Fuzzy Membership Grades Research Articles

Shadowed set approximations of L-fuzzy sets

Pedrycz shadowed sets are three-way approximations of fuzzy sets by transforming the infinite levels of fuzzy set membership grades in the unit interval [0,1] into three levels. The three levels represent qualitatively the sets of the white, grey, and black members of a shadowed set. In this paper, we generalize the notion of shadowed sets to the case of L-fuzzy sets by making three new contributions. First, we consider two representations of a shadowed set. One is a three-valued L-fuzzy set and the other is three pairwise disjoint sets. Second, we introduce two methods for constructing a shadowed set. One divides a finite lattice based on the notion of a pair of a set of designated core membership grades and a set of designated null membership grades. The other uses a pair of threshold sets, which generalizes the method that uses a pair of thresholds. We study formal properties of the two methods and show that they are equivalent. Finally, based on a distance function on a lattice, we present a simple method to build the sets of designated core and null membership grades.

A New Method of Distance Measure Between Intuitionistic Fuzzy Sets and its Application in Admission Procedure

Sundry complex real-world problems involving decision-making have been resolved using the idea of distance measures between intuitionistic fuzzy sets (IFSs). Several distance measuring techniques between IFSs have been developed, but it is only the work of Xie et al. that considered the tendency coefficients of the intuitionistic fuzzy parameters (IFPs), namely, membership grade, nonmembership grade and hesitation grade. Albeit, Xie et al.’s technique uses assumed tendency coefficients for IFPs, which is defective for a reliable result. Sequel to this setback, we develop a new distance measure between IFSs which includes tendency coefficients of the IFPs, where the tendency coefficients are computed from the intuitionistic fuzzy values to enhance reliable results. In addition, the new distance measure between IFSs is applied to discuss students’ admission process to ascertain the most eligible candidate based on academic performance in an entry examination. The application is carried out using two techniques, namely, the recognition principle and the multiple criteria decision-making approach, respectively. Finally, the superiority of the newly developed distance measure between IFSs is shown comparatively with respect to the existing approaches between IFSs. This new distance measure can be applied to clustering analysis, multiple attributes decision-making (MADM), a technique for order preference by similarity to ideal solution (TOPSIS), etc. in future research.

A multi-attribute decision making context for supply chain management using possibility single-valued neutrosophic soft settings

Argued decisions, risk estimation, empirical study, forecasts, apprehension supervision, and productive exposition depend on the degree of possibility. It enables us to assess the degree to which specific results are acceptable and to make more informed decisions by drawing on the information at our disposal and logic. Although some scholars have previously examined hybrid structures resembling fuzzy soft sets with possibility degree settings serving as fuzzy membership grades, the current study introduces an innovative structure that permits more adaptable and comprehensive settings: single-valued neutrosophic grades, to serve as possibility degrees. Thus, this study aims to introduce a new mathematical structure, i.e., possibility single-valued neutrosophic soft set (psv-NSOS), which combines three important theories (i.e., possibility theory, single-valued neutrosophic theory, and soft set theory). The basic notions, and set-theoretic operations, i.e., union and intersection, of psv-NSOS are investigated and manipulated with matrix representations. Considering evaluating suppliers for a real estate construction project as a multi-attribute decision-making issue, an algorithm that utilizes the matrix manipulations of proposed set-theoretic operations is presented. The suggested algorithm?s robustness is confirmed by comparison to evaluate its dependability and adaptability for modeling uncertainties related to the supplier selection problem.

Accelerated Fuzzy C-Means Clustering Based on New Affinity Filtering and Membership Scaling

Fuzzy C-Means (FCM) is a widely used clustering method. However, FCM and its many accelerated variants have low efficiency in the mid-to-late stage of the clustering process. In this stage, all samples are involved in updating their non-affinity centers, and the fuzzy membership grades of most samples, whose assignments remain unchanged, are still updated by calculating the sample-center distances. All these factors lead to the algorithms converging slowly. In this paper, a new affinity filtering technique is developed to recognize a complete set of non-affinity centers for each sample with low computations. Then, a new membership scaling technique is suggested to set the membership grades between each sample and its non-affinity centers to 0 and maintain the fuzzy membership grades for others. By integrating these two techniques, FCM based on new affinity filtering and membership scaling (AMFCM) is proposed to accelerate the whole convergence process of FCM. Numerous experimental results performed on synthetic and real-world data sets have shown the feasibility and efficiency of the proposed algorithm. Compared with state-of-the-art algorithms, AMFCM is significantly faster and more effective. For example, AMFCM reduces the number of FCM iterations by 80 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> on average.

Three-Way Behavioral Decision Making With Hesitant Fuzzy Information Systems: Survey and Challenges

Three-way decision (T-WD) theory is about thinking, problem solving, and computing in threes. Behavioral decision making (BDM) focuses on effective, cognitive, and social processes employed by humans for choosing the optimal object, of which prospect theory and regret theory are two widely used tools. The hesitant fuzzy set (HFS) captures a series of uncertainties when it is difficult to specify precise fuzzy membership grades. Guided by the principles of three-way decisions as thinking in threes and integrating these three topics together, this paper reviews and examines advances in three-way behavioral decision making (TW-BDM) with hesitant fuzzy information systems (HFIS) from the perspective of the past, present, and future. First, we provide a brief historical account of the three topics and present basic formulations. Second, we summarize the latest development trends and examine a number of basic issues, such as one-sidedness of reference points and subjective randomness for result values, and then report the results of a comparative analysis of existing methods. Finally, we point out key challenges and future research directions.

Endmember Estimation Using Fuzzy Grade of Membership and Spectral Matching

Endmember Estimation Using Fuzzy Grade of Membership and Spectral Matching

Discrete choice models with Atanassov-type intuitionistic fuzzy membership degrees

In the real word, due to the existence of uncertainty in decision-making information, it is often difficult to accurately evaluate utility values of alternatives. Recently, a series of discrete choice models based on fuzzy subjective utility have been proposed. Specifically, utility evaluation of each alternative has been expressed by fuzzy membership grades. However, traditional fuzzy membership function has only considered supporting degree, but has not considered the degrees of opposition and indeterminacy involved in decision makers’ evaluations. In this paper, a series of novel discrete choice models based on Atanassov-type intuitionistic fuzzy set are proposed, in which membership degrees, non-membership degrees, and hesitation degrees are simultaneously taken into account to jointly express the utility evaluations. Moreover, the attitudinal character of decision makers and relative weights of attributes are also considered to further extend the proposed models. Compared with existing discrete choice models, these new models are more flexible and general, which increase the applicability of discrete choice models for decision-making under an uncertain and imprecise environment. Two real-world case studies are given to illustrate the effectiveness and rationality of the new models.

An algebraic modeling for tuberculosis disease prognosis and proposed potential treatment methods using fuzzy hypersoft mappings

This study aimed to put forward an Avant-guard mathematical model for assisting the diagnostic process of this Mycobacterium (Tuberculosis (TB) bacterium) based on a novel adaptive fuzzy like structure. It is tough to ascertain the specific type of TB from its seriousness after looking at the symptoms as they overlap with numerous other respiratory infections. This structure, i.e., the fuzzy hypersoft set (FHS), extends the fuzzy soft set used to resolve this issue. The FHS is a more generalized, flexible and reliable algebraic model which is capable of managing the shortcomings of existing fuzzy soft set-like models with the entitlement of multi argument based domain for the approximation of TB patients (alternatives) under examination. It tackles the uncertain observations of medical experts for the approximation of patients with the help of fuzzy membership grade within [0,1]. When the measurements possess sub-values, it is problematic to see refinement in the patient’s progression timelines and anticipate the prescription term in a clinical appraisal. This novel fuzzy-like theory categorizes the distinct attributes into corresponding disjoint attribute-valued sets for better interpretation. It is difficult to distinguish a single upper-respiratory infection due to the sheer number of infections that influence the lungs and associated breathing organs. This investigation involves monitoring and constructing a bridge between the presented symptoms and the treatment given to the patient. The FHS-mapping will recognize the severity of the disease and the proposition of adequate treatment for the patient. The presented structure can prove to be an excellent diagnosis aiding tool as it has infinite analysis potential with mathematical interfacing with the patient’s condition with time.

Trade-off principle for standard shadowed sets and its generalization to five-regions

A shadowed set S interprets and makes decision with a fuzzy set F from its approximation regions and a tri-valued mapping μS:F⟶{0,0.5,1} on fuzzy membership grades. The original idea of shadowed sets is to balance the uncertainty of F in S by a principle of uncertainty relocation. This paper proposes a principle of making a trade-off between uncertainty for certainty to minimize the amount of unclassified data and maximize the number of items for which crisp decisions are made. We provide detailed derivations for determining the optimum partition threshold for a trade-off three-region shadowed set and generalized it to five-region model S5. We investigate the existence and uniqueness of the optimum partition threshold of S5. Also, we outline some application examples where five-region shadowed sets can be reasonably exploited, including fuzzy clustering, decision-making, etc. To deliver guidance on how to construct S5, several detailed numeric examples are also provided.

Aircraft total turnaround time estimation using fuzzy critical path method

Airport Collaborative Decision Making (ACDM) flight scheduling plans rely on accurate predictions of both optimal and reliable aircraft turnaround times, which is one of the most difficult things to complete. In order to account for the effects of randomness and fuzziness on the turnaround process duration, this paper deals with transforming the probability distribution of well-fitted sub-processes into a cumulative density function, which is equivalent to the fuzzy membership function (FMF), and then using goodness-of-fit to determine the fuzzy membership grade of each turnaround sub-process. The turnaround time is calculated using the fuzzy critical path method (FCPM), which is a combination of the Critical Path Method (CPM) and fuzzy set theory. In order to verify this estimate, we created the FMF using historical data and compared it to turnaround times based on FCPM. A linear regression model is used to examine the relationship between arrival delays and the FCPM-based turnaround process. We also use historical data to generate fuzzy sets of different arrival delays using Frankfurt airport data from the summer of 2017 and conclude that delays are positively correlated with the FCPM-based turnaround process.

A fuzzy data augmentation technique to improve regularisation

Deep learning (DL) has achieved superior classification in many applications due to its capability of extracting features from the data. However, the success of DL comes with the tradeoff of possible overfitting. The bias towards the data it has seen during the training process leads to poor generalisation. One way of solving this issue is by having enough training data so that the classifier is invariant to many data patterns. In the literature, data augmentation has been used as a type of regularisation method to reduce the chance for the model to overfit. However, most of the relevant works focus on image, sound or text data. There is not much work on numerical data augmentation, although many real-world problems deal with numerical data. In this paper, we propose using a technique based on Fuzzy C-Means clustering and fuzzy membership grades. Fuzzy-related techniques are used to address the variance problem by generating new data items based on fuzzy numbers and each data item's belongings to different fuzzy clusters. This data augmentation technique is used to improve the generalisation of a Deep Neural Network that is suitable for numerical data. By combining the proposed fuzzy data augmentation technique with the Dropout regularisation technique, we manage to balance the classification model's bias-variance tradeoff. Our proposed technique is evaluated using four popular data sets and is shown to provide better regularisation and higher classification accuracy compared with popular regularisation approaches.

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

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.

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.

Representing uncertainty about fuzzy membership grade

A novel uncertainty representation framework is introduced based on the inter-linkage between the inherent fuzziness and the agent’s confusion in its representation. The measure of fuzziness and this confusion is considered to be directly related to the lack of distinction between membership and non-membership grades. We term the proposed structure as confidence fuzzy set (CFS). It is further generalized as generalized CFS, quasi CFS and interval-valued CFS to take into consideration the DM’s individualistic bias in the representation of the underlying fuzziness. The operations on CFSs are investigated. The usefulness of CFS in multi-criteria decision making is discussed, and a real application in supplier selection is included.

Multistage decision approach for short life cycle products using Pythagorean fuzzy set

In this paper, a multistage decision-making problem concerning uncertainty and ambiguity is discussed using Pythagorean fuzzy sets. Complement Pythagorean fuzzy membership grades and their properties are also considered. Using the definition of an alpha-level set, we introduce the multistage decision-making problems, where the possibility theory and satisfaction grades are declared with the help of Pythagorean membership grades. Pythagorean multistage decision-making is an uncertain theory, where decision-maker has only one opportunity to choose the scenario under the combination of Pythagorean possibility and satisfaction grades at each stage. According to the selection of criteria, a series of decision points are concluded. The payoff collaborates with these decision points at each stage. The multistage decision-making using Pythagorean fuzzy sets is the scenario-based theory in place of other theories like lottery-based theory etc. The results have been calculated using multistage Pythagorean fuzzy sets in which the decision-maker has only one chance to select the optimal solution. The TOPSIS technique has been applied and the comparison between these two techniques is highlighted.

Multidimensional fuzzy finite tree automata

This paper introduces the notion of multidimensional fuzzy finite tree automata (MFFTA) and investigates its closure properties from the area of automata and language theory. MFFTA are a superclass of fuzzy tree automata whose behavior is generalized to adapt to multidimensional fuzzy sets. An MFFTA recognizes a multidimensional fuzzy tree language which is a regular tree language so that for each dimension, a fuzzy membership grade is assigned to each tree. We study MFFTA by extending some classical problems and properties of automata and regular languages such as determinization, reduction, duality and operations on languages. Furthermore, we provided the method of converting every complete fuzzy tree automata to an MFFTA as well as an example to show the efficiency of MFFTA in comparison to FFTA.}

The Application of Fuzzy Mathematics in the Diagnosis of Oil System Malfunction of Jet Engine

In this thesis we draw fuzzy mathematic method into the diagnosis of oil system malfunction of jet engine, bring forward setting up the fuzzy membership grade method which is based on the history data and expert preferential ordinal number, found the fuzzy diagnostic model, resolve to one or several malfunction, how nicety fast find cause malfunction really reason, and proffer scientific and feasible new method to the airplane malfuntion diagnosis service.

A fuzzy-based function approximation technique for reinforcement learning1

5 Abstract. Reinforcement learning is hard to solve optimization problems in multi-agent system because of the inefficiency of function approximation. Sparse distributed memories, which is implemented using Radial Basis Functions or Kanerva Coding, can be used to improve the efficiency. But this approach still often gives poor performance when applied to large-scale multi-agent systems. In this paper, we attempt to solve four-rooms problem in the predator-prey pursuit domain and argue that the poor performance that we observe is caused by frequent prototype collisions. We show that dynamic prototype allocation and adaptation can give better results by reducing these collisions. By using our novel approach about fuzzy Kanerva-based function approximation, that uses a fine-grained fuzzy membership grade to describe a state-action pair's adjacency with respect to each prototype, we give some results that prototype collisions are completely eliminated and learning performance is greatly improved. We further show that prototype density varies widely across the state-action space and that this variation causes prototypes' receptive fields to be unevenly distributed. This distribution limits the ability of fuzzy Kanerva Coding to achieve better results. It can be observed that fuzzy Kanerva Coding allows prototypes to adaptively tune their receptive fields for a target application. We conclude that fuzzy Kanerva Coding with prototype tuning and adaptation can significantly improve a reinforcement learner's ability to solve large-scale multi-agent problems. 6 7 8 9 10 11 12 13 14 15 16 17 18

Influence of structural and operating factors on performance degradation of the diesel particulate filter based on composite regeneration

In order to effectively investigate the effects of various factors on the DPF's performance deterioration, and obtain the primary influence factor, an efficient evaluation method is proposed in this work. Firstly, the maximum wall temperature and the pressure drop are taken as the evaluation indexes of DPF's performance deterioration (thermal aging and filter clogging) respectively, and the orthogonal experimental design is used for obtaining the simulation conditions of test cases. Then, the impacts of four structural factors (wall thickness, mean pore size, porosity and channel width) and five operating factors (exhaust flow rate, exhaust oxygen concentration, microwave power, catalytic additive mass concentration and deposited ash mass) on DPF's performance deterioration are evaluated by fuzzy membership grades and Euclidean grey relational grades, respectively. Finally, fuzzy grey relational analysis is employed to make a comprehensive evaluation. The results show that the wall thickness and the channel width have the most noticeable effect on filter clogging and thermal aging among all structural factors, respectively. Moreover, the deposited ash mass and the microwave power are the most important operating factors for filter clogging and thermal aging, respectively. This work offers us great reference value for optimizing DPF performances and improving its degradation resistance.