Fuzzy Interval Research Articles

ENTREATY OF FUZZY INTERVAL-VALUED EDAS METHOD IN ORDER PREFERENCE OF CUSTOMERS FOR RANKING OPTIMIZATION.

The growing need of a research lab in automotive confirmatory tests is increasing day by day in the competitive market. Testing plays an important part in time and cost to meet the durability and quality requirements of the customers. Decision Making Models [DMM] with order preference supports well in optimizing the process scheduling time and utilization of machines. The analyzed data is of with multi-criterion constraints and unreliable parameters. As the constraints in analyzed data belongs to [-R, R], the problem is modelled with generalized Fuzzy Interval Valued set. The defined FIVs are justified using Novel Accuracy of Membership and Non-Membership values. The unconventionality of the work discussed in this paper is applying FIVs in the existing Evaluation by Distance Average Sum [EDAS] method. The weight values of the criterion are calculated using the Average Distance [AD] formula. In general, Fuzzy VIKOR and Fuzzy TOPOSIS helps in identifying the closeness co-efficient of the parameters. Particularly, VIKOR plays a vital role on group utility and TOPOSIS on Max/Min of negative and positive ideal solutions respectively. Here, the proposed FIVEDAS method is framed with the Relative Distance Values [RDA] and so it provides us an ideal ranking in order preference. The results are compared with the existing lab process utility time in First-Come-First Serve method.

New preference order relationships and their application to multiobjective interval and fuzzy interval optimization problems

Recently, a method to generate preference ordering relationships in interval space, which is based on a family of automorphisms in bidimensional Euclidean space, and the family of φ-interval optimization problems were introduced in the literature. In this article both the method to generate preference ordering relationships in interval space and the family of φ-interval optimization problems are generalized, providing frameworks for dealing with families of multiobjective interval and multiobjective fuzzy interval optimization problems called the family of φ-multiobjective interval optimization problems and the family of φ-multiobjective fuzzy interval optimization problems, respectively. It is shown that those multiobjective interval and multiobjective fuzzy interval optimization problems presented in the literature, whose formulations are based on a given preference order relationship, can be seen as particular cases of a φ-multiobjective interval optimization problem and of a φ-multiobjective fuzzy interval optimization problems, respectively. Some optimality conditions for both these two families of optimization problems are provided and the methods, concepts and results presented herein are illustrated by several examples.

Aiming at low nitrogen leaching diets based on nitrogen fertilizer regulatory policy: A regional bio-economic assessment of the Zayandeh-Rud river basin-Iran

Negative environmental impacts of nitrogen (N) intensive diets have triggered global debates on sustainable nitrogen management. Solutions such as dietary transitions, cropland reallocation and N Regulatory Policy (NRP) have been proposed to mitigate the adverse environmental impacts of N use in food production. However, there is still insufficient understanding of how NRPs could be designed to minimize negative environmental impact across diverse agro-ecological zones without sacrificing human dietary requirements. To increase this understanding, we evaluated the consequences of three NRP scenarios (low, moderate, and high N fertilizer rates) on the amount of livestock and non-livestock diet components as well as the associated N leaching and farmers' Gross Margin (GM) by optimizing the allocation of cropland between food and feed crops. We developed a bio-economic Interval Fuzzy Multi-Objective Programming (bio-economic IFMOP) model for the Zayandeh-Rud river basin, Iran, and a procedure that accounts for annual average availability of calories per capita, calorie sources from livestock and non-livestock components of three dietary preferences, and inequality in calorie distribution. The interaction among soil, climate and weather variability and NRPs across nine sub-regions of the case study region was handled by crop yield simulation using the DSSAT software. The solution of farmers' GM, derived from the optimization problem across possibilities of water fluctuations, was assessed to determine the uncertainty in GM. We also introduced an N leaching per Block of Distributed Calories (BDC) criterion based on solutions of supplied calories and associated N leaching. The upper bound of the moderate NRP scenario resulted in the smallest N leaching per BDC. This corresponded to ∼0.34, ∼0.34, ∼3.77 and 19.00 million BDC of meat, dairy, wheat and potato, respectively. Also, the upper bound of this scenario satisfied the lowest instability in farmers’ GM against water fluctuation compared with low and high NRP scenarios. The affordable volume of N leaching per BDC varied across sub-regions between [1.53,3.49], [1.52,3.33], [0.76,0.99] and [0.05,0.08] kg for meat, dairy, wheat and potato, respectively. Our results highlighted both optimistic and pessimistic prospects of producing low N leaching diets. The approach of this study could also be applied to other regions and countries.

The Road to Sustainable Logistics: Using the Fuzzy Nonlinear Multi-Objective Optimization Model to Build Photovoltaic Stations in Taiwan’s Logistics Centers

In Taiwan, numerous company logistics centers have embraced installing solar photovoltaic power stations (SPPSs) on their rooftops. The primary objective of this study is to expedite the generation of green electricity for sale, bolstering the logistics center’s income and enhancing its environmental, social, and governance (ESG) profile. How can we secure solar photovoltaic power station (SPPS) projects with expedited construction timelines, reduced investment costs, and heightened quality aligned with the long-term ESG objectives? The study applies the critical path method (CPM) to determine the item’s path. Next, the mothed leverages Zimmermann’s mathematical models for nonlinear multi-objectives and Yager’s fuzzy sets to enhance project efficiency, minimizing completion time and cost while maximizing the quality ratio. Subsequently, the project uses Liou and Wang’s defuzzification values and incorporates Dong’s fuzzy to accelerate calculations. In this case, Project HP’s item J, the construction time is reduced from 24.3 to 3.2 days, ensuring that construction quality meets an 85% standard. Item J necessitates expanding the fuzzy cost interval (4549.90, 15,416.65, 26,283.41) (it refers to a scope of possible costs). It becomes evident that construction time plays a pivotal role in controlling costs. For Project HP’s item H, the unit time quality decision ranges from TWD 238,000 to 240,000, to turn into a cost interval of TWD 215,100, 239,000, and 262,900. Consequently, cost transformation transitions from an active to a more passive role, with quality and construction time becoming the driving components. This study uses a fuzzy nonlinear multi-objective model to guide the decision analysis of SPPSs within logistics centers. This strategy enables decision-makers to streamline logistics center operations, ensuring time, cost, and quality (TCQ) alignment during SPPS installation, thereby advancing ESG sustainability goals.

Cubic Pythagorean Hesitant Fuzzy Linear Spaces and Its Relevance in Multi Criteria Decision Making

Pythagorean fuzzy sets and interval valued Pythagorean fuzzy sets have an important role in decision making techniques. Pythagorean hesitant fuzzy sets are time and again used in dealing with uncertain and vague data. The motive of this paper is to introduce the notion cubic Pythagorean hesitant fuzzy linear spaces. We also present the notion of P(R)-intersection, P(R)-union of cubic Pythagorean hesitant fuzzy linear spaces with examples. Secondly, a series of operators like cubic Pythagorean hesitant fuzzy weighted averaging aggregation operators, cubic Pythagorean hesitant fuzzy order weighted averaging aggregation operators and cubic Pythagorean hesitant fuzzy hybrid order weighted averaging aggregation operators are developed. Then, these aggregation operators are further extended to cubic Pythagorean hesitant fuzzy prioritized weighted averaging aggregation operators by assigning priorities to the criteria. A real life MCDM problem has been illustrated and the effectiveness of the results are compared with those solved using cubic picture hesitant fuzzy prioritized weighted averaging aggregation operators.

Multidimensional solution of fuzzy linear programming

There are several approaches to address fuzzy linear programming problems (FLPP). However, due to using standard interval arithmetic (SIA), these methods have some limitations and are not complete solutions. This article establishes a new approach to fuzzy linear programming via the theory of horizontal membership functions and the multidimensional relative-distance-measure fuzzy interval arithmetic. Furthermore, we propose a multidimensional solution based on the primal Simplex approach that satisfies any equivalent form of FLPP. The new solutions of FLPP are also compared with the results of existing methods. Some numerical examples have been illustrated to show the efficiency of the proposed method.

Relational-separable models of monitoring processes at variable and unclear observation intervals

The article is devoted to the development of combined models, methods and tools designed to solve the current problems of modeling and analysis of monitoring process data, which are repre-sented by time series and differ in variable or fuzzy observation intervals (CHRPNI). In the article, a new relational separable model (RSM) and a combined quantile algorithm are proposed to in-crease the accuracy and efficiency of modeling and analysis of the processes of CHRPNI. The rela-tional model is defined by a system of fuzzy relational relations of the first and second order ob-tained on the basis of the original sequence of data. In the combined algorithm, the results of calcu-lations obtained by SPM and models of fuzzy relational relationships were generalized with the op-timal selection of weighting factors for individual components. As a result of the conducted research by means of numerical modeling, it was established that the introduction of combined process models in the case of PNEU is rational and effective. Exam-ples of data analysis of monitoring processes of rehabilitation of diabetic patients showed certain possibilities of ensuring the accuracy of the results of the analysis of indicators and their short-term forecasting.

Mathematical insights into interval solutions of fuzzy relation inequalities for effective Information resource sharing in business education

To examine the connectivity of educational and business institution networks and assess their resource accessibility, we have employed min-max fuzzy relation systems. This piece aims to delve into the outcomes resulting from various factors within a three-compartmental financial system. The research undergoes the dynamical max-min fuzzy solutions, which are expressed in an interval format. These solutions take into consideration variables such as the price index, interest rate, investment demand, fluctuations, cost per investment derived from saved funds, and the elasticity of market demand within the commercial sector. These variables are essential for comprehending the dynamics of the three-compartment financial system. It is difficult to obtain the entire set of solutions for the max-min fuzzy relation system using only minimal solutions. Some of these systems can be solved using optimized fuzzy relation models for both maximal and minimal solutions. Therefore, by converting the business market's financial system into a max-min fuzzy relation inequality, the strategy presented in this article tries to get the broadest and changing solution fluctuating between minimal and maximal solutions. With this suggested strategy for solving the problem, the limiting upper and lower values within which the given quantities fluctuate are identified. By measuring the breadth of the resulting interval, the range of fluctuation may be identified, giving a thorough insight into the system's behaviour. Due to the potential instability of market agents and their respective influences, fluctuations may occur in the demand, supply, and prices of indices in the financial system. Consequently, presenting the financial system in the format of the widest fuzzy interval solution can provide easily accessible information to the general public by illustrating the max-min fuzzy relation system of financial dynamics, outlining the necessary steps, and including a numerical example.

A new state‐of‐health estimation method for Li‐ion batteries based on interpretable belief rule base with expert knowledge credibility

AbstractState‐of‐health (SOH) estimation methods for Li‐ion batteries are important for the safe operation of the entire system. However, it is often challenging due to the uncertainty within the batteries and the criteria for model interpretability. Belief rule base (BRB) is a rule‐based expert system that has certain advantages for both aspects. However, several problems with BRB interpretability need to be solved urgently. First, expert knowledge credibility is often given subjectively, while objective information is neglected to be considered. Second, BRB interpretability is easily ignored or corrupted in the optimization process. Third, expert knowledge is assumed to be completely reliable information to be used as interpretability evaluation criterion. Therefore, a new SOH estimation method for Li‐ion batteries based on interpretable BRB with expert knowledge credibility (IBRB‐c) is proposed. In the IBRB‐c, the calculation method of expert knowledge credibility is given. Then, an optimization algorithm with interpretability strategies is used. Finally, the concept of the fuzzy interpretable interval is proposed to design the interpretable evaluation criterion. The effectiveness of the proposed method is verified by using the experiment of NASA Li‐ion battery as a case study.

Detection of hypersonic weak targets by high pulse repetition frequency radar based on multi‐hypothesis fuzzy‐matching radon transform

AbstractFor the integration detection of near space hypersonic weak targets by high pulse repetition frequency (PRF) radar, a novel method named Multi‐Hypothesis Fuzzy‐Matching Radon transform (MHFM‐RT) is proposed for the near space hypersonic target detection and tracking. For remote hypersonic target detection, to avoid range ambiguity, current radars always use a low PRF mode, which limit the number of pulse accumulations. Using the high PRF mode, the fuzzy folding will appear in the target range measurements when target trajectory crosses range fuzzy intervals. Therefore, there is a contradiction between range ambiguity and energy accumulation. The proposed method is used to match the fuzzy measurements, so as to realise the correct integration in the condition of range ambiguity. Firstly, considering the need of range ambiguity resolution, the mode of staggered PRF is used. Secondly, the first frame measurements are periodically extended for multiple‐fuzzy hypothesis. Finally, the weak target track is accumulated in MHFM‐RT domain, and the signal integration and ambiguity resolution can be realised simultaneously. The proposed method expands the Variable‐Diameter‐Arc‐Helix Radon transform (VDAH‐RT) method to fuzzy folding conditions. Compared with the existing methods, for 7‐scan measurements non‐coherent integration, the detection sensitivity of the proposed method is about 0.5–1 dB higher than that of the IMM hybrid filter algorithm, and about 1 dB higher than that of the RHT‐TBD approach, and it needs less storage space and has higher detection probability.

The Status of Video Games as Self-Involving Interactive Fictions: Fuzzy Intervals and Hard Identifications

The Status of Video Games as Self-Involving Interactive Fictions: Fuzzy Intervals and Hard Identifications

Crop acreage planning for economy- resource- efficiency coordination: Grey information entropy based uncertain model

Reasonable adjustment of crop acreage can improve the sustainability of agriculture in arid zones by promoting economic development, alleviating water scarcity, and improving resource utilization efficiency but meets the challenges of various decision-maker preferences and uncertainties. With the objectives of maximizing economic benefits, minimizing evapotranspiration, and maximizing water productivity and water production efficiency, this study developed a grey entropy based multi-objective fuzzy constraint interval programming model (GEMOFCIP) through incorporation of information entropy technology, fuzzy constraints and interval programming approaches within a general optimization framework. The model is capable of (1) generating the crop acreage management schemes through trading off the different development goals; (2) dealing with the structure and parameter uncertainties of the optimization model; (3) measuring the relative importance of multiple objectives by the introduction of information entropy with the insufficient decision-maker’s preference information. Taking the crop acreage planning problem in Liangzhou, northwest China as a case study, the model was solved under different water-saving and satisfaction degree scenarios. It turned out that, after optimization, the economic benefit, water productivity and water production efficiency have been significantly improved, while the total ET and the total irrigation water have been significantly compressed in the study area. The GEMOFCIP model is superior to the previous models in that it takes into account the randomness of the relative importance of system objective, the vagueness of system constraints and the fluctuations of system coefficients, which would make the model more reasonable, stable and objective. Optimal results can help manage crop pattern with the economy-resource-efficiency consideration and accelerate the healthy development of agriculture in arid zones.

Normed Space of Fuzzy Intervals and Its Topological Structure

The space, Fcc(R), of all fuzzy intervals in R cannot form a vector space. However, the space Fcc(R) maintains a vector structure by treating the addition of fuzzy intervals as a vector addition and treating the scalar multiplication of fuzzy intervals as a scalar multiplication of vectors. The only difficulty in taking care of Fcc(R) is missing the additive inverse element. This means that each fuzzy interval that is subtracted from itself cannot be a zero element in Fcc(R). Although Fcc(R) cannot form a vector space, we still can endow a norm on the space Fcc(R) by following its vector structure. Under this setting, many different types of open sets can be proposed by using the different types of open balls. The purpose of this paper is to study the topologies generated by these different types of open sets.

Особливості розрахунку очікуваної вартості дослідно-конструкторських робіт зі створення космічних апаратів

The aim of this work is to identify the features of expected cost estimation for R&D’s on spacecraft development. The study is based on a methodological approach to expected cost estimation for R&D’s on spacecraft development. The cost estimation model is based on a method of componentwise analogy for relatively simple spacecraft components, moving along the edges of a weighted oriented tree graph that models the spacecraft technical structure, and fuzzy mathematics methods. The methodological approach will allow one to obtain required R&D expected cost indices early in the spacecraft development when the standardized cost estimation method and parametric methods are difficult to use because of the insufficiency of bug-free design and manufacture documentation and statistical data on labor intensiveness and materials consumption. The design novelty, R&D complexity, and work automation coefficients are determined by converting the index value from a fuzzy number in a fuzzy interval into a crisp number, thus allowing one to reduce the effect of subjective factors. Calculating the engineering-and-economical indices of a spacecraft by all R&D participants using the same methodological approach increases the accuracy and shortens the time of the computational process. Conducting the calculations in a systematic way will fill the statistical base of the space sector with labor intensiveness and materials consumption data needed for estimating the cost of new spacecraft and components thereof using a unified concept package – a glossary. The paper presents the operation sequence of estimating the cost of R&D on spacecraft development and describes the required input data and the output data format.

A fuzzy interval based multi-criteria homogeneous group decision making technique: An application to airports ranking problem

This paper aims to develop and introduce a fuzzy Interval based Multi-criteria homogeneous Group Decision making technique (IMGD) to make appropriate decision under fuzzy environment. In fuzzy multi-criteria group decision making process, a group of decision makers often considers several subjective criteria for ranking a set of alternatives. Due to vague and imprecise information, decision makers generally utilize linguistic variables which are mandatorily converted into triangular or trapezoidal fuzzy numbers. The total process then becomes very complex and time consuming. The current investigation advocates fuzzy intervals instead of triangular or trapezoidal fuzzy numbers for simplification of the complex situation and ease of calculation. In this method, fuzzy intervals of performance ratings and weights assessed by homogeneous group decision makers under subjective criteria are converted into first mean fuzzy intervals then into normalized crisp numbers. The normalized crisp performance ratings and normalized crisp weights are combined together to determine initially individual contribution and then into aggregate contribution to each alternative for final ranking and selection of the alternative. The new model is demonstrated with an application to airports ranking and selection problem for better clarification and verification. The outcome of the proposed is validated with the results obtained by well-known existing MCDM techniques. The analysis shows that the proposed method is applicable, useful and effective for appropriate decision making under fuzzy MCDM environment.

The challenges of modeling using fuzzy standard interval arithmetic: A case study in electrical engineering

In this work, the aim is to shed light on the challenges in deriving a mathematical model of dynamical systems when fuzzy standard interval arithmetic (FSIA) serves as a mathematical tool. The challenges in question are investigated through two approaches called the direct and devious approach. Specifically, in the direct approach, the challenges lie in the high complexities of deriving the fuzzy model while maintaining conformity with the laws of physics. Additionally, it is possible that the resulting fuzzy model may not have a solution. Concerning the devious approach, the primary challenge is the potential violation of the physics laws governing the system, which means that the validity of the fuzzy model is not guaranteed. Moreover, in both cases, the UBM phenomenon poses another challenge, preventing the attainment of a unique fuzzy model. As a result, it is demonstrated that FSIA and any related concepts, such as the strongly generalized Hukuhara derivative (SGH-derivative), generalized Hukuhara derivative (gH-derivative), generalized derivative, etc., mainly suffer from the catastrophe of physics laws violation (CPLV), which can be considered the most significant drawback. Furthermore, it is explained that the reason for a fuzzy differential equation under concepts such as the SGH-derivative or gH-derivative having multiple solutions is due to the CPLV. To clarify the CPLV, a simple electrical circuit with uncertain elements is examined as a case study.

Sparrow search algorithm with adaptive t distribution for multi-objective low-carbon multimodal transportation planning problem with fuzzy demand and fuzzy time

In this paper, we present a multi-objective low-carbon multimodal transportation planning problem with fuzzy demand and fuzzy time (MOLCMTPP-FDFT) that minimizes both cost and time while incorporating mandatory carbon emission, carbon tax, carbon trading, and carbon offset policies. Chance constrained programming and interval programming are introduced to formulate the fuzzy demand chance constrained programming model and the fuzzy time interval programming model, respectively. Then, the mathematical model of uncertain MOLCMTPP-FDFT is transformed into a deterministic model. Based on the sparrow search algorithm, t distribution and the concept of Pareto optimality for multi-objective optimization, we also propose a solution strategy for the proposed model. In this algorithm, the number of iterations is used as the degree of freedom of - to update the sparrow location, which strikes a balance between the capabilities of global search and local search. Finally, the proposed algorithm and MOLCMTPP-FDFT are applied to a real case, resulting in a minimum cost of 260730.48 and a time duration of 13.044, which outperform the minimum cost of 268874.88 and minimum time of 18.32 obtained using single-mode transportation. The carbon emissions resulting from the lowest-cost solution obtained using single-mode transportation are 3,198.48, which are significantly more than the allowed emissions. Therefore, the proposed algorithm and mathematical model of MOLCMTPP-FDFT are valuable tools for optimizing multimodal transportation route. Additionally, the experimental results not only validate the superior efficiency and energy-saving benefits of the proposed multimodal transportation routes in comparison to the actual single-modal transportation, but also demonstrate the applicability of different low-carbon policies.

An overlap function-based three-way intelligent decision model under interval-valued fuzzy information systems

One of the expression forms of uncertain information are interval-valued fuzzy information systems (IFISs). Whereas, psychological experiments show that psychological behaviors of decision maker (DM) affect the decision results under uncertain information. Consequently, the main research objectives of this paper are two-fold: 1. To study how to portray the influence of psychological behaviors on decision-making under IFISs, so that the decision-making process is more realistic. 2. To investigate how to efficiently solve decision-making problems in the context of IFISs. Three-way decision (3WD) theory and fuzzy rough sets (FRSs) are effective tools for solving uncertain information. For that reason, this paper develops a 3WD model based on prospect theory (PT) under IFISs, which can provide the best decision action for objects from a viewpoint of optimization. First, an attribute-oriented interval fuzzy set is introduced, which establish a bridge between the state sets in 3WD and the reference points in PT. Furthermore, conditional probability of an object is reasonably estimated by interval-valued fuzzy rough sets (IVFRSs). Meanwhile, an attribute-oriented relative value model is proposed, which can get the prospect values of an object under each action. Second, an intelligent 3WD model is developed from a viewpoint of information granularity. Finally, through the search of the existing literature, relevant research data is obtained, and then case research method, qualitative and quantitative combination method, control variable method are adopted in turn to design the case study, comparative and experimental analyses. In short, the developed model not only expands the development of related theories, 3WD, PT, FRSs, but also offers new methods for solving the decision-making problems under IFISs, which has important practical guidance significance.

Interval Evidential Reasoning-based Fault Detection of Electromagnetic Relay

The electromagnetic relay is a key switch control component, and its fault detection under uncertainties is a challenging problem. In this paper, a fault detection method based on interval evidential reasoning (IER) is proposed and applied to detect the relay’s fault. The method can handle fuzzy uncertainty and interval uncertainty in relay test data, and iteratively aggregate evidence by using the IER algorithm. Firstly, the relay super-path time data is transformed into the form of an interval belief distribution by using the fuzzy threshold, which is optimized by using training data. Secondly, historical and current information is aggregated to update interval belief distribution. Finally, the fault detection result can be obtained from interval belief distribution by a rule. The experimental results show that the presented method can improve the detection effect significantly.

Fuzzy correlational analysis for dynamic consolidation of virtual machines in cloud computing environment

This theoretical research in fuzzy correlation analysis integrates data uncertainty analysis by measuring the strength of the linear relationship restricted to two fuzzy sets. As the relevant contribution to this research area, this paper presents the axiomatic definition of the n-dimensional generalized fuzzy correlation coefficient (nGCC), assigning to n input fuzzy sets an output value in the interval [−1,1]. Thus, the properties of general overlap functions and fuzzy negations are studied, discussing binary non-normed restricted dissimilarity functions, and the n-dimensional non-normed conjunctive functions. This study provides new methods for the n-dimensional generalized fuzzy correlation coefficient analysis, regarding their applications in solving multi-criteria and decision-making problems founded on fuzzy logic extensions. The n-dimensional non-normed conjunctive aggregation functions are also introduced, as range domain extensions from [0,1] to [−1.1], covering the interpretation of negative to positive variable associations. The proposal correlation analysis promotes a better evaluation and data selection even when more than one algorithm is applied to evaluate the reduction methods in the defuzzification process based on Interval-valued Fuzzy Logic. We also investigate the relevance to determine a reliable result from the fuzzy inference system based on the nGCC methodology. This correlation methodology applied to the Interval Fuzzy Load Balancing for Cloud Computing (Int-FLBCC) model contributes as a flexible approach for virtual machines dynamic consolidation enabling improvements in resource usage and power efficiency, improving the computational system’s energy efficiency. So, the nGCC methodology extends the Int-FLBCC model by adding other degrees of reliability to the results obtained with diverse evaluations through n-dimensional generalized fuzzy correlation coefficient expressions, exploring average aggregations as arithmetic and exponential means and the median operator.