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…
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.
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…
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.
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…
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.
Construction is a highly dynamic environment with numerous interacting factors that affect construction processes and decisions. Uncertainty is inherent in most aspects of…
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.
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…
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.
With numerous and ambiguous sets of information and often conflicting requirements, construction management is a complex process involving much uncertainty. Decision…
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.
Although the modern portfolio theory (MPT) asset allocation framework can be adopted to enable decision making for international and direct real estate investing, and that…
Although the modern portfolio theory (MPT) asset allocation framework can be adopted to enable decision making for international and direct real estate investing, and that many institutional investors adopt it to support their decision making, this framework can be enhanced to capture the multi‐causal factors influencing international and direct real estate investing. The purpose of this paper is to explain how a fuzzy decision‐making approach is a more intuitive, yet rigorous alternative in this regard.
This paper is concerned with the model formation and estimation of a unique fuzzy tactical asset allocation (FTAA), which in turn comprises the FTAA flexible programming model and the FTAA robust programming model.
Both these FTAA models enhance the classical, Markowitz MPT portfolio theory on asset allocation through making it more intuitively appropriate for decision making in international and direct real estate investing.
These two FTAA models achieve the benefits of intuitively greater risk diversification by city or real estate sector and enable effective risk management. These two short‐run fuzzy models would be accepted and more such models would emerge as an effective extension of quadratic programming optimization, as more computable software programs of this kind are widespread.
Fuzzy approaches to asset allocation in the short run, are limited by some drawbacks. Fuzzy models possess the common feature of converting the equality function under quadratic programming optimization into inequality functions. Such inequality optimization replaces the point solution of the MPT TAA optimization problem, obtained through the rigid intersection of all functions, via a generalized or intuitive answer over a defined space of alternatives. The product of the fuzzy process with fuzzy inputs, in the form of fuzzy outcome is in actual fact a more natural and intuitive approach to asset optimization.
The aim of the present study is to overcome some of the limitations of the FMEA method by presenting a theoretical base for considering risk evaluation into its assessment…
The aim of the present study is to overcome some of the limitations of the FMEA method by presenting a theoretical base for considering risk evaluation into its assessment methodology and proposing an approach for its implementation.
Fuzzy AHP is used to calculate the weights of the likelihood of occurrence (O), severity (S) and difficulty of detection (D). Additionally, the prospect-theory-based TODIM method was integrated with fuzzy logic. Thus, fuzzy TODIM was employed to calculate the ranking of potential failure modes according to their risk priority numbers (RPNs). In order to verify the results of the study, in-depth interviews were conducted with the participation of industry experts.
The results are very much in line with prospect theory. Therefore, practitioners may apply the proposed method to FMEA. The most crucial failure mode for a firm's attention is furnace failure followed by generator failure, crane failure, tank failure, kettle failure, dryer failure and operator failure, respectively.
The originality of this paper consists in integrating prospect theory with the FMEA method in order to overcome the limitations naturally inherent in the calculation of the FMEA's RPNs.
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.
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…
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.