The compositional rule of inference with several relations

The compositional rule of inference with several relations, which is the mainly used inference rule in approximate reasoning, is considered in this paper. Stability results are given and exact computational formulae are provided

Mining and visualizing uncertain data objects and named data networking traffics by fuzzy self-organizing map

Uncertainty is widely spread in real-world data. Uncertain data-in computer science-is typically found in the area of sensor networks where the sensors sense the environment with certain error. Mining and visualizing uncertain data is one of the new challenges that face uncertain databases. This paper presents a new intelligent hybrid algorithm that applies fuzzy set theory into the context of the Self-Organizing Map to mine and visualize uncertain objects. The algorithm is tested in some benchmark problems and the uncertain traffics in Named Data Networking (NDN). Experimental results indicate that the proposed algorithm is precise and effective in terms of the applied performance criteria.Peer ReviewedPostprint (published version

Assessment of Sustainable Development

The objective of this paper is to introduce fuzzy set theory and develop fuzzy mathematical models to assess sustainable development based on context-dependent economic, ecological, and societal sustainability indicators. Membership functions are at the core of fuzzy models, and define the degree to which indicators contribute to development. Although a decision-making process regarding sustainable development is subjective, fuzzy set theory links human expectations about development, expressed in linguistic propositions, to numerical data, expressed in measurements of sustainability indicators. In the future, practical implementation of such models will be based on elicitation of expert knowledge to construct a membership function. The fuzzy models developed in this paper provide a novel approach to support decisions regarding sustainable development.agriculture;assessment;fuzzy set theory;sustainable development

Implication functions in interval-valued fuzzy set theory

Interval-valued fuzzy set theory is an extension of fuzzy set theory in which the real, but unknown, membership degree is approximated by a closed interval of possible membership degrees. Since implications on the unit interval play an important role in fuzzy set theory, several authors have extended this notion to interval-valued fuzzy set theory. This chapter gives an overview of the results pertaining to implications in interval-valued fuzzy set theory. In particular, we describe several possibilities to represent such implications using implications on the unit interval, we give a characterization of the implications in interval-valued fuzzy set theory which satisfy the Smets-Magrez axioms, we discuss the solutions of a particular distributivity equation involving strict t-norms, we extend monoidal logic to the interval-valued fuzzy case and we give a soundness and completeness theorem which is similar to the one existing for monoidal logic, and finally we discuss some other constructions of implications in interval-valued fuzzy set theory

On topological structures of fuzzy parametrized soft sets

In this paper, we introduce the topological structure of fuzzy parametrized soft sets and fuzzy parametrized soft mappings. We define the notion of quasi-coincidence for fuzzy parametrized soft sets and investigated basic properties of it. We study the closure, interior, base, continuity and compactness and properties of these concepts in fuzzy parametrized soft topological space