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The importance of fuzzy logic (FL) in approximate reasoning, and that of default logic (DL) in reasoning with incomplete information, is well established. Also, the need for a commonsense reasoning framework that handles both these aspects has been widely anticipated. The purpose of this paper is to show that fuzzyfied default logic (FDL) is an attempt at creating such a framework.

The basic syntax, semantics, unique characteristics and examples of its complex reasoning abilities have been presented in this paper.

Interestingly, FDL turns out to be a generalization of traditional DL, with even better support for non‐monotonic reasoning.

The paper presents a generalized tool for commonsense reasoning which can be used for inference under incomplete information.

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 determine an extension of the MIN and MAX general analytical expression for triangular fuzzy intervals to trapezoidal ones when Zadeh's extension principle is considered.

In order to determine the MIN and MAX analytical expressions, the paper exhibits the conventional interval relations and their extension in fuzzy case where trapezoidal fuzzy intervals are assumed. The formalization and the justification of the so‐built analytical expressions are then detailed where mathematical mappings are proposed. The potential use of these operators in the framework of uncertain aggregation operators and ranking fuzzy intervals is shown with illustrative examples.

It is discovered that the MIN and MAX operations for fuzzy intervals can be formulated by a general analytical form.

The proposed methodology can be directly applied for ranking fuzzy intervals and implementing a large class of uncertain aggregation operators, especially for two‐additive Choquet integral.

The originality of the proposed technique resides in exploiting the interval relations between supports and kernels to express a general and compact analytical MIN and MAX expressions for fuzzy intervals.

Melting universality, quantification and relative computability into a meta‐synthesis, pansystems theory develops an investigation on W‐fuzziness and 0*‐fuzziness connected with generalized conceptions such as derivative, equation, variational principle and OR. The purpose of this paper is to unify various mathematical structures, fuzziness categories, definitions of systems are unified within a general framework.

The paper includes topics: pansystems approach to fuzzy systems and relations, pansystems variational principle and Zadeh's extension principle, pansystems clustering and its fuzzy embodiment, pansystems topology and approximation to fuzziness, relative unification of fuzziness and roughness.

Zadeh extension principle about fuzziness transmission can be considered as a specific model of pansystems extremum principle, and so the more modes can be developed. Based on them a further investigation is present on pansystems clustering, which is a W‐fuzzy clustering, an extension or sublation of traditional one and fuzzy one.

Pansystems clustering embodies mutuality of many logoi of different subbraches with classification‐styled OR, including related interpromotions of the principles among knowledge rediscovery, data mining, mathematical reasoning and the investigations of fuzzy systems. W‐fuzziness and 0*‐fuzziness realize a relative unification for many logoi and principles.

The attributes that influence the selection of applicants and the relevant crediting decisions are naturally distinguished by interactions and interdependencies. A new method of possibilistic discrimination analysis (MPDA) was developed for the second stage to address this phenomenon. The method generates positive and negative discrimination measures for each alternative applicant in relation to a particular attribute. The obtained discrimination pair reflects the interaction of attributes and represents intuitionistic fuzzy numbers (IFNs). For the aggregation of applicant's discrimination intuitionistic fuzzy assessments (with respect to attributes), new intuitionistic aggregation operators, such as AsP-IFOWA and AsP-IFOWG, are defined and studied. The new operators are certain extensions of the well-known Choquet integral and Yager OWA operators. The extensions, in contrast to the Choquet aggregation, take into account all possible interactions of the attributes by introducing associated probabilities of a fuzzy measure.

For optimal planning of investments distribution and decreasing of credit risks, it is crucial to have selected projects ranked within deeply detailed investment model. To achieve this, a new approach developed in this article involves three stages. The first stage is to reduce a possibly large number of applicants for credit, and here, the method of expertons is used. At the second stage, a model of improved decisions is built, which reduces the risks of decision making. In this model, as it is in multi-attribute decision-making (MADM) + multi-objective decision-making (MODM), expert evaluations are presented in terms of utility, gain, and more. At the third stage, the authors construct the bi-criteria discrete intuitionistic fuzzy optimization problem for making the most profitable investment portfolio with new criterion: 1) Maximization of total ranking index of selected applicants' group and classical criterion and 2) Maximization of total profit of selected applicants' group.

The example gives the Pareto fronts obtained by both new operators, the Choquet integral and Yager OWA operators also well-known TOPSIS approach, for selecting applicants and awarding credits. For a fuzzy measure, the possibility measure defined on the expert evaluations of attributes is taken.

The comparative analysis identifies the applicants who will receive the funding sequentially based on crediting resources and their requirements. It has become apparent that the use of the new criterion has given more credibility to applicants in making optimal credit decisions in the environment of extended new operators, where the phenomenon of interaction of all attributes was also taken into account.

Time modeling is a crucial feature in many application domains. However, temporal information often is not crisp, but is subjective and fuzzy. The purpose of this paper is to address the issue related to the modeling and handling of imperfection inherent to both temporal relations and intervals.

On the one hand, fuzzy extensions of Allen temporal relations are investigated and, on the other hand, extended temporal relations to define the positions of two fuzzy time intervals are introduced. Then, a database system, called Fuzzy Temporal Information Management and Exploitation (Fuzz-TIME), is developed for the purpose of processing fuzzy temporal queries.

To evaluate the proposal, the authors have implemented a Fuzz-TIME system and created a fuzzy historical database for the querying purpose. Some demonstrative scenarios from history domain are proposed and discussed.

The authors have conducted some experiments on archaeological data to show the effectiveness of the Fuzz-TIME system. However, thorough experiments on large-scale databases are highly desirable to show the behavior of the tool with respect to the performance and time execution criteria.

The tool developed (Fuzz-TIME) can have many practical applications where time information has to be dealt with. In particular, in several real-world applications like history, medicine, criminal and financial domains, where time is often perceived or expressed in an imprecise/fuzzy manner.

The social implications of this work can be expected, more particularly, in two domains: in the museum to manage, exploit and analysis the piece of information related to archives and historic data; and in the hospitals/medical organizations to deal with time information inherent to data about patients and diseases.

This paper presents the design and characterization of a novel and intelligent database system to process and manage the imperfection inherent to both temporal relations and intervals.

The purpose of this paper is to develop the Pythagorean fuzzy extension of CODAS method.

Supplier selection is a critical issue for manufacturing companies since it is a multidimensional problem including several conflicting criteria. A suitable multi criteria decision making (MCDM) method that could consider vagueness and impreciseness in the assessments should be used for this kind of problems. Pythagorean fuzzy sets (PFSs) are characterized by a membership degree and a non-membership degree satisfying the condition that their square sum is equal to or less than 1. PFSs extend the concept of intuitionistic fuzzy sets (IFSs). COmbinative Distance-based Assessment (CODAS) method is relatively a new MCDM technique introduced by Keshavarz Ghorabaee et al. (2016).

Pythagorean fuzzy CODAS gives better results than ordinary fuzzy CODAS since it considers the hesitancy of decision makers and presents a larger space for membership and non-membership definition.

The value of this paper is the proposal of a new method to use for the solutions of MCDM problems under vagueness and impreciseness. To show validity and effectiveness of the proposed method, an application to the supplier selection problem is given.

There is an increasing interest in the use of knowledge graphs to represent real-world knowledge and a common need to manage imprecise knowledge in many real-world applications. This paper aims to study approaches to solve flexible queries over knowledge graphs.

By introducing fuzzy logic in the query answering process, the authors are able to obtain a novel algorithm to solve flexible queries over knowledge graphs. This approach is implemented in the FUzzy Knowledge Graphs system, a software tool with an intuitive user-graphical interface.

This approach makes it possible to reuse semantic web standards (RDF, SPARQL and OWL 2) and builds a fuzzy layer on top of them. The application to a use case shows that the system can aggregate information in different ways by selecting different fusion operators and adapting to different user needs.

This approach is more general than similar previous works in the literature and provides a specific way to represent the flexible restrictions (using fuzzy OWL 2 datatypes).

For some specific multi-criteria decision-making (MCDM) problems, especially in emergency situations, because of the feature of criteria and other fuzzy factors, it is more appropriate that values of different criteria are expressed in their correspondingly appropriate value types. The purpose of this paper is to build a multi-criteria group decision-making (MCGDM) model dealing with heterogeneous information based on distance-based VIKOR to solve emergency supplier selection in practice appropriately and flexibly, where a compromise solution is more acceptable and suitable.

This paper extends the classical VIKOR to a generalized distance-based VIKOR to handle heterogeneous information containing crisp number, interval number, intuitionistic fuzzy number and hesitant fuzzy linguistic value, and develops an MCGDM model based on the distance-based VIKOR to handle the multi-criteria heterogeneous information in practice. This paper also introduces a parameter called non-fuzzy degree for each type of heterogeneous value to moderate the computation on aggregating heterogeneous hybrid distances.

The proposed distance-based model can handle the heterogeneous information appropriately and flexibly because the computational process is directly operated on the heterogeneous information based on generalized distance without a transformation process, which can improve the decision-making efficiency and reduce information loss. An example of emergency supplier selection is given to illustrate the proposed method.

This paper develops an MCGDM model based on the distance-based VIKOR to handle heterogeneous information appropriately and flexibly. In emergency supplier selection situations, the proposed decision-making model allows the decision-makers to express their judgments on criteria in their appropriate value types.