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By combining the subjective probabilistic viewpoint of fuzziness with the entropy of deterministic functions, it is possible to expand an information theory of fuzzy sets which is fully compatible and consistent with the classical Shannonian information theoretic framework. A model of transinformation between fuzzy sets, which could be of help in approximate reasoning can be obtained, an interesting feature of which is that it can be duplicated in the framework of fuzzy set theory.

In this paper we propose a strategy for investing in new companies for which there is relatively little hard data available. We use fuzzy set theory to represent these new companies as finite fuzzy subsets of established companies for which there is a history of investment data. A fuzzy set is also used to represent the economic environment in which the proposed new investments will be made. From this fuzzy information we construct a fuzzy expected return for each new investment under consideration. These expected returns are then defuzzified, and those proposed investments whose defuzzified expected returns fail to meet some specified criteria are discarded. An investment strategy is then proposed for investing available capital in those new companies that meet the criteria.

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 paper aims to consider a soft computing approach to pattern classification using the basic tools of fuzzy relational calculus (FRC) and genetic algorithm (GA).

The paper introduces a new interpretation of multidimensional fuzzy implication (MFI) to represent the author's knowledge about the training data set. It also considers the notion of a fuzzy pattern vector (FPV) to handle the fuzzy information granules of the quantized pattern space and to represent a population of training patterns in the quantized pattern space. The construction of the pattern classifier is essentially based on the estimate of a fuzzy relation Ri between the antecedent clause and consequent clause of each one‐dimensional fuzzy implication. For the estimation of Ri floating point representation of GA is used. Thus, a set of fuzzy relations is formed from the new interpretation of MFI. This set of fuzzy relations is termed as the core of the pattern classifier. Once the classifier is constructed the non‐fuzzy features of a test pattern can be classified.

The performance of the proposed scheme is tested on synthetic data. Subsequently, the paper uses the proposed scheme for the vowel classification problem of an Indian language. In all these case studies the recognition score of the proposed method is very good. Finally, a benchmark of performance is established by considering Multilayer Perceptron (MLP), Support Vector Machine (SVM) and the proposed method. The Abalone, Hosse colic and Pima Indians data sets, obtained from UCL database repository are used for the said benchmark study. The benchmark study also establishes the superiority of the proposed method.

This new soft computing approach to pattern classification is based on a new interpretation of MFI and a novel notion of FPV. A set of fuzzy relations which is the core of the pattern classifier, is estimated using floating point GA and very effective classification of patterns under vague and imprecise environment is performed. This new approach to pattern classification avoids the curse of high dimensionality of feature vector. It can provide multiple classifications under overlapped classes.

This paper seeks to identify and propose a standard approach for the selection and optimization of fuzzy sets used in fuzzy decision‐making systems.

The design was based on two principles: selection and optimization. The selection methodology was based on the “Fuzzimetric Arcs” principle, which is an analogy of the trigonometric circle principle. This would allow an initial sinusoidal fuzzy set shape. Other shapes may also be selected using the described formula (trapezoidal, triangular, … , etc.). As the proposal methodology is based on the trigonometric circle, other trigonometric formulae can be applied. For example, linguistic hedges can be defined using standard trigonometric formulae. Regarding optimization, the initial fuzzy set selection was assumed to be of regular shape (sinusoidal, trapezoidal or triangular). An irregular shape may be required by some systems. Hence, a genetic algorithm was proposed as a methodology to optimize the performance of fuzzy systems by mutating different regular shapes.

A simplified business decision‐making application was described and the proposed selection methodology was explained in the form of an example. Currently, there is no standard for the selection of fuzzy sets as this is dependent on knowledge engineering and the type of application chosen. The proposed methodology offers an easy‐to‐use possible standard which all developers/researchers may adopt irrespective of their application field. Moreover, the proposed methodology may integrate well with object‐oriented technology.

The paper presents standardization of the fuzzy sets selection and optimization technique used in any type of management information systems. This will aid all developers and researchers to enhance their technical communication. It would also enhance the simplicity and effectiveness of optimizing the performance of such systems.

In this paper, the problem of determining a maximizing decision in the multistage control of a fuzzy system in a fuzzy environment is considered. In the fuzzy system under control, the state is assumed to be fuzzy, while the control, not fuzzy. The fuzzy environment is given by fuzzy constraints and fuzzy goals imposed on particular control stages. The number of control stages, i.e. the termination time, is assumed to be fixed and specified; the same applies to the initial state. The fuzzy decision is defined as the intersection of fuzzy goals and fuzzy constraints. For solving the above problem, a branch‐and‐bound algorithm is proposed. The algorithm is simple and relatively efficient. Two examples are given.

The purpose of this paper is to answer the question that what the best shape of fuzzy sets is in fuzzy systems for function approximation which is essential in many applications of fuzzy systems.

The uniform approximation rates indicate the approximating capabilities of fuzzy systems for function approximation. By Fourier analysis, the uniform approximation rates are estimated for the fuzzy systems with various shapes of if‐part fuzzy sets in the case of single‐input and single‐output. Based on the approximation rates, the relationships between the approximating capabilities and the shapes of fuzzy sets are developed and compared.

The since functions as the input membership functions in fuzzy systems are proved to have the almost best approximation property in a particular class of membership functions.

From the viewpoint of function approximation, the input membership functions are not necessarily positive in fuzzy systems.

For engineers, the sinc‐shaped membership function is a good choice to improve their fuzzy systems in real applications.

The uniform approximation rates of fuzzy systems for function approximation are estimated. Mathematically, the relationships between the approximating capabilities and the shapes of fuzzy sets are analyzed for fuzzy systems.

Examines the growth of a new technology called fuzzy logic and its significance for microcontroller‐based embedded control solutions. Outlines the reasons for the emergence of fuzzy logic and explains the mathematic principles behind fuzzy set theory. Using the example of an oven temperature control system, describes how fuzzy logic is applied to the practical solution of a control problem rather than a conventional solution. Concludes that fuzzy logic has been used primarily in embedded control application as a software‐based methodology in closed‐loop control systems whilst a dedicated fuzzy hardware processor would optimally be based on a parallel architecture, allowing the entire rule base to be evaluated in a parallel fashion.

The systematic assessment of working capital requirement in construction projects deals with the analysis of various quantitative and qualitative factors in which information is subjective and based on uncertainty. There exists an inherent difficulty in the classical approach to evaluate the impact of qualitative factors for the assessment of working capital requirement. This paper presents a methodology to incorporate linguistic variables into workable mathematical propositions for the assessment of working capital using fuzzy set theory. This article takes into consideration the uncertainty associated with many of the project resource variables and these are reflected satisfactorily in the working capital computations. A case study illustrates the application of the fuzzy set approach. The results of the case study demonstrate the superiority of the fuzzy set approach to classical methods in the assessment of realistic working capital requirements for construction projects.

The purpose of this paper is to attempt supplier selection considering economic, environmental and social sustainability issues.

Subjective human judgment bears some kind of vagueness and ambiguity; fuzzy set theory has immense potential to overcome this. Owing to the advantage of intuitionistic fuzzy numbers set over classical fuzzy numbers set; three decision-making approaches have been applied here in intuitionistic fuzzy setting (namely, intuitionistic-TOPSIS, intuitionistic-MOORA and intuitionistic-GRA) to facilitate supplier selection in sustainable supply chain.

The stated objective of this research “to verify application potential of different decision support systems (in intuitionistic fuzzy setting) in the context of sustainable supplier selection” has been carried out successfully. A case empirical research has been conducted by applying three different decision-making approaches: intuitionistic fuzzy-TOPSIS, intuitionistic fuzzy-MOORA and intuitionistic fuzzy-GRA to an empirical data set of sustainable supplier selection problem. The ranking orders thus obtained through exploration of aforesaid three approaches have been explored and compared.

As compared to generalized fuzzy numbers, intuitionistic fuzzy numbers exhibit a membership degree, a non-membership degree and the extent of hesitation; a better way to capture inconsistency, incompleteness and imprecision of human judgment. Application potential of aforesaid three decision support approaches has been demonstrated in this reporting for a case sustainable supplier selection.