FUZZY RELATIONAL DATABASE MODEL AND MANAGEMANT SYSTEM FOR IMPRECISE INFORMATION

This paper introduces a fuzzy relational database model (FRDB) and the management system for it. FRDB is built by extending the classical relational database model with the fuzzy membership degree of tuples in relations. The management system for FRDB with the querying language like SQL is built by using a classical open-source management system.

Assisting Users in Decisions Using Fuzzy Ontologies: Application in the Wine Market

Nowadays, wine has become a very popular item to purchase. There are a lot of brands and a lot of different types of wines that have different prices and characteristics. Since there is a lot of options, it is easy for buyers to feel lost among the high number of possibilities. Therefore, there is a need for computational tools that help buyers to decide which is the wine that better fits their necessities. In this article, a decision support system built over a fuzzy ontology has been designed for helping people to select a wine. Two different possible architecture implementation designs are presented. Furthermore, imprecise information is used to design a comfortable way of providing information to the system. Users can use this comfortable communication system to express their preferences and provide their opinion about the selected products. Moreover, mechanisms to carry out a constant update of the fuzzy ontology are exposed.

Belief and Plausibility Measures on Intuitionistic Fuzzy Sets with Construction of Belief-Plausibility TOPSIS

Belief and plausibility measures in Dempster–Shafer theory (DST) and fuzzy sets are known as different approaches for representing partial, uncertainty, and imprecise information. There are several generalizations of DST to fuzzy sets proposed in the literature. But, less generalization of DST to intuitionistic fuzzy sets (IFSs), that can somehow present imprecise information better than fuzzy sets, was proposed. In this paper, we first propose a simple and intuitive way to construct a generalization of DST to IFSs with degrees of belief and plausibility in terms of degrees of membership and nonmembership, respectively. We then give belief and plausibility measures on IFSs and construct belief-plausibility intervals (BPIs) of IFSs. Based on the constructed BPIs, we first use Hausdorff metric to define the distance between two BPIs and then establish similarity measures in the generalized context of DST to IFSs. By employing the techniques of ordered preference similarity to ideal solution (TOPSIS), the proposed belief and plausibility measures on IFSs in the framework of DST enable us to construct a belief-plausibility TOPSIS for solving multicriteria decision-making problems. Some examples are presented to manifest that the proposed method is reasonable, applicable, and well suited in the environment of IFSs in the framework of generalization of DST.

A Review on Some Arithmetic Concepts of Z-Number and Its Application to Real-World Problems

Zadeh introduced the concept of Z-numbers in 2011 to deal with imprecise information. In this regard, many research works have been published in an attempt to introduce some basic theoretical concepts of Z-numbers to model real-world problems. To understand the current challenges when dealing with Z-numbers and the feasibility of using Z-number in solving real-world problems, a comprehensive review of the existing work on Z-number is paramount. This paper consists of an overview of existing literature on Z-number and identifies some of the key areas that are required for further improvement.

A Hybrid Relational Database Model for Uncertain and Imprecise Information

Recent years, many fuzzy or probabilistic database models have been built for representing and handling imprecise or uncertain information of objects in real-world applications. However, relational database models combining the relevance and strength of both fuzzy set and probability theories have rarely been proposed. This paper introduces a new relational database model, as a hybrid one combining consistently fuzzy set theory and probability theory for modeling and manipulating uncertain and imprecise information, where the uncertainty and imprecision of a relational attribute value are represented by a fuzzy probabilistic triple, the computation and combination of relational attribute values are implemented by using the probabilistic interpretation of binary relations on fuzzy sets, and the elimination of redundant data is dealt with by coalescing e-equivalent tuples. The basic concepts of the classical relational database model are extended in this new model. Then the relational algebraic operations are formally defined accordingly. A set of the properties of the relational algebraic operations is also formulated and proven.