Membership Grades Research Articles

Cost Comparison of Selective Laser Sintering with Injection Molding in the Presence of Uncertainties

The application of additive manufacturing (AM) has increased exponentially in recent years. Industries are keen to explore this innovative technology but are apprehensive about the high processing cost of the process. Hence, it is crucial to carry out a cost analysis of the process. This paper presents an approach to compare the costs of an AM process (selective laser sintering (SLS)) and a traditional manufacturing process (injection molding (IM)) in the presence of uncertainties. Initially, the deterministic cost models comprising necessary cost variables for SLS and IM are described. The deterministic models are converted to fuzzy set-based models for tackling uncertainties. For this purpose, important uncertain variables are treated as fuzzy members and fuzzy arithmetic is employed. Only linear triangular fuzzy numbers are used in this work. Fuzzy cost estimates produce three values (low, most likely and high estimates) of cost corresponding to membership grades. A methodology to compare two fuzzy costs of the processes is proposed for a variable demand scenario. Concept of fuzzy reliability is suitably utilized and variability in demand is tackled from probability theory. Variable demand is assumed to follow uniform as well as normal probability distributions. The methodology is illustrated with the help of two examples.

Pythagorean fuzzy likelihood function based on beta distributions and its based dominance ordering model in an uncertain multiple criteria decision support framework

The concept of Pythagorean fuzzy (PF) sets represents a superior tool to model complex uncertainties in an ambiguous and equivocal decision-making framework. In consideration of the significant capacity for exhibiting the uncertainty of subjective appraisals and estimations under the aegis of the PF theory, this paper presents a simple-to-operate decision-making approach that is grounded in some beneficial concepts of original likelihood functions and measurements of dominating and dominated characters. On the strength of beta distributions, this paper seeks to propound new notions of PF likelihood functions and likelihood-oriented dominating/dominated characters and to launch an exploitable multiple criteria evaluation method by means of a dominance ordering model for treating decision analysis within PF environments. This paper initiates an efficient beta distribution-based approach to the construction of novel PF likelihood functions that can quantify the possibility degrees of outranking and outranked relationships between Pythagorean membership grades. The applicable satisfaction and dissatisfaction estimations are established on the likelihood-oriented dominating and dominated characters, respectively. Furthermore, this paper formulates a straightforward dominance ordering model to obtain the ultimate dominance ranking orders of candidate alternatives and accomplish multiple criteria decision-making issues involving complicated uncertainty. A financing decision-making problem concerning working capital requirements is investigated to validate the application results using the advanced methodology. The real-world application is implemented to examine the reasonableness and efficacy of the established techniques. Moreover, comparative studies through the utility of a sensitivity analysis are performed to demonstrate the efficacy and merits of the dominance ordering model. The comparison results manifest that the initiated methodology is an advantageous and reliable decision-making technique that can enhance the methodological development regarding the multiple criteria evaluation model under PF uncertainty. Finally, recommendations for future research directions are also presented in the conclusions.

Membership-Function-Dependent Control Design and Stability Analysis of Interval Type-2 Sampled-Data Fuzzy-Model-Based Control System

This article investigates the design and stability analysis of the interval type-2 (IT2) sampled-data (SD) fuzzy-model-based (FMB) control system with the optimal guaranteed cost performance. An IT2 Takagi–Sugeno (T-S) fuzzy model is applied to describe the dynamics of the nonlinear systems where the parameter uncertainties are captured by the lower and upper membership functions. To conduct the stability analysis for the SD FMB control system, a looped-functional approach taking the advantage of the information about the sampling periods is employed. Because of the SD control strategy, the state will be sampled at each sampling instant and the control signal generated by the IT2SD fuzzy controller will be kept by the zero-order holder during the sampling period, which will result in mismatched membership grades between IT2 T-S fuzzy model and IT2SD fuzzy controller that leads to the complexity in carrying out stability analysis. Thanks to the imperfect premise matching concept, which allows the difference on the number of rules and the premise membership functions between model and controller, the design of the IT2SD fuzzy controller can be more flexible. To further relax the stability conditions and minimize the upper bound of the guaranteed cost index, the membership-function-dependent stability analysis approach which can make use of the features of the IT2 membership functions is adopted. The performance of the control system can also be adjusted through the choice of the weighting matrices in the cost function. The stability conditions building on the Lyapunov stability theory and the performance conditions building on the concept of the guaranteed cost control in the shape of linear matrix inequalities are established to assure the system stability and acquire the optimal guaranteed cost performance. The proposed IT2SDFMB control design is tested on the inverted pendulum system and the simulation results verify the effectiveness of the proposed approach.

Novel Adaptive Hysteresis Regime and Data Fusion on Crisp Logic in IoT-based Terrarium System for Improving Plant Growth Rate

In the present, autonomous environmental supervision and management are still insufficient. The approach of independent parameter controlling emerges to restraining plant growth and resource inefficiency. Developing a new method to control environmental parameters for accelerating plant growth should be deployed to satisfy the optimum condition and resource efficiency. In this paper, we propose a novel advanced crisp logic-based integrated with adaptive hysteresis control and data fusion algorithm to adapt the behaviour of each plant parameter in a certain condition. The objective of the proposed system is to control each plant parameter into the optimum regime while considering the coupling relationship between them. The measurement results show that our proposed system has a more sustained optimum condition and faster change into the desired grade of membership by adapting the hysteresis regime. Based on the measurements, the proposed system produces an optimum condition that are more sustain and stable and produce accelerated plant growth by 35.33%.

Novel score functions of generalized orthopair fuzzy membership grades with application to multiple attribute decision making

Novel score functions of generalized orthopair fuzzy membership grades with application to multiple attribute decision making

Multi-criteria decision making in robotic agri-farming with q-rung orthopair m-polar fuzzy sets.

q-Rung orthopair fuzzy set (qROFS) and m-polar fuzzy set (mPFS) are rudimentary concepts in the computational intelligence, which have diverse applications in fuzzy modeling and decision making under uncertainty. The aim of this paper is to introduce the hybrid concept of q-rung orthopair m-polar fuzzy set (qROmPFS) as a hybrid model of q-rung orthopair fuzzy set and m-polar fuzzy set. A qROmPFS has the ability to deal with real life situations when decision experts are interested to deal with multi-polarity as well as membership and non-membership grades to the alternatives in an extended domain with q-ROF environment. Certain operations on qROmPFSs and several new notions like support, core, height, concentration, dilation, α-cut and (α, β)-cut of qROmPFS are defined. Additionally, grey relational analysis (GRA) and choice value method (CVM) are presented under qROmPFSs for multi-criteria decision making (MCDM) in robotic agri-farming. The proposed methods are suitable to find out an appropriate mode of farming among several kinds of agri-farming. The applications of proposed MCDM approaches are illustrated by respective numerical examples. To justify the feasibility, superiority and reliability of proposed techniques, the comparison analysis of the final ranking in the robotic agri-farming computed by the proposed techniques with some existing MCDM methods is also given.

Robust Jointly Sparse Fuzzy Clustering With Neighborhood Structure Preservation

Fuzzy clustering techniques, especially fuzzy C-means (FCM) and its weighted variants, are typical partitive clustering models that are widely used for revealing possible hidden structures in data. Although they can quantitatively depict the overlapping areas with a partition matrix, their performances deteriorate when dealing with high-dimensional data because the distance computations may be negatively impacted by the irrelevant features, and then the concentration effect may arise. Moreover, they are sensitive to noisy environments. To tackle these obstacles, a robust jointly sparse fuzzy clustering method (RJSFC) is proposed in this study. The representative prototypes, sparse membership grades, and an orthogonal projection matrix are simultaneously learnt when optimizing RJSFC. The obtained low-dimensional embeddings can preserve the local neighborhood structure, and the clustering is conducted in the transformed lower dimensional space rather than the original space, which improves the capability of fuzzy clustering for dealing with high-dimensional scenarios. Furthermore, <inline-formula><tex-math notation="LaTeX">${L_{2,1}}$</tex-math></inline-formula>-norm is exploited as the basic metric for both loss and regularization parts in RJSFC, the robustness of the model and the interpretability of the extracted features are enhanced. The notions of fuzzy clustering, neighborhood structure preservation, and feature extraction are seamlessly integrated into a unified model. The limitation of the previous two-stage clustering framework when dealing with high-dimensional data entailing dimensionality reduction and clustering procedures separately can be effectively addressed. Extensive experimental results on various well-known datasets demonstrate the usefulness of RJSFC when comparing with some state-of-the-art methods.

A bird’s eye view of the connections among L-fuzzy i-covers, c-covers and (L-fuzzy) tolerances of L-fuzzy (point) set.

It is known that, for any L-fuzzy set X, there is an associated L-fuzzy point set, which is a crisp set. Further, for these sets X and, there are four associated objects of study, namely: the poset of L-fuzzy i-covers of X, the poset of L-fuzzy tolerance relations on X, and the poset of L-fuzzy sc-covers of, the poset of tolerance relations on . In this paper, we establish Lagois connection between certain type of crisp covers of L-fuzzy point set, certain type of tolerance relations on the same set and construct a commutative diagram involving the said four objects in terms of Galois/Lagois connections among them. Further, we show how the Galois/Lagois connections among the sets of L-fuzzy i-covers, L-fuzzy tolerance relations, and their associated objects, together capture the improvement in strengthening the fuzzy membership grade of L-fuzzy i-covers, L-fuzzy tolerance relations.

The Distributive Laws of Convolution Operations Over Meet-Convolution and Join-Convolution on Fuzzy Truth Values

Type-2 fuzzy sets (T2FSs) were introduced by Zadeh in 1975 as an extension of type-1 fuzzy sets (T1FSs). The membership grades of T2FSs are T1FSs in interval [0, 1], which are referred to as fuzzy truth values (that is, functions from [0, 1] to [0, 1]). Recently, (convolution) operations on T2FSs have become a hot research topic, such as type-2 t-norms, type-2 aggregation operations, type-2 implications, and so on. So, the distributive laws between these convolution operations have become an interesting and natural research area. In this article, we investigate the distributive laws of convolution operations over meet-convolution and join-convolution (two basic operations on fuzzy truth values), respectively. At first, we consider whether the distributive laws hold in various subsets of the set of all fuzzy truth values, such as set-valued T2FSs, singletons, interval-valued T2FSs, and the set of all normal convex fuzzy truth values. Then, we discuss whether the distributive laws hold for some specific convolution operations. Finally, we give a necessary and sufficient condition under which join-convolution is distributive over meet-convolution, and similarly give a necessary and sufficient condition under which meet-convolution is distributive over join-convolution.

A hybrid model of environmental impact assessment of PM2.5 concentration using multi-criteria decision-making (MCDM) and geographical information system (GIS)—a case study

In the last decades, Tehran, as the capital of Iran, has faced severe air pollution. Considering the importance of air pollution, particularly PM2.5, the study assesses the environmental impacts (EIA) of PM2.5 in the Tehran metropolis using 4-year consecutive data (2014–2017). For this purpose, the inverse distance weighting model, geographically weighted regression (GWR) model, and fuzzy analytic network process (FANP) for interpolation of PM2.5 concentration, measuring the relationship between main factors and PM2.5 concentration, and EIA were utilized, respectively. The research findings showed that the highest PM2.5 concentration was 56 μg/m3 from 2014 to 2015, then with a decreasing trend in 2016 and 2017. Moreover, the local R2 ranges obtained from the GWR model between PM2.5 concentration and traffic, population distribution, land use, gas, and fuel consumption are 30–69%, 14–23%, 44–76%, 31–42%, and 1–35%, respectively. In the following, in order to study the EIA of PM2.5 using the FANP model, four alternatives, strict environmental management in the surrounding neighborhoods, change in the country’s economic capital, change in the urban management, and NO action, were proposed. Then, the relationships of dependence and pairwise comparisons among criteria and alternatives were performed through grades of membership for linguistic variables of fuzzy sets. Next, the unweighted fuzzy supermatrix was constructed, and the weighted fuzzy supermatrix and limit supermatrix were calculated, respectively. Finally, the centroid of area technique was applied for the defuzzification process and prioritization of the alternatives. The EIA results of the FANP model demonstrated that strict environmental management in surrounding neighborhoods by having the highest weight (38%) is the best alternative.

An Advanced Optimization Technique for Smart Production Using α-Cut Based Quadrilateral Fuzzy Number

In the design phase of a new smart product, production costs are unpredictable due to location, transport, and engineering design. In these situations, consequently, cost optimization becomes ambiguous. This paper presents a methodology to obtain optimization through a fuzzy linear programming problem (FLPP) in which fuzzy numbers signify the right-side parameters. The comparative investigation of modeling and optimizing creation cost through a new α-cut based quadrilateral fuzzy number is proposed to solve the fuzzy linear programming and the necessary operations on the proposed number. Due to the probabilistic increase and decrease in the accessibility of the various constraints, the actual expected total cost fluctuates. In this respect, a unique situation of instability is incorporated, and reasonable models to reduce the cost of eradication in the creation process are presented. The main endeavor is made to look at the credibility of optimized cost utilizing the α-cut based quadrilateral FLPP models, and the outcome is contrasted with its augmentation. The data of the production cost of RCF Kapurthala is taken, and the creation expenses of various mentors from the year 2010–2011 are considered as input parameters. The aggregate cost is focused on the objective function. The least low, lower, upper, and most upper bounds are computed for each situation, and then systems of optimized fuzzy LPP are constructed. The credibility of quadrilateral fuzzy LPP concerning all situations is obtained and using this membership grade, the minimum, and highest minimum costs are illustrated.

Using Fuzzy Inference Systems for the Creation of Forex Market Predictive Models

This paper presents a method for creating Forex market predictive models using multi-agent and fuzzy systems, which have the objective of simulating the interactions that provoke changes in the price. Agents in the system represent traders performing buy and sell orders in a market, and fuzzy systems are used to model the rules followed by traders performing trades in a live market and intuitionistic fuzzy logic to model their decisions’ indeterminacy. We use functions to restrict the agents’ decisions, which make the agents become specialized at particular market conditions. These “specialization” functions use the grades of membership obtained from an agent’s fuzzy system and thresholds obtained from training data sets, to determine if that agent is specialized enough to handle a market’s current conditions. We have performed experiments and compared against the state of the art. Results demonstrate that our method obtains predictive errors (using mean absolute error) that are in the same order of magnitude than those errors obtained by models generated using deep learning and models generated by random forest, AdaBoost, XGBoost, and support-vector machines. Furthermore, we performed experiments that show that identifying specialized agents yields better results.

Medical Diagnosis and Life Span of Sufferer Using Interval Valued Complex Fuzzy Relations

Fuzzy set theory resolved the crux of modeling uncertainty, vagueness, and imprecision. Many researchers have contributed to the development of the theory. This paper intends to define the innovative concept of the interval valued complex fuzzy relations (IVCFRs) using the proposed Cartesian product of two interval valued complex fuzzy sets (IVCFSs). Moreover, the types of IVCFRs are devised with some exciting results and properties. Furthermore, a couple of prodigious applications have been established as an illustration of the modeling capabilities of the proposed structures. The concept of interval valued complex fuzzy (IVCF) composite relations is used in the medical diagnosis of patients on the basis of symptoms. The inclusion of phase term in the grade of membership of IVCFRs facilitated modeling the periodic diseases. Additionally, another application of the Cartesian products and the IVCF equivalence relations is proposed that studies the life expectancies or mortality rates of patients with certain diseases. In addition, the effects of multiple illnesses on the life expectancy of a patient are also deliberated through IVCFRs. The proposed framework is also compared with the existing structures in the field of fuzzy set theory.

Approach-oriented and avoidance-oriented measures under complex Pythagorean fuzzy information and an area-based model to multiple criteria decision-aiding systems

The purpose of this paper is to evolve a novel area-based Pythagorean fuzzy decision model via an approach-oriented measure and an avoidance-oriented measure in support of multiple criteria decision analysis involving intricate uncertainty of Pythagorean fuzziness. Pythagorean membership grades embedded in a Pythagorean fuzzy set is featured by tensible functions of membership, non-membership, indeterminacy, strength, and direction, which delivers flexibility and adaptability in manipulating higher-order uncertainties. However, a well-defined ordered structure is never popular in real-life issues, seldom seen in Pythagorean fuzzy circumstances. Consider that point operators can make a systematic allocation of the indeterminacy composition contained in Pythagorean fuzzy information. This paper exploits the codomains of the point operations (i.e., the quantities that express the extents of point operators) to launch new measurements of approach orientation and avoidance orientation for performance ratings. This paper employs such measurements to develop an area-based performance index and an area-based comprehensive index for conducting a decision analysis. The applications and comparative analyses of the advanced area-based approach to some decision-making problems concerning sustainable recycling partner selection, company investment decisions, stock investment decisions, and working capital financing decisions give support to methodological advantages and practical effectiveness.

Solid Waste Collection System Selection Based on Sine Trigonometric Spherical Hesitant Fuzzy Aggregation Information

Spherical fuzzy set (SFS) as one of several non-standard fuzzy sets, it introduces a number triplet (a,b,c) that satisfies the requirement a² + b² + c² ≤ 1 to express membership grades. Due to the expression, SFS has a more extensive description space when describing fuzzy information, which attracts more attention in scientific research and engineering practice. Just for this reason, how to describe the fuzzy information more reasonably and perfectly is the hot that scholars pay close attention to. In view of this hot, in this paper, the notion of spherical hesitant fuzzy set is introduced as a generalization of spherical fuzzy sets. Some basic operations using sine trigonometric function are presented for spherical hesitant fuzzy sets. We define spherical hesitant fuzzy weighted average and spherical hesitant fuzzy weighted geometric aggregation operators. Based on these new aggregation operators, we propose a method for multi-criteria decision making (MCDM) in the spherical hesitant fuzzy information. Besides, a numerical real-life application about solid waste collection system selection is provided to demonstrate the validity of the proposed approaches along with relevant discussions, the merits of proposed approaches are also analyzed by validity test.

(3, 2)-Fuzzy Sets and Their Applications to Topology and Optimal Choices.

The purpose of this paper is to define the concept of (3, 2)-fuzzy sets and discuss their relationship with other kinds of fuzzy sets. We describe some of the basic set operations on (3, 2)-fuzzy sets. (3, 2)-Fuzzy sets can deal with more uncertain situations than Pythagorean and intuitionistic fuzzy sets because of their larger range of describing the membership grades. Furthermore, we familiarize the notion of (3, 2)-fuzzy topological space and discuss the master properties of (3, 2)-fuzzy continuous maps. Then, we introduce the concept of (3, 2)-fuzzy points and study some types of separation axioms in (3, 2)-fuzzy topological space. Moreover, we establish the idea of relation in (3, 2)-fuzzy set and present some properties. Ultimately, on the basis of academic performance, the decision-making approach of student placement is presented via the proposed (3, 2)-fuzzy relation to ascertain the suitability of colleges to applicants.

Score-Based Multiple Criteria Decision Making Process by Using P-Rung Orthopair Fuzzy Sets

A p-rung orthopair fuzzy set (p-ROFS) describes a generalization of intuitionistic fuzzy set and Pythagorean fuzzy set in the case where we face a larger representation space of acceptable membership grades, and moreover, it gives a decision maker more flexibility in expressing his/her real preferences. Under the p-rung orthopair fuzzy environment, we are going to propose a novel and parametrized score function of p-ROFSs by incorporating the idea of weighted average of the degree of membership and non-membership functions. In view of this fact, this study is further undertaken to investigate and present different properties of the proposed score function for p-ROFSs. Moreover, we indicate that this ranking technique reduces some of the drawbacks of the existing ones. Eventually, we develop an approach based on the above-mentioned ranking technique to deal with multiple criteria decision making problems with p-rung orthopair fuzzy information.

Climate Profiles in Brazilian Microregions

Brazil’s territory is considerably large and characterized by a variety of climate patterns, which allows the identification of regional climate specificities. The objective of this study was to identify a typology of climatic characteristics for the microregions of Brazil using the grade of membership (GoM) method, which is a multivariate technique based on the fuzzy sets theory. The meteorological variables used were: precipitation (mm), relative humidity (%), maximum and minimum temperature (°C) and wind speed (m/s), obtained from the interpolated database elaborated by Xavier comprising the period from January 1981 to December 2013. Three predominant homoclimatic profiles were found. The GoM method also allowed the identification of five mixed profiles, which is unprecedent in studies in Brazil and corroborates the regional climate diversity in the country. Furthermore, the heterogeneities of Brazilian climates could be better outlined. The extreme profiles—“predominant 1—P1”, “predominant 2—P2” and “predominant 3—P3”—accounted for 42.9% (236) of the total microregions. Additionally, approximately half (53.9%) of the microregions were classified as featuring characteristics of at least two profiles—that is, they presented mixed profiles with hybrid characteristics. These hybrid microregions were located mostly at transition zones between climates.

Predicting stock price trends based on financial news articles and using a novel twin support vector machine with fuzzy hyperplane

This study extracts the hidden topic model and emotional information from news articles. A novel fuzzy twin support vector machine is also developed to merge the large volume of information from on-line news, using this to predict stock price trends. Fuzzy set theory is very useful for this approach because the texts use fuzzy terminology, such as high/low and big/small, and the boundary between rising and falling categories is poorly defined. By using fuzzy partial ordering relation, the decision function of our approach is generalized such that the values assigned to the stocks fall within a specified range and indicate the membership grade of these stocks in the positive class (rising trends). The proposed approach is useful for dealing with outliers. Outliers only slightly increase the spread of the fuzzy decision boundary and the estimation of the mode of fuzzy hyperplane remains unchanged. Therefore, our model is more robust compared with other methods when the data contain some outliers. Besides, the membership grade estimated by the fuzzy decision boundary gives a better insight into the degree of confidence in the predicted outputs. The explicable characteristic for the degree of confidence is a vital aspect for decision-making applications.

Incremental fuzzy probability decision-theoretic approaches to dynamic three-way approximations

As a special model of three-way decision, three-way approximations in the fuzzy probability space can be interpreted, represented, and implemented as dividing the universe into three pair-wise disjoint regions, i.e., the positive, negative and boundary regions, which are transformed from the fuzzy membership grades with respect to the fuzzy concept. To consider the temporality and uncertainty of data simultaneously, this paper focuses on the integration of dynamics and fuzziness in the context of three-way approximations. We analyze and investigate three types of fuzzy conditional probability functions based on the fuzzy T-norm operators. Besides, we introduce the matrix-based fuzzy probability decision-theoretic models to dynamic three-way approximations based on the principle of least cost. Subsequently, to solve the time-consuming computational problem, we design the incremental algorithms by the updating strategies of matrices when the attributes evolve over time. Finally, a series of comparative experiments is reported to demonstrate and verify the performance of proposed models.