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This study is aimed to develop a novel intuitionistic fuzzy P-graph with Gaussian membership function to help decision-makers deal with complex process network systems.

Two fuzzy P-graph case studies of the cogeneration system were selected, and relevant data were collected, including the structure and flow sequence of the system, and the rate of material and product transitions between the operating units. Gaussian function membership was set according to the restriction of fuzzy upper and lower bounds. Then the α-cut was used to obtain different upper and lower bound restrictions of each membership degree. After finding the optimal and suboptimal solutions for different membership degrees, the results of non-membership and hesitation were calculated.

The proposed method will help the decision maker consider the risk and provide more feasible solutions to choose the optimal and suboptimal solutions based on their own or through experience. The proposed model in this study has more flexibility in operation and decision making.

This study is the first to propose a novel intuitive fuzzy P-graph and demonstrates the effectiveness and flexibility of the method by two case studies of the cogeneration system. However, the addition of hesitation can increase the error tolerance of the system. Even for the solutions with a high degree of membership, optimal and suboptimal solutions still exist for the decision maker to select. Since decision makers expect the higher achievement of the target requirements; thus, it is important to have more feasible solutions with a high degree of membership.

In a risk analysis system, different underlying indices often play different roles in identifying the risk scale of the total target in a system, so a concept of discriminatory weight is introduced first. With the help of discriminatory weight and membership functions, a new method for information security risk analysis is proposed. The purpose of this paper is to discuss the above issues.

First, a concept of discriminatory weight is introduced. Second, with the help of fuzzy sets, risk scales are captured in terms of fuzzy sets (namely their membership functions). Third, a new risk analysis method involving discriminatory weights is proposed to realize a transformation from the membership degrees of the underlying indices to the membership degrees of the total target. At last, an example of information security risk analysis shows the effectiveness and feasibleness of the new method.

The new method generalizes the weighted-average method. The comparative analysis done with respect to other two methods show that the proposed method exhibits higher classification accuracy. Therefore, the proposed method can be applied to other risk analysis system with a hierarchial.

This paper proposes a new method for information security risk analysis with the help of membership functions and the concept of discriminatory weight. The new method generalizes the weighted-average method. Comparative analysis done with respect to other two methods show that the proposed method exhibits higher classification accuracy in E-government information security system. What is more, the proposed method can be applied to other risk analysis system with a hierarchial.

Construction is a highly dynamic environment with numerous interacting factors that affect construction processes and decisions. Uncertainty is inherent in most aspects of construction engineering and management, and traditionally, it has been treated as a random phenomenon. However, there are many types of uncertainty that are not naturally modelled by probability theory, such as subjectivity, ambiguity and vagueness. Fuzzy logic provides an approach for handling such uncertainties. However, fuzzy logic alone has some limitations, including its inability to learn from data and its extensive reliance on expert knowledge. To address these limitations, fuzzy logic has been combined with other techniques to create fuzzy hybrid techniques, which have helped solve complex problems in construction. In this chapter, a background on fuzzy logic in the context of construction engineering and management applications is presented. The chapter provides an introduction to uncertainty in construction and illustrates how fuzzy logic can improve construction modelling and decision-making. The role of fuzzy logic in representing uncertainty is contrasted with that of probability theory. Introductory material is presented on key definitions, properties and methods of fuzzy logic, including the definition and representation of fuzzy sets and membership functions, basic operations on fuzzy sets, fuzzy relations and compositions, defuzzification methods, entropy for fuzzy sets, fuzzy numbers, methods for the specification of membership functions and fuzzy rule-based systems. Finally, a discussion on the need for fuzzy hybrid modelling in construction applications is presented, and future research directions are proposed.

The aim of this paper is mainly to handle the fuzzy uncertainties present in structures appropriately. In general, uncertainties of variables are classified as aleatory and epistemic. The different sources of uncertainties in reinforced concrete structures include the randomness, mathematical models, physical models, environmental factors and gross errors. The effects of imprecise data in reinforced concrete structures are studied here by using fuzzy concepts. The aim of this paper is mainly to handle the uncertainties of variables with unclear boundaries.

To achieve the intended objective, the reinforced concrete beam subjected to flexure and shear was designed as per Euro Code (EC2). Then, different design parameters such as corrosion parameters, material properties and empirical expressions of time-dependent material properties were identified through a thorough literature review.

The fuzziness of variables was identified, and their membership functions were generated by using the heuristic method and drawn by MATLAB R2018a software. In addition to the identification of fuzziness of variables, the study further extended to design optimization of reinforced concrete structure by using fuzzy relation and fuzzy composition.

In the design codes of the concrete structure, the concrete grades such as C16/20, C20/25, C25/30, C30/37 and so on are provided and being adopted for design in which the intermediate grades are not considered, but using fuzzy concepts the intermediate grades of concrete can be recognized by their respective degree of membership. In the design of reinforced concrete structure using fuzzy relation and composition methods, the optimum design is considered when the degree of membership tends to unity. In addition to design optimization, the level of structural performance evaluation can also be carried out by using fuzzy concepts.

This study aims to investigate a reliability-level demand-oriented pharmaceutical supply chain design with maximal anticipated demand coverage. Different hospitals with the particular reliability value associated with the various pharmaceutical items (PIs) are considered. An inter-connected multi-period supply chain comprising manufacturers, distribution centers, hospitals and patients is assumed for the smooth flow of health-care items, enhancing supply chain reliability. A reliability index for PIs is depicted to highlight product preference and facilitate hospitals’ service levels for patients.

A mixed-integer multi-objective programming problem that maximizes maximal demand coverage minimizes the total economic costs and pharmaceutical delivery time is depicted under intuitionistic fuzzy uncertainty. Further, a novel interactive neutrosophic programming approach is developed to solve the proposed pharmaceutical supply chain management (PSCM) model. Each objective’s marginal evaluation is elicited by various sorts of membership functions such as linear, exponential and hyperbolic types of membership functions and depicted the truth, indeterminacy and falsity membership degrees under a neutrosophic environment.

The proposed PSCM model is implemented on a real case study and solved using an interactive neutrosophic programming approach that reveals the proposed methods’ validity and applicability. An ample opportunity to generate the compromise solution is suggested by tuning various parameters. The outcomes are evaluated with practical managerial implications based on the significant findings. Finally, conclusions and future research scope are addressed based on the proposed work.

The propounded study has some limitations that can be addressed in future research. The discussed PSCM model can be merged with and extended by considering environmental factors such as the health-care waste management system, which is not included in this study. Uncertainty among parameters due to randomness can be incorporated and can be tackled with historical data. Besides, proposed interactive neutrosophic programming approach (INPA), various metaheuristic approaches may be applied to solve the proposed PSCM model as a future research scope.

The strategy advised is to provide an opportunity to create supply chains and manufacturing within India by helping existing manufacturers to expand, identifying new manufacturers, hand-holding and facilitating, teams of officers, engineers and scientists deployed and import only if necessary to meet timelines. Thus, any pharmaceutical company or organization can adopt the production and distribution management initiatives amongst hospitals to strengthen and enable the pharmaceutical company while fighting fatal diseases during emergencies. Finally, managers or policy-makers can take advantage of the current study and extract fruitful pieces of information and knowledge regarding the optimal production and distribution strategies while making decisions.

This research work manifests the demand-oriented extension of the integrated PSCM design with maximum expected coverage, where different hospitals with pre-determined reliability values for various PIs are taken into consideration. The practical managerial implications are explored that immensely support the managers or practitioners to adopt the production and distribution policies for the PIs to ensure the sustainability in supply chain design.

Spaciousness is defined as “the feeling of openness or room to wander” that has been affected by various physical factors. The purpose of this paper is to assess the spaciousness of space to determine how spacious the space is. Furthermore, the study intends to propose a fuzzy-based model to assess the degree of spaciousness in terms of physical parameters such as area, proportion, the ratio of window area to floor area and color value.

Fuzzy logic is the most appropriate mathematical model to assess uncertainty using nonhomogeneous variables. In contrast to conventional methods, fuzzy logic depends on partial truth theory. MATLAB Fuzzy Logic Toolbox was used as a computational model including a fuzzy inference system (FIS) using linguistic variables called membership functions to define parameters. As a result, fuzzy logic was used in this study to assess the spaciousness degree of design studios in universities in the Iraqi Kurdistan region.

The findings of the presented fuzzy model show the degree to which the input variables affect a space perceived as larger and more spacious. The relationship between parameters has been represented in three-dimensional surface diagrams. The positive relationship of spaciousness with the area, window-to-floor area ratio and color value has been determined. In contrast, the negative relationship between spaciousness and space proportion is described. Moreover, the three-dimensional surface diagram illustrates how the changes in the input values affect the spaciousness degree. Besides, the improvement in the spaciousness degree of the design studio increases the quality learning environment.

This study attempted to assess the degree of spaciousness in design studios. There has been no attempt carried out to combine educational space learning environments and computational methods. This study focused on the assessment of spaciousness using the MATLAB Fuzzy Logic toolbox that has not been integrated so far.

The purpose of this paper is to advance a novel grey variable dual precision rough set model for grey concept.

To obtain the approximation of a grey object, the authors first define the concepts of grey rough membership degree and grey degree of approximation on the basic thinking logic of variable precision rough set. Based on grey rough membership degree and grey degree of approximation, the authors proposed a grey variable dual precision rough set model. It uses a clear knowledge concept to approximate a grey concept, and the output result is also a clear concept.

The result demonstrates that the proposed model may be closer to the actual decision-making situation, can effectively improve the rationality and scientificity of the approximation and reduce the risk of decision-making. It can effectively achieve the whitenization of grey objects. The model can be degenerated to traditional variable precision rough fuzzy set model, variable precision rough set model and classic Pawlak rough set, when some specific conditions are met.

The method exposed in the paper can be used to solve multi-criteria decision problems with grey decision objects and provide a decision rule. It can also help us better realize knowledge discovery and attribute reduction. It can effectively achieve the whitenization of grey object.

This method proposed in this paper implements a rough approximation of grey decision object and obtains low-risk probabilistic decision rule. It can effectively achieve a certain degree of whitenization of some grey objects.

With respect to multiple attribute group decision-making (MAGDM) in which the assessment values of alternatives are denoted by normal discrete fuzzy variables (NDFVs) and the weight information of attributes is incompletely known, this paper aims to develop a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and then applies the proposed method for selecting the most desirable investment alternative under uncertain environment.

First, by aggregating the membership degrees of an alternative to a scale provided by all decision-makers into a triangular fuzzy number, the credibility degree and expect the value of a triangular fuzzy number are calculated to construct the group fuzzy stochastic decision matrix. Second, based on determining the credibility distribution functions of NDFVs, the fuzzy stochastic dominance relations between alternatives on each attribute are obtained and the fuzzy stochastic dominance degree matrices are constructed by calculating the dominance degrees that one alternative dominates another on each attribute. Subsequently, calculating the overall fuzzy stochastic dominance degrees of an alternative on each attribute, a single objective non-linear optimization model is established to determine the weights of attributes by maximizing the relative closeness coefficients of all alternatives to positive ideal solution. If the information about attribute weights is completely unknown, the idea of maximizing deviation is used to determine the weights of attributes. Finally, the ranking order of alternatives is determined according to the descending order of corresponding relative closeness coefficients and the best alternative is determined.

This paper proposes a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and a case study of investment alternative selection problem is provided to illustrate the applicability and sensitivity of the proposed method and its effectiveness is demonstrated by comparison analysis with the proposed method with the existing fuzzy stochastic MAGDM method. The result shows that the proposed method is useful to solve the MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known.

The contributions of this paper are that to describe the dominance relations between fuzzy variables reasonably and quantitatively, the fuzzy stochastic dominance relations between any two fuzzy variables are redefined and the concept of fuzzy stochastic dominance degree is proposed to measure the dominance degree that one fuzzy variable dominate another; Based on credibility theory and fuzzy stochastic dominance, a novel fuzzy stochastic MAGDM method is proposed to solve MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known. The proposed method has a clear logic, which not only can enrich and develop the theories and methods of MAGDM but also provides decision-makers a novel method for solving fuzzy stochastic MAGDM problems.

The impact of ‘context of use’ to the whole life costs (WLC) of building elements has not yet been studied in previous researches. Lack of hard and detailed historical data constrained the use of traditional methods for this purpose. A fuzzy rule‐based system (FRBS) for any type of carpet cleaning cost estimate is one of a series of fuzzy models developed to estimate the WLC of building elements with the consideration of context of use to the elements. The fuzzy reasoning method, as the representation of human reasoning, is applied to WLC for the first time for carpet cleaning cost. The data used are the linguistic judgments from some experienced experts based on interview surveys. The implementation of the model is demonstrated in a case study. The result is assessed by the experts as an acceptable estimate.The paper concludes that Fuzzy Rule Based System is an appropriate method to model running costs of building elements. The model allows user to predict the cost variation of cleaning cost of carpet flooring according to its designed context of use.

This paper aims to present a new term weighting approach for text classification as a text mining task. The original method, neutrosophic term frequency – inverse term frequency (NTF-IDF), is an extended version of the popular fuzzy TF-IDF (FTF-IDF) and uses the neutrosophic reasoning to analyze and generate weights for terms in natural languages. The paper also propose a comparative study between the popular FTF-IDF and NTF-IDF and their impacts on different machine learning (ML) classifiers for document categorization goals.

After preprocessing textual data, the original Neutrosophic TF-IDF applies the neutrosophic inference system (NIS) to produce weights for terms representing a document. Using the local frequency TF, global frequency IDF and text N's length as NIS inputs, this study generate two neutrosophic weights for a given term. The first measure provides information on the relevance degree for a word, and the second one represents their ambiguity degree. Next, the Zhang combination function is applied to combine neutrosophic weights outputs and present the final term weight, inserted in the document's representative vector. To analyze the NTF-IDF impact on the classification phase, this study uses a set of ML algorithms.

Practicing the neutrosophic logic (NL) characteristics, the authors have been able to study the ambiguity of the terms and their degree of relevance to represent a document. NL's choice has proven its effectiveness in defining significant text vectorization weights, especially for text classification tasks. The experimentation part demonstrates that the new method positively impacts the categorization. Moreover, the adopted system's recognition rate is higher than 91%, an accuracy score not attained using the FTF-IDF. Also, using benchmarked data sets, in different text mining fields, and many ML classifiers, i.e. SVM and Feed-Forward Network, and applying the proposed term scores NTF-IDF improves the accuracy by 10%.

The novelty of this paper lies in two aspects. First, a new term weighting method, which uses the term frequencies as components to define the relevance and the ambiguity of term; second, the application of NL to infer weights is considered as an original model in this paper, which also aims to correct the shortcomings of the FTF-IDF which uses fuzzy logic and its drawbacks. The introduced technique was combined with different ML models to improve the accuracy and relevance of the obtained feature vectors to fed the classification mechanism.