Fuzzy Set System Research Articles

The application of fuzzy logic techniques to improve decision making in apparel size

Traditional set theory, or crisp set theory, is built on the concept of crisp sets. These are sets for which the membership of an element within a set is defined as either true or false; in or out; 1 or 0. This construction is extremely useful, as mathematics has shown, but it struggles to model concepts of our world that possess vagueness or uncertainty. Therefore, we explore an expansion of set theory to allow an element to be partially within a set, thus constituting what is known as a fuzzy set. This paper introduces the basic concept of fuzzy sets, which includes fuzzy sets and crisp sets, as well as the operations of a fuzzy set and fuzzy classification systems. Fuzzy logic has been utilized to solve numerous textile-related difficulties, one of which was determining the proper clothing size. In this study, we examined fuzzy logic applications in textiles, such as the construction of fuzzy expert systems and fuzzy logic for predicting clothing size. This research demonstrates that when determining the correct size of clothing, the outcome is heavily reliant on fuzzy logic.

IoT-based patient stretcher movement simulation in smart hospital using type-2 fuzzy sets systems

The healthcare facilities in the modern age are the key challenge in developing countries where remote areas lack immense-quality hospitals and medical experts. The idea here is to provide an intelligent smart health system using some sensors and fuzzy controllers which are implemented in stretchers, and the update of the patient stretcher monitoring is implemented to monitor the immovable stretchers and rectify the problem of immovable stretchers, which can be solved by Type-2 fuzzy sets and systems, which is featured by three-dimensional characteristics. This study proposes IoT-based Patient Stretcher Movement Simulation for Smart Hospitals using Type-2 fuzzy sets and systems. Type-2 fuzzy logic is a generalisation of conventional fuzzy logic in which the stretcher movement simulation and exact location of the stretcher are monitored by the sensor-based fuzzy set and let the model minimise the effects of uncertainties which is found to have very wide applicability in rule-based fuzzy logic systems. The results presented in this paper prove the concept and provide the IoT-based patient stretcher creation. The results of the experiments also show that the proposed approach is more reliable and intelligent enough to provide efficient monitoring applications through the type-2 fuzzy logic systems.

Interval-valued intuitionistic fuzzy rough set system over a novel conflict distance measure with application to decision-making

Conflict analysis is one of the most critical application domains whose importance is increasing rapidly nowadays. Attributes involving conflicts frequently occur with opinion, negotiations, and collaborators in decision-making. Taking advantage of the uncertainty present in decision-making, in this paper, we have proposed a system that can solve the problems involving conflicts more adequately.•A new interval-valued intuitionistic fuzzy rough set (IVIFRS) system is introduced to handle a decision-making problem involving a conflict of interests.•The proposed system exploits both the notions of rough set and interval-valued intuitionistic fuzzy set theories in sharpening the boundaries of conflicts.•In the IVIFRS system, the disputes amongst the objectives are measured by the novel conflict distance measure. Further, an interval-valued intuitionistic fuzzy conflict analysis system formulated on the IVIFRS is designed for deciding the conflicting attributesThe formulated system is then studied for weight vectors too. The intended conflict analysis system is studied with reference to the well-known existing intuitionistic fuzzy rough set system. The real-life socio-economic problems are dealt with, and the experimental results validate the efficacy of the proposed system.

Recurrent fuzzy fractal generated by iterated fuzzy set system with recurrent structure

Recurrent fuzzy fractal generated by iterated fuzzy set system with recurrent structure

Novel Complex Pythagorean Fuzzy Sets under Aczel–Alsina Operators and Their Application in Multi-Attribute Decision Making

Aggregation operators (AOs) are utilized to overcome the influence of uncertain and vague information in different fuzzy environments. A multi-attribute decision-making (MADM) technique plays a vital role in several fields of different environments such as networking analysis, risk assessment, cognitive science, recommender systems, signal processing, and many more domains in ambiguous circumstances. In this article, we elaborated the notion of Aczel–Alsina t-norm (TNM) and t-conorm (TCNM) under the system of complex Pythagorean fuzzy (CPyF) sets (CPyFSs). Some basic operational laws of Aczel–Alsina TNM and TCNM are established including Aczel–Alsina sum, product, scalar multiplication, and power operations based on CPyFSs. We established several AOs of CPyFSs such as CPyF Aczel–Alsina weighted average (CPyFAAWA), and CPyF Aczel–Alsina weighted geometric (CPyFAAWG) operators. The proposed CPyFAAWA and CPyFAAWG operators are symmetric in nature and satisfy the properties of idempotency, monotonicity, boundedness and commutativity. To solve an MADM technique, we established an illustrative example to select a suitable candidate for a vacant post in a multinational company. To see the advantages of our proposed AOs, we compared the results of existing AOs with the results of newly established AOs.

"A characterization of fuzzy fractals generated by an orbital fuzzy iterated function system"

"Orbital fuzzy iterated function systems are obtained as a combination of the concepts of iterated fuzzy set system and orbital iterated function system. It turns out that, for such a system, the corresponding fuzzy operator is weakly Picard, its fixed points being called fuzzy fractals. In this paper we present a structure result concerning fuzzy fractals associated to an orbital fuzzy iterated function system by proving that such an object is perfectly determined by the action of the initial term of the Picard iteration sequence on the closure of the orbits of certain elements."

An integrated SWOT-multi-criteria analysis of implementing sustainable waste-to-energy in Pakistan

Waste-to-energy (WtE) technologies present attractive and sustainable solutions for transforming waste into clean energy. These technologies offer best solution for Pakistan to tackle environmental and public health problems stemming from increasing amount of waste and uncontrolled manner of waste management. Also, clean energy generated from waste can aid the country to mitigate her energy crisis and reduce hazardous emissions. Successful implementation of WtE however requires preliminary investigation to examine various strategic aspects and challenges before policy formulation and implementation, respectively. So, this study performs SWOT analysis to explore SWOT factors of WtE implementation and then draws SWOT strategies by matching internal and external factors of SWOT matrix. Twenty-eight SWOT sub-factors (seven under each factor) were identified through literature survey, while twelve SWOT strategies were formulated. To obtain the quantitative importance of factors and sub-factors, and prioritize strategies, SWOT analysis is integrated with hybrid MCDM. Fuzzy set and grey system theories are incorporated to enhance the efficacy of proposed model. The quantitative importance of ‘Opportunities’ main factor transcends other factors. Renewable energy generation ‘O-2’ sub-factor topped among overall sub-factors. The prioritization of SWOT strategies provides foundation for devising the WtE policy hierarchy, which shall help decision-makers to take right policy steps.

L-fuzzy cosets in universal algebras

AbstractIn this paper, we introduce the notion of fuzzy costs in a more general context, in universal algebra by the use of coset terms. We study the structure of fuzzy cosets by applying the general theory of algebraic fuzzy systems. Fuzzy cosets generated by a fuzzy set are characterized in different ways. It is also proved that the class of fuzzy cosets determined by an element forms an algebraic closure fuzzy set system. Finally, we give a set of necessary and sufficient conditions for a given variety of algebras to be congruence permutable by applying the theory of fuzzy cosets.

A Review on the Development of Fuzzy Classifiers with Improved Interpretability and Accuracy Parameters

This review paper of fuzzy classifiers with improved interpretability and accuracy parameter discussed the most fundamental aspect of very effective and powerful tools in form of probabilistic reasoning, The fuzzy logic concept allows the effective realization of ap-proximate, vague, uncertain, dynamic, and more realistic conditions, which is closer to the actual physical world and human thinking. The fuzzy theory has the competency to catch the lack of preciseness of linguistic terms in a speech of natural language. The fuzzy theory provides a more significant competency to model humans like com-mon-sense reasoning and conclusion making to fuzzy set and rules as good membership functions. Also, in this paper reviews discussed the evaluation of the fuzzy set, type-1, type-2, and interval type-2 fuzzy system from traditional Boolean crisp set logic along with interpretability and accuracy issues in the fuzzy system.

Fuzzy logic and fuzzy information technology

With the introduction of the concept of fuzzy logic by Lotfi Zadeh, the world of information technology has changed dramatically, because now there are not two states of the system, as in Boolean logic, but also intermediate states. In the twentieth century, the world was faced with the fact that existing systems made mistakes due to the accuracy of calculations, which is not applicable to solving real-world problems, but is applicable to solving mathematical problems. It was necessary to create systems that would mimic human thinking to solve complex problems and make decisions in an environment of uncertainty and constantly changing conditions. The article gives the concept of fuzzy logic, shows the difference between fuzzy logic and Boolean logic. The authors present the history of the concepts of fuzzy logic, fuzzy set, and fuzzy system. Indicate the stages of development of fuzzy logic and the main results of the development of fuzzy logic at these stages. The article presents the architecture of a fuzzy system, explains the main stages of passing data in this system to solve a specific problem. The authors presented a solution to a small decision-making problem, namely, the selection of boxers in the national team, based on fuzzy logic, using the functionality of the MATLAB software product and the Fuzzy Logic Modeler extension. The article gives the concept of hard and soft computing, their differences from each other. The authors present the main soft computing technologies based on fuzzy logic, and describe their algorithms. The following are examples of the use of fuzzy logic in the modern world, such as control systems, fuzzy expert systems, automatic systems. Thus, the authors focus on the role of fuzzy logic and fuzzy technologies in everyday life.

Designing Robust Control for Permanent Magnet Synchronous Motor: Fuzzy Based and Multivariable Optimization Approach

This article proposed a novel optimal robust control design approach to solve the uncertain parameter problem in the permanent magnet synchronous motor (PMSM) system by integrating the fuzzy set theory and system control theory. First, we adopt the prescribed fuzzy number to describe the time-varying but bounded uncertain parameter in the PMSM system. Second, based on the estimated bound of the uncertain parameter and the nominal dynamical model, we design a deterministic robust control scheme characterized by model-based control and feedback control. The control objective is to guarantee the PMSM system with uncertain parameters satisfies the desired motion equation with deterministic system performance: uniform boundedness (UB) and uniform ultimate boundedness (UUB). Third, using the fuzzy uncertain parameter, a performance index relevant to the steady-state performance and control cost is constructed. A parameters design optimization problem is formulated by minimizing the performance index, whose analytical solution is successfully solved and proved to always exists and is unique. As a result, the resulting PMSM system under the proposed control approach has two-level system performance: the guaranteed deterministic performance and optimal performance. Finally, the results of numerical simulation and experiment are presented for demonstration.

How to Vary the Input Space of a T–S Fuzzy Model: A TP Model Transformation-Based Approach

The motivation behind 15 years of continuous development within the topic of the Tensor Product (TP) model transformation is that the greater the number of parameters or components of the Takagi Sugeno (TS) fuzzy model one can manipulate, the larger the complexity reduction or control optimization one can achieve. The paper proposes a radically new type of extension to the TP model transformation: while earlier variants of the TP model transformation focused on how the antecedent - consequent fuzzy set system of a given TS fuzzy model could be varied, the present work, in contrast, focuses on how the number of inputs to a given TS fuzzy model can be manipulated. The proposed extension is capable of changing the number of inputs or transforming the non-linearity between the fuzzy rules and the input dimensions. These new features considerably increase the modeling power of the TP model transformation, allowing for further complexity reduction and more powerful control optimisation to be achieved. The paper provides two examples to show how the proposed extension can be used in a routine-like fashion.

On Fuzzy Deductive Systems of Hilbert Algebras

In this paper, we study fuzzy deductive systems of Hilbert algebras whose truth values are in a complete lattice satisfying the infinite meet distributive law. Several characterizations are obtained for fuzzy deductive systems generated by a fuzzy set. It is also proved that the class of all fuzzy deductive systems of a Hilbert algebra forms an algebraic closure fuzzy set system. Furthermore, we obtain a lattice isomorphism between the class of fuzzy deductive systems and the class of fuzzy congruence relations in the variety of Hilbert algebras.

Expertise and Uncertainty Processing with Nonlinear Scaling and Fuzzy Systems for Automation

Abstract Integration of domain expertise and uncertainty processing is increasingly important in automation solutions which rely on data analytics and artificial intelligence. We need a level to assess what is approximately correct. Uncertainties of the inputs are taken into account by using fuzzy numbers as the inputs of different fuzzy and parametric systems. Nonlinear scaling functions (NSFs) integrate these solutions and make them easier to tune. Fuzzy rule-based systems are represented with scaled fuzzy inputs. Membership functions (MFs) can be developed from NSFs and existing MFs can be used in developing NSFs. Fuzzy set systems and linguistic equation (LE) systems become consistent within the limits of detail. In recursive analysis, both meanings and interactions on all levels can be tuned together with genetic algorithms. In applications, the modular overall system consists of similar subsystems, which are normally used, with extensions to fuzzy. The compact fuzzy modules can be developed for specific tasks which are combined within Cyber Physical Systems (CPS). Uncertainty processing is embedded in the recursive analysis. The fuzzy extensions provide a feasible way for the sensitivity analysis of the solution.

System dynamics modeling with fuzzy logic application to mitigate the bullwhip effect in supply chains

Purpose A plethora of studies focused on the cause and solutions for the bullwhip effect, and consequently many have successfully experimented to dampen the effect. However, the feasibility of such studies and the actual contribution for supply chain performance are yet up for debate. This paper aims to fill this gap by providing a holistic system-based perspective and proposes a fuzzy logic decision-making implementation for a single-product, three-echelon and multi-period supply chain system to mitigate such effect. Design/methodology/approach This study uses system dynamics (SD) as the central modeling method for which Vensim® is used as a tool for hybrid simulation. Further, the authors used MATLAB for undertaking fuzzy logic modeling and constructing a fuzzy inference system that is later on incorporated into SD model for interaction with the main supply chain structure. Findings This research illustrated the usefulness of fuzzy estimations based on experts’ linguistically and logically defined parameters instead of relying merely on the traditional demand forecasting based on time series. Despite the increased complexity of the calculations and structure of the fuzzy model, the bullwhip effect has been considerably decreased resulting in an improved supply chain performance. Practical implications This dynamic modeling approach is not only useful in supply chain management but also the model developed for this study can be integrated into a corporate financial planning model. Further, this model enables optimization for an automated system in a company, where decision-makers can adjust the fuzzy variables according to various situations and inventory policies. Originality/value This study presents a systemic approach to deal with uncertainty and vagueness in dynamic models, which might be a major cause in generating the bullwhip effect. For this purpose, the combination between fuzzy set theory and system dynamics is a significant step forward.

Multiple Criteria Decision Analysis under uncertainty in sustainable construction: a neutrosophic modified best-worst method

Capturing uncertainty in multiple criteria decision analysis (MCDA) is not a new theme but a largely developing topic which is in close connection with uncertainty theories such as fuzzy set and grey systems theories. Due to growing complexity of construction processes mainly because of implementation of sustainability aspects it would be necessary to take advantage of a novel MCDA methodology as an efficient tool to handle the uncertainty in sustainable construction decision making. In this study, we utilise a novel neutrosophic modified best-worst method (NM-BWM) to deal with the uncertainty in decision making in the context of sustainable construction. The method is an integration of neutrosophic set theory (NST) and the modified best-worst method (M-BWM). The NST can provide insights on efficient uncertainty handling of decision makers (DMs) subjective judgements. The BWM is a MCDA method which utilises two vectors of pairwise comparisons (the best criterion to others and others to the worst criterion) to obtain the weights of evaluation criteria. Merits of the BWM include its capability in effectively remedying the inconsistency derived from pairwise comparisons as well as simplicity and less pairwise comparisons compared to other similar methods like analytic hierarchy process (AHP). We show the applicability of the method in a case study with focus on the implementation of sustainable construction.

Formalization of Fuzzy Control in Possibility Theory via Rule Extraction

Possibility system has been recently recognized as a potential foundational theory for fuzzy set theory though the concept of possibility originated from the membership function of fuzzy sets. As an application of fuzzy set theory, fuzzy control has been widely used in engineering practices, where control laws are described by fuzzy if-then rules. This paper intends to formulate fuzzy control in the framework of possibility theory by regarding the fuzzification procedure of fuzzy control as extraction process of the fuzzy variable from crisp input, and the fuzzy if-then rules as extracted rules between fuzzy input/output. Typical procedures of fuzzy control, such as fuzzification, implication, aggregation, and defuzzification, are eventually formulated as a series of conditional possibilities operated by “max-product” operators. The reformulated fuzzy controller has a more general form, which encompasses the Mamdani fuzzy controller as a special case. Some fundamental concepts of possibility theory, such as randomness/fuzziness, possibility, and conditional possibility, are also discussed, which may be helpful for the correct understanding of possibility theory. Efforts have been made to bridge the two systems of possibility theory and fuzzy sets by the derivation of composition rule of fuzzy relations from conditional possibility. All results are derived for both normalized possibility and non-normalized possibility. This paper strengthened the role of possibility theory as a foundation for fuzzy sets, and as a complementary method to probability theory for handling information with fuzzy uncertainty.

Ronald R. Yager, 2018 Lotfi A. Zadeh Pioneer Award Winner: A Pioneering Figure of the Fuzzy Set and Intelligent System Community

In 2018, IEEE Fellow Prof. Ronald R. Yager (Figure 1) was awarded the 2018 Lotfi A. Zadeh Pioneer Award of the IEEE Systems, Man, and Cybernetics Society (SMCS) his fundamental contributions to the theory of fuzzy sets, human behavioral modeling, multicriteria aggregation, decision-making under uncertainty, and the fusion of information. This award was established courtesy of generous donations from Norm Zadeh (son of the late Prof. Lotfi Zadeh) and the SMCS and is granted to exceptional researchers for outstanding and innovative contributions to academic and/or industrial research in systems science and engineering, human-machine systems, and/or cybernetics. This is great news for all of us who have had the chance to work and interact with Prof. Yager as well as the entire Systems, Man, and Cybernetics (SMC) Society, since he has been a longtime member of the SMC community and a frequent contributor to Society publications and conferences for many years.

Comparing the Performance Potentials of Interval and General Type-2 Rule-Based Fuzzy Systems in Terms of Sculpting the State Space

This paper provides application-independent perspectives on why improved performance usually occurs as one goes from an interval type-2 (IT2) fuzzy system to a general type-2 (GT2) fuzzy system. This is achieved by using the horizontal-slice representation of a GT2 fuzzy set and GT2 fuzzy system and by examining first- and second-order rule partitions as well as novelty partitions for the horizontal slices. It demonstrates that, for triangle and trapezoid secondary membership functions, the numbers of first- and second-order rule partitions are exactly the same for IT2 and GT2 fuzzy systems, but that a maximum amount of change always occurs in every second-order rule partition of a GT2 fuzzy system. This does not always occur in such partitions of an IT2 fuzzy system. Furthermore, when type reduction (TR) is used in a GT2 fuzzy system, the total number of novelty partitions is directly proportional to the number of horizontal slices; consequently, there are many more such partitions in a GT2 fuzzy system that uses TR than occur in an IT2 fuzzy system that also uses TR. It is the author's conjecture that it is the maximum changes that occur in every second-order rule partition, as well as the greater number of novelty partitions when TR is used, that provide a GT2 fuzzy system with the potential to outperform an IT2 fuzzy system.

A Fuzzy Logic Based Intelligent System for Measuring Customer Loyalty and Decision Making

In this paper, an intelligent approach is presented to measure customers’ loyalty to a specific product and assist new customers regarding a product’s key features. Our approach uses an aggregated sentiment score of a set of reviews in a dataset and then uses a fuzzy logic model to measure customer’s loyalty to a product. Our approach uses a novel idea of measuring customer’s loyalty to a product and can assist a new customer to take a decision about a particular product considering its various features and reviews of previous customers. In this study, we use a large sized data set of online reviews of customers from Amazon.com to test the performance of the customer’s reviews. The proposed approach pre-processes the input text via tokenization, Lemmatization and removal of stop words and then applies fuzzy logic approach to take decisions. To find similarity and relevance to a topic, various libraries and API are used in this work such as SentiWordNet, Stanford Core NLP, etc. The approach utilized focuses on identifying polarity of the reviews that may be positive, negative and neutral. To find customer’s loyalty and help in decision making, the fuzzy logic approach is applied using a set of membership functions and rule-based system of fuzzy sets that classify data in various types of loyalty. The implementation of the approach provides high accuracy of 94% of correct loyalty to the e-commerce products that outperforms the previous approaches.