Interval-valued algebras and fuzzy logics

In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter

A commentary on some of the intrinsic differences between grey systems and fuzzy systems

The aim of this paper is to distinguish between some of the more intrinsic differences that exist between grey system theory (GST) and fuzzy system theory (FST). There are several aspects of both paradigms that are closely related, it is precisely these close relations that will often result in a misunderstanding or misinterpretation. The subtly of the differences in some cases are difficult to perceive, hence why a definitive explanation is needed. This paper discusses the divergences and similarities between the interval-valued fuzzy set and grey set, interval and grey number; for both the standard and the generalised interpretation. A preference based analysis example is also put forward to demonstrate the alternative in perspectives that each approach adopts. It is believed that a better understanding of the differences will ultimately allow for a greater understanding of the ideology and mantras that the concepts themselves are built upon. By proxy, describing the divergences will also put forward the similarities. We believe that by providing an overview of the facets that each approach employs where confusion may arise, a thorough and more detailed explanation is the result. This paper places particular emphasis on grey system theory, describing the more intrinsic differences that sets it apart from the more established paradigm of fuzzy system theory

Fuzzy linear programming problems : models and solutions

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately

A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information

Single-valued trapezoidal neutrosophic numbers (SVTNNs) have a strong capacity to depict uncertain, inconsistent, and incomplete information about decisionmaking problems. Preference relations represent a practical tool for presenting decision makers’ preference information regarding various alternatives

Evaluating aggregate functions on possibilistic data

The need for extending information management systems to handle the imprecision of information found in the real world has been recognized. Fuzzy set theory together with possibility theory represent a uniform framework for extending the relational database model with these features. However, none of the existing proposals for handling imprecision in the literature has dealt with queries involving a functional evaluation of a set of items, traditionally referred to as aggregation. Two kinds of aggregate operators, namely, scalar aggregates and aggregate functions, exist. Both are important for most real-world applications, and are thus being supported by traditional languages like SQL or QUEL. This paper presents a framework for handling these two types of aggregates in the context of imprecise information. We consider three cases, specifically, aggregates within vague queries on precise data, aggregates within precisely specified queries on possibilistic data, and aggregates within vague queries on imprecise data. These extensions are based on fuzzy set-theoretical concepts such as the extension principle, the sigma-count operation, and the possibilistic expected value. The consistency and completeness of the proposed operations is shown

Multivalued logic systems for technical applications

Velmi často je vyžadováno, aby automatizovaná zařízení byla jistým způsobem "inteligentní", tedy aby jejich řídicí systémy uměly emulovat rozhodovací proces. Tato diplomová práce poskytuje obecný formální popis vícehodnotových logických systémů schopných zmíněné emulace a jejich souvislost s teorií fuzzy množin. Jsou uvedeny způsoby vytváření matematických modelů založených na lingvistických datech. Dále se práce zabývá znalostními bázemi a jejich vlastnostmi. Součástí této práce je také počítačový program sloužící k tvorbě slovních modelů.Automated devices are very often required to exhibit some kind of an intelligent behaviour, which means that their control systems must be able to emulate the reasoning process. This diploma thesis provides a general formal description of multivalued logic systems capable of such an emulation and their connection with the fuzzy set theory. Ways of constructing mathematical models based on linguistic data are described. Also, knowledge bases and their properties are discussed. A computer program serving as a linguistic model development tool is a part of this thesis.

A Model of User Preference Learning for Content-Based Recommender Systems

This paper focuses to a formal model of user preference learning for content-based recommender systems. First, some fundamental and special requirements to user preference learning are identified and proposed. Three learning tasks are introduced as the exact, the order preserving and the iterative user preference learning tasks. The first two tasks concern the situation where we have the user's rating available for a large part of objects. The third task does not require any prior knowledge about the user's ratings (i.e. the user's rating history). Local and global preferences are distinguished in the presented model. Methods for learning these preferences are discussed. Finally, experiments and future work will be described