Fuzzy Interval Research Articles

Design and research of hybrid forecasting system for wind speed point forecasting and fuzzy interval forecasting

Wind energy forecasting and analysis are essential for the management and operation of wind farms. Precise point forecasting of wind speed can assist operators in achieving the optimal dispatching of the power grid and diminish the cost of wind energy production. Interval forecasting can provide an effective reference for determining the rotating reserve of wind farms. Most existing studies have focused on either point forecasting or interval forecasting, and cannot serve as a reference for ensuring the reliability and stability of the power grid. In this study, we designed a novel hybrid forecasting system that includes point forecasting, interval forecasting, and evaluation, to provide technical support for the optimal coordinated dispatching of the power grid. Point forecasting is performed using a data preprocessing model and combined model to achieve higher precision. Interval forecasting estimates the upper and lower limits of the wind speed, which is used to determine the rotating reserve of wind farms and can effectively improve the stability of the power grid. The performance of the forecasting system was evaluated through numerical simulations of the wind speed at four sites in the Penglai wind farm. The results revealed that the proposed hybrid system not only provides accurate wind speed forecasting for coordinated dispatching of the power grid but also serves as a reference for determining the grid rotation reserve.

Interval Type-2 Fuzzy Differential Equations and Stability

This article is devoted to present a framework for studying type-2 fuzzy calculus. Some new concepts pertaining to interval type-2 fuzzy functions (IT2FF) and interval type-2 fuzzy differential equations (IT2FDE) with their stability analysis are introduced. A new definition of type-2 fuzzy derivative called type-2 granular derivative (T2gr-derivative) is defined to overcome the disadvantages of the previous definitions of type-2 fuzzy derivatives. Furthermore, the definitions of elementary arithmetic on the set of interval type-2 fuzzy numbers (IT2FNs) and the set of interval type-2 fuzzy complex numbers are presented. The notion of granular metric on the set of IT2FNs is also defined. Besides, the concepts of continuity, integral, and limit of IT2FFs are introduced. Using the concept of type-2 granular fuzzy Laplace transform and the approximations of T2gr-derivative proposed in this article, the exact and approximate solutions of interval T2FDE are presented. Then, some new concepts such as fuzzy node, fuzzy saddle spiral point, fuzzy star, and so forth lay the groundwork for the analysis of interval T2FDE stability. Several examples are given to illustrate the presented notions.

Interval-Fuzzy Fixed Charge Transportation Problems

The fixed charge transportation problem (FCTP) is a variant of the well-known transportation problem in which the price of conveying products from a source to a sink is made up of a set cost and a continuous cost proportionate to the number of goods sent. The transportation system and FCTP with uncertain parameters are inextricably linked. Fuzzy numbers or interval numbers can be used to successfully handle these imprecise values. The cost coefficients, supplies, and demands are all represented as interval numbers in this paper. A modified interval version of Vogel's Approximation process is used to obtain the initial basic feasible solution (IBFS) of the interval fixed charge transportation problem (IFCTP), which is then optimized using interval version of MODI method. A numerical example is provided to show the efficiency of the proposed method.

Entropy-Based Fuzzy TOPSIS Method for Investment Decision Optimization of Large-Scale Projects.

Investment of large-scale projects must consider various factors, such as economic conditions and investment environment when making decisions. In large-scale project investment problems, almost 90% of them are completed in a multiobjective context. To this end, the authors of this paper have proposed an entropy-based fuzzy TOPSIS synthesis method to assist in the decision-making optimization of large-scale project investment. Firstly, in accordance with the background of the development of multiattribute decision-making method (MADM), closely related to large-scale project investment, the related research works were studied, and the relevant methods are sorted out. Then, the improved vague-entropy-weight based fuzzy TOPSIS (VEWF-TOPSIS) method, entropy and interval language intuitionistic fuzzy sets based TOPSIS (EILIF-TOPSIS) method, and information entropy attribute importance based intuitionistic fuzzy TOPSIS (IEAI-IF-TOPSIS) method were introduced, and a synthesis MADM method that comprehensively combines the above three methods was proposed. Finally, a numerical case was constructed to properly show the effectiveness of the method proposed in the present work, and the conclusions were put forward for providing ideas and methods for large-scale project investment decision-making. It is of great significance that the proposed framework would make large-scale project investment decisions more reasonable and practical, which enriches the research methods of MADM problems to a certain extent and can provide reference for the actual large-scale project investment decision-making problems.

Fuzzy Confidence Intervals by the Likelihood Ratio: Testing Equality of Means—Application on Swiss SILC Data

We propose a practical procedure of construction of fuzzy confidence intervals by the likelihood method where the observations and the hypotheses are considered to be fuzzy. We use the bootstrap technique to estimate the distribution of the likelihood ratio. The chosen bootstrap algorithm consists on randomly drawing observations by preserving the location and dispersion measures of the original fuzzy data set. A metric d_{SGD}^{theta ^{star }} based on the well-known signed distance measure is considered in this case. We expose a simulation study to investigate the influence of the fuzziness of the computed maximum likelihood estimator on the constructed confidence intervals. Based on these intervals, we introduce a hypothesis test for the equality of means of two groups with its corresponding decision rule. The highlight of this paper is the application of the defended approach on the Swiss SILC Surveys. We empirically investigate the influence of the fuzziness vs. the randomness of the data as well as of the maximum likelihood estimator on the confidence intervals. In addition, we perform an empirical analysis where we compare the mean of the group “Swiss nationality” to the group “Other nationalities” for the variables Satisfaction of health situation and Satisfaction of financial situation.

An Optimized Decision Support Model for COVID-19 Diagnostics Based on Complex Fuzzy Hypersoft Mapping

COVID-19 has shaken the entire world economy and affected millions of people in a brief period. COVID-19 has numerous overlapping symptoms with other upper respiratory conditions, making it hard for diagnosticians to diagnose correctly. Several mathematical models have been presented for its diagnosis and treatment. This article delivers a mathematical framework based on a novel agile fuzzy-like arrangement, namely, the complex fuzzy hypersoft (CFHS) set, which is a formation of the complex fuzzy (CF) set and the hypersoft set (an extension of soft set). First, the elementary theory of CFHS is developed, which considers the amplitude term (A-term) and the phase term (P-term) of the complex numbers simultaneously to tackle uncertainty, ambivalence, and mediocrity of data. In two components, this new fuzzy-like hybrid theory is versatile. First, it provides access to a broad spectrum of membership function values by broadening them to the unit circle on an Argand plane and incorporating an additional term, the P-term, to accommodate the data’s periodic nature. Second, it categorizes the distinct attribute into corresponding sub-valued sets for better understanding. The CFHS set and CFHS-mapping with its inverse mapping (INM) can manage such issues. Our proposed framework is validated by a study establishing a link between COVID-19 symptoms and medicines. For the COVID-19 types, a table is constructed relying on the fuzzy interval of [0,1]. The computation is based on CFHS-mapping, which identifies the disease and selects the optimum medication correctly. Furthermore, a generalized CFHS-mapping is provided, which can help a specialist extract the patient’s health record and predict how long it will take to overcome the infection.

Analysis of Factors Affecting the Sustainable Success of Airlines During the COVID-19 Pandemic.

The COVID-19 pandemic increased the risk of financial distress, bankruptcy, or both, in the airline industry. Whether airlines can survive or not during and/or after the pandemic is closely related to their decisions and actions which will enable their success by increasing their resilience. In crisis periods such as COVID-19, the decisions taken by airlines are strategically important for achieving sustainable success. Thus, it is critical to understand which factors are more important for airlines to shape their actions and make correct decisions. This paper investigates the sustainable success factors on which airlines should focus to provide resilience during the COVID-19 pandemic crisis. It provides a robust model using the interval type-2 fuzzy analytic hierarchy process (IT2FAHP) and interval type-2 fuzzy Decision Making Trial and Evaluation Laboratory (IT2FDEMATEL) to identify and rank success factors. The findings indicate that financial and operational factors are extremely important to ensure resilience for airlines. In addition, the results of the study reveal that operational factors and information sharing factors have an impact on financial factors and customer satisfaction.

Interval Type-2 Fuzzy Envelope of Proportional Hesitant Fuzzy Linguistic Term Set: Application to Large-Scale Group Decision Making

Large-scale group decision-making (LS-GDM) problems are common in the daily life of human beings. Both information fusion and computing with words (CWW) technologies in LS-GDM suffer from challenges. In the current research, a proportional hesitant fuzzy linguistic term set (PHFLTS) will be applied to capture the preferences of sub-groups in LS-GDM, which decreases the information lost in information fusion processes. Novel fuzzy semantic representation models of PHFLTS, such as type-1 fuzzy envelope and interval type-2 fuzzy envelope, are respectively studied. The application of the proposed fuzzy entropies facilitates the CWW process with the PHFLTS under the framework of a fuzzy linguistic approach. In particular, linguistic uncertainties contained in the PHFLTS can be reflected in a comprehensive way when the type-2 fuzzy envelope is applied, which contributes to the decrease in the information lost during the CWW process. A novel LS-GDM method cooperating with the fuzzy semantic models of PHFLTS is proposed, in which weights for the sub-groups are determined by size, cohesion, and degree of reliability among the sub-groups. Finally, the proposed decision method as well as CWW tools are applied to the process of urban renewal plan selection.

Least Squares Method for Solving Fuzzy LR Interval Algebraic Linear Systems

We first investigate the solvability conditions of fuzzy LR interval algebraic linear systems with fuzzy LR interval coefficient matrix and fuzzy LR interval hand-right vector. Next, we compute the solution of FLRIALS (fuzzy LR interval algebraic linear systems) using the least squares approach. We show that solving the least squares problem is equivalent to solving a quadratic programming problem. Indeed, instead of the FLRIALS, this quadratic programming has a non-convex constraint. Thus, we relax this constraint to have a convex search space. Then, from the solution obtained from quadratic programming on convex search space, we give an approximate solution for FLRIALS.

New Method for Solving Fuzzy LR Interval Linear Systems Using Least Squares Models

Recently, Ghanbari and Mahdavi-Amiri [2015, Soft Computing] have proposed a model to characterize exact solutions and presented an algorithm to compute approximate solutions. Here, inspired by Ghanbari and Mahdavi-Amiri, we show that solving fuzzy LR interval linear systems is equivalent to solving fuzzy LR linear systems (FLRLSs). Then we develop some necessary and sufficient conditions for the solvability of FLRLSs. We then provide a new general concept for an approximate solution when an FLRLS lacks a solution. To compute an approximate solution, we propose an algorithm using a least squares method. Finally, we show the appropriateness of our proposed approximate solution recently introduced numerically.

Bankruptcy problem under uncertainty of claims and estate

In this paper we focus on real situations where certain perfectly divisible estate has to be divided among claimants who can merely indicate the range of their claims, and the available amount is smaller than the aggregated claim. Funds' allocation of a firm among its divisions, taxation problems, priority problems, distribution of costs of a joint project among the agents involved, various disputes including those generated by inheritance, or by cooperation in joint projects based on restricted willingness to pay, fit into this framework. The corresponding claim of each claimant can vary within a closed interval or fuzzy interval. For claims, fuzzy intervals are applied whenever the claimants can distinguish a possibility of attaining the amount of estate, and/or its membership degree of a possibility of attainment. When claims of claimants have fuzzy interval uncertainty, we settle such type of division problems by transforming it into bankruptcy problems under interval uncertainty by interval valued mappings. A similar approach is applied to deal with uncertainty of estate to be divided. Here, a probability interpretation can also be considered e.g. in taxation problems. We consider the division problems under uncertainty of claims and/or estate and present bankruptcy rule, which are consistent with the classical bankruptcy proportional rule. Several examples are presented to illustrate particular problems and solution concepts.

Dynamic collaborative optimization for disaster relief supply chains under information ambiguity.

Large-scale disasters occur worldwide, with a continuing surge in the frequency and severity of disruptive events. Researchers have developed several optimization models to address the critical challenges of disaster relief supply chains (e.g., emergency material reserving and scheduling inefficiencies). However, most developed algorithms are proven to have low fault tolerance, which makes it difficult for disaster relief supply chain managers to obtain optimal solutions and meet the emergency distribution requirements within a limited time frame. Considering the uncertainty and ambiguity of disaster relief information and using Interval Type-2 Fuzzy Set (IT2TFS), this paper presents a collaborative optimization model based on an integrative emergency material supplier evaluation framework. The optimal emergency material suppliers are first selected using a multi-attribute group decision-making ranking method. Multi-objective fuzzy optimization is then run in three emergency phases: early -, mid-, and late-disaster relief stages. Focusing on a massive flash flood disaster event in Yunnan Province as a case study, a comprehensive numerical analysis tests and validates the developed model. The results revealed that the proposed optimization method can optimize emergency material planning while ensuring that reserve material safety inventory is always maintained at a reasonable level. The presented method suggests a fuzzy interval to prevent emergency materials’ safety inventory shortage and minimize continuous life/property losses in disaster-affected areas.

An [formula omitted]-cut interval based IF-importance measure for intuitionistic fuzzy fault tree analysis of subsea oil and gas production system

The subsea production system is very important for having deep water oil and gas production. The leakage of the oil and gas in the subsea production system may result in enormous adverse consequences on marine lives, high production loss, and serious deadly disasters to humans. For the safety analysis of subsea production system, importance measures play an important role to rank the components of the system according to their contribution to the leakage of oil and gas for preventive and corrective purposes. In conventional fault tree analysis and fuzzy fault tree analysis, various importance measures are developed for criticality analysis of the system. The objective of the present study is to develop a novel IF-importance measure by employing the concept of α-cut interval under intuitionistic fuzzy environment. The failure possibilities of basic events in fault tree analysis are quantified by triangular and trapezoidal intuitionistic fuzzy numbers. The presented research study applies α-cut intervals of intuitionistic fuzzy numbers, intuitionistic fuzzy fault tree analysis and interval arithmetic operations. The validation is carried out by comparing the developed importance measure with some pre-existing importance measures.

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.

Type-2 fuzzy logic applications designed for active parameter adaptation in metaheuristic algorithm for fuzzy fault-tolerant controller

PurposeIn recent times, fuzzy logic is gaining more and more attention, and this is because of the capability of understanding the functioning of the system as per human knowledge-based system. The main contribution of the work is dynamically adapting the important parameters throughout the execution of the flower pollination algorithm (FPA) using concepts of fuzzy logic. By adapting the main parameters of the metaheuristics, the performance and accuracy of the metaheuristic have been improving in a varied range of applications.Design/methodology/approachThe fuzzy logic-based parameter adaptation in the FPA is proposed. In addition, type-2 fuzzy logic is used to design fuzzy inference system for dynamic parameter adaptation in metaheuristics, which can help in eliminating uncertainty and hence offers an attractive improvement in dynamic parameter adaption in metaheuristic method, and, in reality, the effectiveness of the interval type-2 fuzzy inference system (IT2 FIS) has shown to provide improved results as matched to type-1 fuzzy inference system (T1 FIS) in some latest work.FindingsOne case study is considered for testing the proposed approach in a fault tolerant control problem without faults and with partial loss of effectiveness of main actuator fault with abrupt and incipient nature. For comparison between the type-1 fuzzy FPA and interval type-2 fuzzy FPA is presented using statistical analysis which validates the advantages of the interval type-2 fuzzy FPA. The statistical Z-test is presented for comparison of efficiency between two fuzzy variants of the FPA optimization method.Originality/valueThe main contribution of the work is a dynamical adaptation of the important parameters throughout the execution of the flower pollination optimization algorithm using concepts of type-2 fuzzy logic. By adapting the main parameters of the metaheuristics, the performance and accuracy of the metaheuristic have been improving in a varied range of applications.

Planning Location of Mobility Hub for Sustainable Urban Mobility

• Location selection problem for the mobility hubs is an essential and strategic task faced by municipalities. • This paper aims to select the best location for a new mobility hub location in the Anatolian side of Istanbul. • An integrated MCDM methodology that consists of interval type-2 fuzzy AHP and interval type-2 fuzzy WASPAS is proposed. • Kadıköy is found as the best location for building a mobility hub to expand shared-use mobility and public transport options. • To validate results of the proposed approach, Sensitivity analysis is conducted at the end of the study. Mobility hubs facilitate access to many transportation modes, such as public transportation, bike sharing, bus rapid transit (BRT), metro or car sharing, to enable travelers become more mobilized by providing advantage of their socio-economic benefits. Mobility hubs also help to lessen greenhouse gas emissions by decreasing private vehicle usage and giving equal priority to all modes of travel, including walking, cycling and other active forms of transport, i.e. public transport, ridesharing, taxis and private motor vehicles. Thus, emerging and inspiring the usage of diverse modes of transportation with less influence on the environment is one of the main policy to decrease people's environmental footprint. Since the locations of mobility hubs play an important role to achieve this goal by attracting travelers and encouraging people to use different modes of mobility options that has less impact on environment, the location selection of such hubs requires a strategic decision for authorities and policy makers. With this motivation, in this study, an integrated fuzzy multi criteria decision-making (MCDM) methodology that consists of interval type-2 fuzzy Analytic Hierarchy Process (AHP) and interval type-2 fuzzy Weighted Aggregated Sum Product Assessment (WASPAS) is proposed to select the best location for a new mobility hub location in the Anatolian side of Istanbul. Among alternative locations Kadıköy is found as the best location for building a mobility hub to expand shared-use mobility and public transport options at a major transit station for Istanbulers in Anatolian side. At the end of the study, Sensitivity analysis is conducted to validate results of the proposed approach.

МЕТОД И АЛГОРИТМ ПЛАНИРОВАНИЯ ОПЕРАЦИЙ НА ОСНОВЕ МОДЕЛИ НЕЧЕТКОГО КОНЕЧНОГО АВТОМАТА

In this paper the planning and scheduling problem as an important optimization problem inmany transportation and robotic applications is discussed. To solve planning problems, the mainapproaches are based on optimization methods, sampling-based methods, and usually such kindsof problems are NP-hard and high dimensional. In this work, the method for planning and schedulingbased on the fuzzy finite state machine model is developed. Fuzzy graph presentation of thescheduling problem and operation planning is given. The paper presents two approaches to theformulation of the planning problem with limited resources and temporal variables: state-oriented(with transitions between states), temporal ordering-oriented (on a time scale). Temporal modelingfor planning problems implies a qualitative approach to managing the distribution of operationsor topological ordering, as well as a quantitative approach to handling imprecise durationsrelationships between operations in multiple parameters. The concepts of fuzzy intervals and fuzzyrelations are introduced for planning operations on a graph. A planning algorithm based on thetheory of automata and temporal modeling under uncertainty has been developed. Using this formalism,a path planning problem is solved by successively altering a state using various operationsuntil a solution is found. The idea of temporal-ordered partial schedule associated with theplanning state of the system is discussed. A model of a finite automaton for a planning system underconditions of uncertainty is proposed. A method and algorithm for scheduling operationsbased on a non-deterministic finite automaton and an enumeration scheme have been developed.The non-deterministic computation for a scheduling problem is a decision tree whose root correspondsto the beginning of the scheduling process, and each branch point in the tree correspondsto a computation point at which the machine has multiple choices. And the finite state machinemodel (automata) for the planning system under uncertainty is suggested.

Hermite-Hadamard and Schur-Type Inequalities for Strongly h -Convex Fuzzy Interval Valued Functions

The concept of fuzzy theory was developed in 1965 and becomes an acknowledged research subject in both pure and applied mathematics and statistics, showing how this theory is highly applicable and productive in many applications. In the present study, we introduced the definition of fuzzy interval valued strongly h -convex function and investigated some of its properties. We established Hermite-Hadamard and Schur-type inequalities for the class of fuzzy interval valued strongly h -convex function.

Development of a Bounded Two-Stage Data Envelopment Analysis Model in the Intuitionistic Fuzzy Environment

Data Envelopment Analysis is a powerful tool for evaluating the efficiency of decision-making units for the purpose of ranking, comparing, and differentiating efficient and inefficient units. Classical Data Envelopment Analysis methods operate by measuring the efficiency of each DMU compared to similar units without considering their internal workings and structures, which make them unsuitable for cases where DMUs are multistaged processes with intermediate products or when inputs and outputs are ambiguous or nonconfigurable. In problems that involve uncertainty, intuitionistic fuzzy sets can offer a better representation and interpretation of information than classic sets. In this paper, the noncooperative network data envelopment analysis model of Liang et al. (2008), which is based on Stackelberg game theory and efficiency decomposition, is expanded using the concepts of best and worst relative returns Data Envelopment Analysis model of Azizi et al. (2013) into an interval efficiency estimation model with α-β cuts for two-stage DMUs with trapezoidal intuitionistic fuzzy data. Furthermore, the method of Yue (2011) is used to rank these DMUs in terms of their intuitionistic fuzzy interval efficiency. A numerical example is also provided to illustrate the application of the proposed bounded two-stage intuitionistic Data Envelopment Analysis model.

Fuzzy confidence interval construction and its application in recovery time for COVID-19 patients

An approach is proposed to construct fuzzy confidence intervals for unknown parameters in statistical models. In this approach, a family of confidence intervals of the unknown crisp parameter has been considered. Such confidence intervals are used to obtain a fuzzy confidence interval for the parameter of interest. ‎The proposed approach benefits a wide range of confidence intervals to obtain a trapezoidal shaped fuzzy set of the parameter space as the fuzzy confidence interval for the parameter of interest. By using the resolution identity, it is shown that the constructed fuzzy confidence intervals are really fuzzy sets of the parameter space.Some numerical examples are provided to explain the approach in one-sided and two-sided fuzzy confidence intervals. ‎‎Moreover, ‎an‎‎‎ application in health sciences ‎‎‎is provided about the ‎‎‎‎recovery time of olfactory and gustatory dysfunctions for COVID-19 patients.