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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.

This paper is a continuation of our paper10,11 and formulates a fuzzy team decision problem of type 2. The concept of fuzzy sets of type 2 is introduced to formulate the team decision processes which contain fuzzy‐fuzzy states, fuzzy‐fuzzy information functions, fuzzy‐fuzzy information signals, fuzzy‐fuzzy decision functions and fuzzy‐fuzzy actions. After some definitions of fuzzy‐fuzzy relations and fuzzy‐fuzzy mappings, a model of fuzzy team decision of type 2 is proposed.

The purpose of this paper is to study free L‐fuzzy left R‐module, using the language of categories and functors for the general description of L‐fuzzy left R‐modules generated by L‐fuzzy set. In the language of categories and functors, an L‐fuzzy left R‐modules generated by L‐fuzzy set is called a free object in the category of L‐fuzzy left R‐modules determined by L‐fuzzy set.

Category theory is used to study the existent quality, unique quality and material structure of L‐fuzzy left R‐modules generated by L‐fuzzy set.

The paper gives the uniqueness, structure and existence theorems of free object in the category of L‐fuzzy left R‐modules determined by L‐fuzzy set, and the authors prove that the fuzzy free functor is left adjoint to the fuzzy underlying functor.

Some property of free L‐fuzzy left R‐modules will need to be further researched.

The paper defines a new class of L‐fuzzy left R‐modules, i.e. free L‐fuzzy left R‐modules, research and explore free L‐fuzzy left R‐modules in theory.

Time to market is the essential aim of any new product introduction process. Performance measures are simple quantities that indicate the state of manufacturing organisations and are used as the basis of decision‐making at this crucial early stage of the process. Fuzzy set theory is a method for using qualitative data and subjective opinion. Fuzzy sets have been used extensively in manufacturing for applications including control, decision‐making, and estimation. Type‐2 fuzzy sets are a novel extension of type‐1 fuzzy sets. Aims to examine this subject.

This research explores the increased use of type‐2 fuzzy sets in manufacturing. In particular, type‐2 fuzzy sets are used to model “the words that mean different things to different people”.

A model that can leverage design process knowledge and predict time to market from performance measures is a potentially valuable tool for decision making and continuous improvement. A number of data sources, such as process maps, from previous research into time to market in a high technology products company, are used to structure and build a type‐2 fuzzy logic model for the prediction of time to market.

This paper presents a demonstration of how the type‐2 fuzzy logic model works and provides directions for further research into the design process for time to market.

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.

The purpose of this research is to develop a new approach for analyzing the fuzzy reliability of a series and parallel system. Also to introduce definition of L‐R type interval valued triangular vague set and certain Tω‐based arithmetic operations between two L‐R type interval valued triangular vague sets.

In the proposed approach using a fault tree an interval valued vague fault tree is developed for the system in which the fuzzy reliability of each component of the system is represented by a L‐R type interval valued triangular vague set. Then with the help of a developed interval valued vague fault tree an algorithm is developed to analyze the fuzzy system reliability.

For numerical verification of the proposed approach the fuzzy reliability of the basement flooding has been analyzed using the existing approaches and the proposed approach. Comparing the results of existing approaches and the proposed approach, it has been shown that the uncertainty about the reliability is minimized using the proposed approach and the results are exact. While using the existing approaches the results are approximate due to approximate product of triangular vague sets and interval valued triangular vague sets.

The paper introduces a new approach for analyzing the fuzzy system reliability using Tω‐based arithmetic operations over L‐R type interval valued triangular vague sets.

In this paper we discuss a mechanism for making business decisions on the basis of an expected penalty function associated with cost variance. We assume that the decision maker is knowledgeable of the economic environment in which the decision will be made, but that he has no hard data” such as a market research report. In this setting fuzzy logic is more applicable than ordinary statistical decision theory. We develop a method of computing a fuzzy expected penalty based on a fuzzy distribution of cost variance and a fuzzy penalty function. These fuzzy expected penalties are then defuzzified” so that a non‐fuzzy decision can be made.

Two solution concepts for a FMP problem are suggested. The first one makes use of level sets of the fuzzy set of feasible alternatives. The second solution is based on the concept of Pareto maximum in vector optimization. It is shown that both solutions are equivalent in a sense that they give the same fuzzy value of a function maximized. It is suggested that if a decision‐maker is to choose a single element, then his choice must be based not only on the membership value of this element in the solution fuzzy set but also on the corresponding value of the function maximized. In this respect the situation is similar to that typical for vector optimization. The approach suggested in this paper is further used for analysing games with fuzzy sets of strategies of the players. A fuzzy equilibrium solution is introduced, which can provide a base for an agreement between the players.

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.