A Fuzzy Syllogistic Reasoning Schema for Generalized Quantifiers

In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional, comparative and exception) taken from Theory of Generalized Quantifiers and similarity quantifiers, taken from statistics, are considered and (ii) any number of premises can be taken into account within the reasoning process. Furthermore, a systematic reasoning procedure to solve the syllogism is also proposed, interpreting it as an equivalent mathematical optimization problem, where the premises constitute the constraints of the searching space for the quantifier in the conclusion.Comment: 22 pages, 6 figures, journal pape

Understanding Customers' Affective Needs with Linguistic Summarization

Abstract: To increase the chance of launching a successful product into market, it is essential to satisfy customers’ affective needs during the product design stage. However, understanding customers’ affective needs is very difficult task and product designers might misunderstand the customers’ affective needs. In this study, linguistic summarization with fuzzy set is used to present customers’ affective needs with natural language statements which could be easily understood by human beings. The relations between customers’ affective needs and product design elements are represented by type-I and type-II fuzzy quantified sentences. To illustrate the applicability of the linguistic summarization with fuzzy set in translating customers’ affective needs to natural language statements, a case study is conducted on mobile phone design. The results indicate that the linguistic summarization with fuzzy set can be a useful tool to assist designers to create products satisfying affective needs of customer

Evaluation of Quantified Statements using Gradual Numbers - 64

Dr. Ludovic Liétard is currently assistant professor at the University of Rennes 1 (IUT Lannion) in France. His research mainly concerns flexible querying of relational databases using fuzzy set theory and various applications of fuzzy set theory in databases. Dr. Daniel Rocacher is currently assistant professor at the University of Rennes 1 (ENSSAT Lannion) in France. He has proposed new directions to define gradual numbers in the framework of fuzzy set theory. His current research concerns their applications in databases. Evaluation of Quantified Statements using Gradual Numbers -2 -Abstract. This paper is devoted to the evaluation of quantified statements which can be found in many applications as decision-making, expert systems or flexible querying of relational databases using fuzzy set theory. Its contribution is to introduce the main techniques to evaluate such statements and to propose a new theoretical background for the evaluation of quantified statements of type "Q X are A" and "Q B X are A". In this context, quantified statements are interpreted using an arithmetic on gradual numbers from ℕ f , ℤ f and ℚ f . It is shown that the context of fuzzy numbers provides a framework to unify previous approaches and can be the base for the definition of new approaches

Application of fuzzy sets in data-to-text system

This PhD dissertation addresses the convergence of two distinct paradigms: fuzzy sets and natural language generation. The object of study is the integration of fuzzy set-derived techniques that model imprecision and uncertainty in human language into systems that generate textual information from numeric data, commonly known as data-to-text systems. This dissertation covers an extensive state of the art review, potential convergence points, two real data-to-text applications that integrate fuzzy sets (in the meteorology and learning analytics domains), and a model that encompasses the most relevant elements in the linguistic description of data discipline and provides a framework for building and integrating fuzzy set-based approaches into natural language generation/data-to-ext systems

Fuzzy Natural Logic in IFSA-EUSFLAT 2021

The present book contains five papers accepted and published in the Special Issue, “Fuzzy Natural Logic in IFSA-EUSFLAT 2021”, of the journal Mathematics (MDPI). These papers are extended versions of the contributions presented in the conference “The 19th World Congress of the International Fuzzy Systems Association and the 12th Conference of the European Society for Fuzzy Logic and Technology jointly with the AGOP, IJCRS, and FQAS conferences”, which took place in Bratislava (Slovakia) from September 19 to September 24, 2021. Fuzzy Natural Logic (FNL) is a system of mathematical fuzzy logic theories that enables us to model natural language terms and rules while accounting for their inherent vagueness and allows us to reason and argue using the tools developed in them. FNL includes, among others, the theory of evaluative linguistic expressions (e.g., small, very large, etc.), the theory of fuzzy and intermediate quantifiers (e.g., most, few, many, etc.), and the theory of fuzzy/linguistic IF–THEN rules and logical inference. The papers in this Special Issue use the various aspects and concepts of FNL mentioned above and apply them to a wide range of problems both theoretically and practically oriented. This book will be of interest for researchers working in the areas of fuzzy logic, applied linguistics, generalized quantifiers, and their applications