncertain multi-decisive environment with the support of explicatory proofs.

Integrated Planning for Regional Development Planning with Low Carbon Development Constraint under Uncertainty: A Case Study of Qingpu District, Shanghai

Regional development planning systems contain multiple uncertainties which come from economic restructuring, resource management, carbon peak action, environmental protection, and other factors, it is difficulty to handle all of these uncertainties in one method. In order to solve this problem, a new model developed in this study combines an interval fuzzy program with an environmental quality model for regional development planning in order to provide optimal solutions. The interval fuzzy program is put forward based on interval parameter programming (IPP) and fuzzy programing (FP). The environmental quality model is used to calculate water environmental capacity and atmospheric capacity, which are set as constraint conditions in the model. In order to meet the requirements of carbon peak action, a low carbon development constraint is added to the model. In this model, decision makers can choose the satisfaction level of constraints based on their preferences. The results suggest that the methodology is applicable for the regional development planning system within the planning period. The developed model can be used to generate a series of optimization schema under multiple credibility levels, ensuring that the regional development planning system can meet both societal demands and environmental quality requirements, considering a proper balance between the expected system benefits and risks of violating the resource constraint and low carbon development constraint.

Wetland Restoration Planning Approach Based on Interval Fuzzy Linear Programming under Uncertainty.

When planning wetland restoration projects, the planting area allocation and the costs of the restoration measures are two major issues faced by decision makers. In this study, a framework based on the interval fuzzy linear programming (IFLP) method is introduced for the first time to plan wetland restoration projects. The proposed framework can not only effectively deal with interval and fuzzy uncertainties that exist in the planning process of wetland restorations but also handle trade-offs between ecological environment benefits and economic cost. This framework was applied to a real-world wetland restoration planning problem in the northeast of China to verify its validity and examine the credibility of the constraints. The optimized results obtained from the framework that we have developed indicate that higher ecological and social benefits can be obtained with optimal restoration costs after using the wetland restoration decision-making framework. The optimal restoration measure allocation schemes obtained by IFLP under different credibility levels can help decision makers generate a range of alternatives, which can also provide decision suggestions to local managers to generate a satisfactory decision-making plan. Furthermore, a comparison was made between the IFLP model and ILP model in this study. The comparison results indicate that the IFLP model provides more information regarding ecological environment and economic trade-offs between the system objective, certainty, and reliability. This framework provides managers with an effective way to plan wetland restoration projects, while transference of the model may help solve similar problems.

Cascade Adaptive MPC with Type 2 Fuzzy System for Safety and Energy Management in Autonomous Vehicles: A Sustainable Approach for Future of Transportation

A sustainable circular economy involves designing and promoting new products with the least environmental impact through increasing efficiency. The emergence of autonomous vehicles (AVs) has been a revolution in the automobile industry and a breakthrough opportunity to create more sustainable transportation in the future. Autonomous vehicles are supposed to provide a safe, easy-to-use and environmentally friendly means of transport. To this end, improving AVs’ safety and energy efficiency by using advanced control and optimization algorithms has become an active research topic to deliver on new commitments: carbon reduction and responsible innovation. The focus of this study is to improve the energy consumption of an AV in a vehicle-following process while safe driving is satisfied. We propose a cascade control system in which an autonomous cruise controller (ACC) is integrated with an energy management system (EMS) to reduce energy consumption. An adaptive model predictive control (AMPC) is proposed as the ACC to control the acceleration of the ego vehicle (the following vehicle) in a vehicle-following scenario, such that it can safely follow the lead vehicle in the same lane on a highway. The proposed ACC appropriately switches between speed and distance control systems to follow the lead vehicle safely and precisely. The computed acceleration is then used in the EMS component to find the optimal engine torque that minimizes the fuel consumption of the ego vehicle. EMS is designed based on two methods: type 1 fuzzy logic system (T1FLS) and interval type 2 fuzzy logic system (IT2FLS). Results show that the combination of AMPC and IT2FLS significantly reduces fuel consumption while the ego vehicle follows the lead vehicle safely and with a minimum spacing error. The proposed controller facilitates smarter energy use in AVs and supports safer transportation.

An evolving concept in the identification of an interval fuzzy model of Wiener-Hammerstein nonlinear dynamic systems

This paper presents a new approach for identifying interval fuzzy models, which enables estimating fuzzy model structures, parameters, and upper and lower bounds simultaneously and online. It is based on a filtered recursive least squares method combined with an incrementally evolving Gaussian clustering. The proposed method generates interval fuzzy models online, on the fly, and in an evolving manner. This means that the algorithm starts with no a priori information, evolves the structure of the model, adjusts the model parameters simultaneously, and computes the upper and lower intervals simultaneously. The fuzzy partitioning of the input–output data space is based on the eGauss + method; the parameters of the local linear models, which together form the fuzzy model, are determined using a recursive least squares method. The interval fuzzy model, used in a predictive manner as a single or multi-level predictor, can be successfully applied in on-line monitoring, fault detection, and the control of dynamic systems. The proposed identification procedure was used to identify the fuzzy interval model of two different processes: a simplified Hammerstein-type nonlinear dynamic process and a realistic industrial continuously stirred tank reactor.The main contribution and advantage of the proposed new method is the identification of an interval fuzzy model in an online manner, which means that the structural and parametric identification of nonlinear systems is done simultaneously and from the data stream. The structural and parametric uncertainties are modeled and integrated into the upper and lower fuzzy models, which form the fuzzy interval in which the measured data samples of the process output are located with a certain probability. The approach is limited to processes that have Wiener-Hammerstein structures.

تحلیل پوششی داده‌ها در شرایط عدم قطعیت برای بهبود انرژی مصرفی باغات کیوی استان مازندران

Introduction: One of the principal requirements for sustainable agriculture is efficient energy use. Energy use in agriculture has been increasing in response to the growing global population, limited arable land and desire for higher living standards. It should be noted that agriculture contributes significantly to atmospheric GHG emissions, with 10-12% of the net global CO2 (carbon dioxide) emissions. The scientific community believes global warming will pose one of the major environmental challenges in the future, with the bulk of GHG originating from fossil fuel consumption. Kiwifruit is an economically important fruit crop in northern Iran, because the northern region of Iran is a suitable, natural habitat for kiwifruit cultivation. The high kiwifruit production in Iran has reached a point that Iran is now well-known on global markets and in recent years this fruit has contributed a large share to agricultural exports. More recently, Mazandaran horticulturists have been encouraged to produce more kiwifruit. Increased production leads to greater energy consumption by Iranian kiwifruit orchards due to the added application of inputs, such as fertilizers and fuel. Besides, where there is no clear energy consumption pattern in agricultural production, especially fruit orchards, a lot of energy dissipates in the fruit production cycle. Therefore, it seems necessary to provide a model for the energy consumption of kiwifruit orchards in Mazandaran Province to prevent excessive energy utilization. Energy analysis is one of the methods has been used to evaluate the status of agricultural production. In this regard, many researchers have used Data Envelopment Analysis (DEA) for optimization the energy consumption in agricultural productions. DEA is recognized as a methodology widely used to evaluate the relative efficiency of a set of decision-making units (DMUs) involved in a production process. Although DEA is a powerful tool to measure efficiency but the uncertainty in the applied data in this model is inevitable and there is need to use different models that be able to control this uncertainty. Materials and Methods: In this study, in order to determine the efficiency of kiwifruit orchards in Mazandaran province and in terms of uncertainty of input data, the Robust Data Envelopment Analysis model (RDEA) and Fuzzy Interval Data Envelopment Analysis model (FIDEA) were used. The method incorporates the degree of conservatism in the maximum probability bound for constraint violation. The required data were collected by distributing and completing a questionnaire and face-to-face interview using random sampling method in 1397-98. Results and Discussion: The results showed that the average technical efficiency of all kiwi fields in RDEA model at three levels of probability include: 10, 50 and 100% is equal to 0.93, 0.96 and 0.98%, respectively. The results of FIDEA model showed that if the level of parameter α (optimal use of production factors) increases, the average efficiency of kiwi fields will increase. The highest energy savings are related to chemical pesticides and the lowest amount of savings is related to the chemical fertilizers and electricity inputs, respectively. So, holding the training courses on the correct and optimal use of production inputs from an economic and managerial point of view and improving the level of knowledge of farmers and factors involved in kiwi production in Mazandaran province can improve the efficiency and save energy consumptions. Conclusion: Evaluating the performance of many activities by a traditional DEA approach requires precise input and output data. However, input and output data in real-world problems are often imprecise or vague. To deal with imprecise data, this study uses RDEA and FIDEA approaches as a way to quantify vague data in DEA models. It is shown that the approaches can be a useful tool in DEA models without introducing additional complexity into the problem. A case study of kiwifruit orchard units is presented to illustrate the reliability and flexibility of the models. As a result, efficiency decreases as the constraint violation probability increased. Additionally, the RDEA approach provides both a deterministic guarantee about the efficiency level of the model, as well as a probabilistic guarantee that is valid for all symmetric distributions.

Evaluating the Efficiency of Water and Wastewater Companies under Uncertainty by Using Interval Fuzzy Data Envelopment Approach (Case Study: Markazi Province)

شرکت‌های آب و فاضلاب به‌عنوان ارائه‌دهندگان خدمات آب شرب نقش حیاتی در جامعه ایفا می‌کنند. بنابراین اندازه‌گیری کارایی این شرکت‌ها معیاری است که می‌تواند به تخصیص بهینه توزیع آب میان مشترکین کمک شایانی کند. ازاین‌رو این پژوهش با هدف ارزیابی کارایی شرکت‌های آب و فاضلاب استان مرکزی انجام شد. برای این منظور از روش تحلیل پوششی داده‌های فازی بازه‌ای استفاده شد. فرض اساسی این روش برخلاف روش سنتی تحلیل پوششی داده‌ها عدم‌قطعیت در ارتباط با نهاده‌ها و ستانده‌ها است. توجه به اینکه عدم‌قطعیت‌ها در دنیای واقعی امری اجتناب‌ناپذیرند بنابراین ضرورت استفاده از الگوهایی که توانایی کنترل این عدم‌قطعیت را دارند، به‌شدت احساس می‌شود. از‌این‌رو یک روش موفق، بهره‌گیری از روش تحلیل پوششی داده‌های فازی است. نتایج ارزیابی مربوط به 17 شرکت آب و فاضلاب در استان مرکزی نشان داد که شرکت‌های آب و فاضلاب اراک، خمین، دلیجان، ساوه، کمیجان، مامونیه، محلات و نراق با کسب بازه کارایی (1، 83/0) بیشترین میزان کارایی فنی را دارند که می‌توان گفت به‌طور کلی شرکت‌های آب و فاضلاب استان مرکزی کارایی مناسبی داشتند. علاوه بر این در بین واحدهای تحت بررسی شرکت آب و فاضلاب غرق‌آباد با کسب بازه کارایی (56/0، 46/0) کمترین میزان کارایی فنی را داشت. همچنین بر یافته‌های پژوهش در استفاده از کلیه نهاده‌ها مازاد مصرف وجود دارد. بنابراین پیشنهاد شد با کاربرد درست و بهینه نهاده‌های تولید و استفاده کمتر از منابع می‌توان مقدار کارایی را تا رسیدن به مرز کارایی ارتقا داد.

An application of neutrosophic hypersoft mapping to diagnose brain tumor and propose appropriate treatment

Brain tumors are one of the leading causes of death around the globe. More than 10 million people fall prey to it every year. This paper aims to characterize the discussions related to the diagnosis of tumors with their related problems. After examining the side effects of tumors, it encases similar indications, and it is hard to distinguish the precise type of tumors with their seriousness. Since in practical assessment, the indeterminacy and falsity parts are frequently dismissed, and because of this issue, it is hard to notice the precision in the patient’s progress history and cannot foresee the period of treatment. The Neutrosophic Hypersoft set (NHS) and the NHS mapping with its inverse mapping has been design to overcome this issue since it can deal with the parametric values of such disease in more detail considering the sub-parametric values; and their order and arrangement. These ideas are capable and essential to analyze the issue properly by interfacing it with scientific modeling. This investigation builds up a connection between symptoms and medicines, which diminishes the difficulty of the narrative. A table depending on a fuzzy interval between [0, 1] for the sorts of tumors is constructed. The calculation depends on NHS mapping to adequately recognize the disease and choose the best medication for each patient’s relating sickness. Finally, the generalized NHS mapping is presented, which will encourage a specialist to extricate the patient’s progress history and to foresee the time of treatment till the infection is relieved.

On the fuzzy interval equal surplus sharing solutions

PurposeThis paper deals with cooperative games whose characteristic functions are fuzzy intervals, i.e. the worth of a coalition is not a real number but a fuzzy interval. This means that one observes a lower and an upper bound of the considered coalitions. This is very important, for example, from a computational and algorithmic viewpoint. The authors notice that the approach is general, since the characteristic function fuzzy interval values may result from solving general optimization problems.Design/methodology/approachThis paper deals with cooperative games whose characteristic functions are fuzzy intervals, i.e. the worth of a coalition is not a real number but a fuzzy interval. A situation in which a finite set of players can obtain certain fuzzy payoffs by cooperation can be described by a cooperative fuzzy interval game.FindingsIn this paper, the authors extend a class of solutions for cooperative games that all have some egalitarian flavour in the sense that they assign to every player some initial payoff and distribute the remainder of the worth v(N) of the grand coalition N equally among all players under fuzzy uncertainty.Originality/valueIn this paper, the authors extend a class of solutions for cooperative games that all have some egalitarian flavour in the sense that they assign to every player some initial payoff and distribute the remainder of the worth v(N) of the grand coalition N equally among all players under fuzzy uncertainty. Examples of such solutions are the centre-of-gravity of the imputation-set value, shortly denoted by CIS value, egalitarian non-separable contribution value, shortly denoted by ENSC value and the equal division solution. Further, the authors discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS value, the ENSC value and the equal division solution. The authors provide several characterizations of this class of solutions on variable and fixed player set. Specifications of several properties characterize specific solutions in this class.

Comparative Study between Type I and Type II Fuzzy Controller for Semi Active Suspension System

In this article, a type-2 fuzzy interval controller is proposed to solve the nonlinear control problems of semi-active suspension system. A suspension model with two degrees of freedom and A fuzzy approach for controller synthesis were proposed. The performance of the IT2FLC-based semi-active vehicle suspension system in terms of sprung mass displacement, suspension deflection and tire deflection are compared to the homologous fuzzy type-1 controller (T1FLC), and to the passive suspension system conventional using MATLAB / SIMULINK software for simulation and controller design. The vehicle parameters, called suspension deflection and speed of suspended mass are given as inputs for both controllers. The Csemi control signal is the variable damping coefficient. Inputs and outputs are presented by triangular membership functions. Mamdani inference system is used, along with a Karnik-Mendel algorithm to locate the center of gravity in reduction type for IT2FLC controller. Simulation results show that IT2FLC-based semi-active suspension system outperforms T1FLC and passive suspension system. Thus, they show a major improvement in control signal i.e. IT2FLC controller generates a lower damping coefficient than T1FLC controller. In addition, a remarkable reduction in signal energy by IT2FLC compared to same semi-active suspension system with T1FLC.

Solving Multi-Objective Linear Programming Problems with Fuzzy Interval Based on Decomposition Method

Most of the problems in real-world situations have a multi-objective, in these situations, available information in the system is not exact or imprecise. In this paper, solving multi-objective linear programming problems with fuzzy non-negative intervals such as objective function coefficients, technical coefficients, and fuzzy variables by using an approximation but a convenient method called decomposition method has been proposed. In the composition method, ranking functions are not used. With the help of numerical examples, the method is illustrated.

A methodology for supplier selection under the curse of dimensionality problem based on fuzzy quality function deployment and interval data envelopment analysis.

Supplier selection is an important decision-making problem, which involves many quantitative and qualitative factors incorporating vagueness and imprecision. This study proposes a novel fuzzy multi-criteria decision-making framework for supplier selection, which integrates quality function deployment (QFD) and interval data envelopment analysis (DEA). The proposed methodology allows for considering the relationships among the product features and supplier evaluation criteria (SEs) and the impacts of inner dependence among SEs by constructing a house of quality (HOQ). Considering that the number of supplier evaluation indicators is greater than the number of suppliers in some cases, the curse of dimensionality problem usually exists. To solve this problem, we combine the HOQ, interval DEA models, and forward-stepwise selection approach to screen supplier evaluation indicators and select the best supplier(s). Through the two-stage supplier selection method, we can achieve the double screening of indicators and determine the final supplier(s). Finally, the application of the proposed framework is demonstrated through a numerical example and a sensitivity analysis is also carried out to verify the stability of the proposed methodology. This study focuses on supplier selection based on the combination of fuzzy QFD and interval DEA, and also provide a new two-phase methodology for DEA indicator screening.

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.

Reliability evaluation for colliery machine based on fuzzy interval model

The mechanical reliability design method is a common method, and it is the most direct and effective method to carry out the mechanical reliability design at present. The reliability optimization design is an effective optimization design method which is developed in combination with the reliability design theory on the basis of the conventional optimization design. Taking the antifriction bearing as an example, this paper systematically expounds all kinds of mechanical reliability design methods. Through comprehensive analysis of various factors that affect the reliability of colliery machine, the index system of colliery machine reliability evaluation is established. Because of the complexity and diversity of the use of colliery machine in the evaluation system, and the fuzziness of human thinking, it is difficult to give the deterministic evaluation information in numerical form, so this paper also analyzes the design method of colliery mechanical reliability, and puts forward an interval fuzzy evaluation method for colliery mechanical reliability evaluation to avoid overload operation of colliery machine and ensure safety production and safety of workers. The simulation results show that the inherent law of reliability is effectively characterized by this method, and it provides a evidence for security produce and scientific decision-making of colliery mechine.