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The problem of expanding a meaningful entropic theory for fuzzy information cannot be thought of as being a mere (more or less formal) extension of Shannon theory. By using the information theory of deterministic functions, the present author had already obtained some results in this way, and he herein continues this approach. After a short background on the different entropies of deterministic functions and on membership entropy of fuzzy sets, successively mixed entropy of fuzzy sets, joint membership functions of independent fuzzy sets, and conditional entropy of fuzzy sets with respect to other fuzzy sets are considered; the problem of defining transinformation between fuzzy sets, as a generalisation of the well known Shannon concept, is then examined. One of the conclusions of the article is that it is possible to build up a meaningful information theory of fuzzy sets by using the entropy of deterministic functions.

General Systems Theory postulates the existence of many general theories that serve to describe isomorphisms across systems. The theory of Fuzzy Sets can be considered as one particular general theory which describes the phenomenon of ambiguity across all systems displaying this property and its consequences. Fuzzy Set Theory is a mathematical development that holds great promise in becoming the metalanguage of ambiguity, in a way parallel to Statistics and Probability Theory which represent the metalanguage of uncertainty. Fuzzy Sets appear particularly well suited to model ambiguity in the context of the systems paradigm which has been offered as a counterpart to the traditional science paradigm. A decision model is used to discuss the differences between these two paradigms and to show the role which Fuzzy Sets can play in resolving some of the epistemological problems in the domain of the social sciences.

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.

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.

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.

With numerous and ambiguous sets of information and often conflicting requirements, construction management is a complex process involving much uncertainty. Decision makers may be challenged with satisfying multiple criteria using vague information. Fuzzy multi-criteria decision-making (FMCDM) provides an innovative approach for addressing complex problems featuring diverse decision makers’ interests, conflicting objectives and numerous but uncertain bits of information. FMCDM has therefore been widely applied in construction management. With the increase in information complexity, extensions of fuzzy set (FS) theory have been generated and adopted to improve its capacity to address this complexity. Examples include hesitant FSs (HFSs), intuitionistic FSs (IFSs) and type-2 FSs (T2FSs). This chapter introduces commonly used FMCDM methods, examines their applications in construction management and discusses trends in future research and application. The chapter first introduces the MCDM process as well as FS theory and its three main extensions, namely, HFSs, IFSs and T2FSs. The chapter then explores the linkage between FS theory and its extensions and MCDM approaches. In total, 17 FMCDM methods are reviewed and two FMCDM methods (i.e. T2FS-TOPSIS and T2FS-PROMETHEE) are further improved based on the literature. These 19 FMCDM methods with their corresponding applications in construction management are discussed in a systematic manner. This review and development of FS theory and its extensions should help both researchers and practitioners better understand and handle information uncertainty in complex decision problems.

The purpose of this paper is to present a new method for evaluation of emergency plans for unconventional emergency events by using the soft fuzzy rough set theory and methodology.

In response to the problems of insufficient risk identification, incomplete and inaccurate data and different preference of decision makers, a new model for emergency plan evaluation is established by combining soft set theory with classical fuzzy rough set theory. Moreover, by combining the TOPSIS method with soft fuzzy rough set theory, the score value of the soft fuzzy lower and upper approximation is defined for the optimal object and the worst object. Finally, emergency plans are comprehensively evaluated according to the soft close degree of the soft fuzzy rough set theory.

This paper presents a new perspective on emergency management decision making in unconventional emergency events. Also, the paper provides an effective model for evaluating emergency plans for unconventional events.

The paper contributes to decision making in emergency management of unconventional emergency events. The model is useful for dealing with decision making with uncertain information.

In the present literature on fuzzy sets and fuzzy information, there is much confusion between entropies of fuzzy sets and fuzzy sets of entropies. After a thorough critical review of this question, proposes a unified approach based on the theory of deterministic functions. One must carefully distinguish between index of fuzziness, uncertainty of fuzziness and uncertainty of randomness on the one hand; and uncertainty of fuzzy sets and uncertainty of possibility on the other hand. This new framework could provide new approaches to management of uncertainty originating from both probability and possibility distributions.

Provides an overview of major developments pertaining to generalized information theory during the lifetime of Kybernetes. Generalized information theory is viewed as a collection of concepts, theorems, principles, and methods for dealing with problems involving uncertainty‐based information that are beyond the narrow scope of classical information theory. Introduces well‐justified measures of uncertainty in fuzzy set theory, possibility theory, and Dempster‐Shafer theory. Shows how these measures are connected with the classical Hartley measure and Shannon entropy. Discusses basic issues regarding some principles of generalized uncertainty‐based information.

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.