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In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature. Fuzzy real numbers, fuzzy logic, possibility theory, probability theory, Dempster‐Shafer theory, artificial neural nets, neuro‐fuzzy, fractals and multifractals, etc. are some of the paradigms to help us to understand complex systems. We present a very detailed discussion on the mathematical theory of fuzzy dynamical system (FDS), which is the most fundamental theory from the point of view of evolution of any fuzzy system. We have made considerable extension of FDS in this paper, which has great practical value in studying some of the very complex systems in society and nature. The theories of fuzzy controllers, fuzzy pattern recognition and fuzzy computer vision are but some of the most prominent subclasses of FDS. We enunciate the concept of fuzzy differential inclusion (not equation) and fuzzy attractor. We attempt to present this theoretical framework to give an interpretation of cyclogenesis in atmospheric cybernetics as a case study. We also have presented a Dempster‐Shafer's evidence theoretic analysis and a classical probability theoretic analysis (from general system theoretic outlook) of carcinogenesis as other interesting case studies of bio‐cybernetics.

The purpose of this paper is to construct innovative exact and approximative sampling plans for acceptance sampling in statistical quality control. These sampling plans are determined for crisp and fuzzy formulation of quality limits, various lot sizes and common α- and β-levels.

The authors use generalized fuzzy hypothesis testing to determine sampling plans with fuzzified quality limits. This test method allows a consideration of the indifference zone related to expert opinion or user priorities. In addition to the exact sampling plans calculated with the hypergeometric operating characteristic function, the authors consider approximative sampling plans using a little known, but excellent operating characteristic function. Further, a comprehensive sensitivity analysis of calculated sampling plans is performed, in order to examine how the inspection effort depends on crisp and fuzzy formulation of quality limits, the lot size and specifications of the producer’s and consumer’s risks.

The results related the parametric sensitivity analysis of the calculated sampling plans and the conclusions regarding the approximation quality provide the user a comprehensive basis for a direct implementation of the sampling plans in practice.

The constructed sampling plans ensure the simultaneous control of producer’s and consumer’s risks with the smallest possible inspection effort on the one hand and a consideration of expert opinion or user priorities on the other hand.

The purpose of this paper is to study a nascent theory and an emerging concept of solving a fully fuzzy linear system (FFLS) with no non negative restrictions on the triangular fuzzy numbers chosen as parameters. Two new simplified computational methods are proposed to solve a FFLS without any sign restrictions. The first method eliminates the non‐negativity constraint from the coefficient matrix while the second method eliminates the constraint of non‐negativity on the solution vector. The methods are introduced with an objective to broaden the domain of fuzzy linear systems to encompass a wide range of problems occurring in reality.

The design of numerical methods is motivated by decomposing the fuzzy based linear system into its equivalent crisp linear form which can be further solved by variety of classical methods to solve a crisp linear system. Further the paper investigates Schur complement technique to solve the crisp equivalent of the FFLS.

The results that are obtained reveal interesting properties of a FFLS. By using the proposed methods, the authors are able to check the consistency of the fuzzy linear system as well as obtain the nature of obtained solutions, i.e. trivial, unique or infinite. Further it is also seen that an n×n FFLS may yield finitely many solutions which may not be entirely feasible (strong). Also the methods successfully remove the non‐negativity restriction on the coefficient matrix and the solution vector, respectively.

Evolving methods with better computational complexity and that which remove the non‐negativity restriction jointly on all the parameters are left as an open problem.

The proposed methods are new and conceptually simple to understand and apply in several scientific areas where fuzziness persists. The methods successfully remove several constraints that have been employed exhaustively by researchers and thus eventually tend to widen the breadth of applicability and usability of fuzzy linear models in real life situations. Heretofore, the usability of FFLS is largely dormant.

Qualitative Comparative Analysis (QCA), initiated by Charles C. Ragin, is a research strategy with distinctive added value for organization studies. QCA constitutes in essence two configurational approaches, each grounded in set theory. One approach uses crisp-sets (dichotomous variables) to analyze cases. The other approach uses fuzzy-sets. While the use of fuzzy-sets has been increasing over the last few years, the crisp-set (csQCA) approach is still used in a majority of empirical applications. This chapter discusses in-depth the application of csQCA in organization studies. This chapter starts with a stylized presentation of two dominant research strategies, case-based research and variable-based research, and how csQCA relates to them. Subsequently, csQCA is further introduced and the different applications in organization studies are discussed. This section ends with a brief step-wise “how to” presentation. The chapter then turns to a presentation of the main distinctive strengths of the approach. In the final part, the chapter discusses extensively the main criticisms which have been raised with regard to (cs)QCA and draws out some of the main implications of this discussion.

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.

Addresses the problem of matching two fuzzy sets. Proposes a matching method that considers the extent to which both fuzzy sets have the same meaning. For a given degree of similarity between two sets, the same meaning decreases as the fuzziness increases and, in particular, for equal fuzzy sets the degree of matching is a function of the fuzziness only. A complete matching of two sets is obtained only when they are equal and crisp. Finally, the inverse problem is studied, of characterizing one of the sets used in the match when knowing the other set and the result of the matching.

Purpose – This chapter examines the potential of qualitative comparative analysis (QCA) for strategy research.

Methodology/approach – We introduce the set-theoretic framework of QCA and provide an overview of recent methodological developments.

Findings – We utilize a variety of examples relevant to strategy research to illustrate the action steps and key concepts involved in conducting a QCA study.

Originality/value of paper – We develop examples from core research areas in strategic management to illustrate QCA's potential for examining issues of causality and diversity in strategy research, and in settings involving medium-N samples. We conclude by emphasizing that QCA offers an alternative mode of inquiry to open and redirect important lines of strategy research.

Research in entrepreneurship is increasingly exploring how archetypes, taxonomies, typologies, and configurations can help scholars understand complex entrepreneurial phenomena. We illustrate the potential for set-theoretic methods to inform this literature by offering best practices regarding how qualitative comparative analysis (QCA) can be used to explore research questions of interest to entrepreneurship scholars. Specifically, we introduce QCA, document how this approach has been used in management research, and provide step-by-step guidance to empower scholars to use this family of methods. We put a particular emphasis on the analytical procedures and offer solutions to dealing with potential pitfalls when using QCA-based methods and highlight opportunities for future entrepreneurship research.

This paper aims to permit the system reliability analysts/managers/practitioners/engineers to analyze the system failure behavior using fuzzy methodology (FM)

In order to deal with both qualitative and quantitative information related to system performance the authors have adopted failure mode effect analysis (FMEA) and Petrinets (PNs), the well‐known tools for reliability analysis, to build an integrated framework aimed at helping the reliability and maintenance managers in decision‐making.

Using the proposed framework an industrial case from the paper mill is examined. From the results it is observed that the limitations associated with the traditional procedure of risk ranking in FMEA are efficiently modeled using fuzzy decision‐making system (FDMS) based on FM. Also, the fuzzy synthesis of system failure and repair data helps to quantify the system behavior in a more realistic manner.

The simultaneous adoption of the proposed techniques to model, analyze and predict the uncertain behavior of an industrial system will not only help the reliability engineers/managers/practitioners to understand the behavioral dynamics of system but also to plan/adapt suitable maintenance practices to improve system reliability, availability and maintainability (RAM) aspects.

The purpose of this paper is to demonstrate the use of artificial intelligence methods in quality control and improvement. The paper introduces a systematic approach for the design of fuzzy control charts of tip shear carpets.

There are certain steps for designing fuzzy control charts. All input, state and output variables of the carpet plant and partition of the universe of discourse were first determined. The interval spanned by each variable and the number of fuzzy subsets each assigned with a linguistic label were identified. Then, the adaptive capability of neural network was used to determine the membership functions for each fuzzy subset. The fuzzy relationship functions between the inputs and outputs were assigned to form the fuzzy rule base (controller) in order to normalize the variables and certain intervals. Fuzzification of input parameters and max‐min composition of rules for inferring crisp outputs was the next step. The aggregation of fuzzified outputs and defuzzification of the outputs were the last step of this study, which helped to produce crisp outputs for latex weight.

Fuzzy linguistic terms were employed for overall quality assessment and rating of the end product. The outcomes of neuro‐fuzzy system were good supplements to other statistical process control tools.

Lack of qualified domain experts, knowledge acquisition of process parameters and time limitation for training of neuro‐fuzzy model were primary limitations.

The approach is more flexible and meaningful to identify the quality distribution of a product. The qualitative aspect of human reasoning for decision making was employed in this approach.

The paper is original and the first such work for local industry.