Fuzzy Logic

Mathematical Principles of Fuzzy Logic, 1999

Mathematical Principles of Fuzzy Logic, 1999

Allied Journals, 2015

The problems of uncertainty, imprecision and vagueness have been discussed for many years. These problems have been major topics in philosophical arenas with series of debate, in particular, about the nature of vagueness and the ability of traditional Boolean logic to cope with concepts and perceptions that are imprecise or vague. These sometimes make experts to rely on common sense when they solve problems. Interestingly, a lot of experts such as scientists, philosophers, psychologists, great mathematicians and others, researched vehemently on fuzzy logic, putting each other under constant scrutiny in response to their individual propositions coupled with fuzzy logic not until Zadeh Lotfi, eventually conceived fuzzy logic in 1971. Fuzzy logic is not logic that is fuzzy, but logic that is used to describe fuzziness. Fuzzy logic is the theory of fuzzy sets, sets that calibrate vagueness. Fuzzy logic is based on the idea that all things admit of degrees. Temperature, height, speed, distance, beauty, handsome, ugly, walk, stand all comes on a sliding scale. My car is running really hot. Elvis is a very tall guy. Fuzzy logic reflects how people think. It attempts to model our sense of words, our decision making and our common sense. As a result, it is leading to new, more human, intelligent systems.

1999

MLQ, 2004

The paper proposes a flexible way to build concepts within fuzzy logic and set theory. The framework is general enough to capture some important particular cases, with their own independent interpretations, like "antitone" or "isotone" concepts constructed from fuzzy binary relations, but also to allow the two universes (of objects and attributes) to be equipped each with its own truth structure. Perhaps the most important feature of our approach is that we do not commit ourselves to any kind of logical connector, covering thus the case of a possibly non-commutative conjunction too.

Logical Models of Reasoning with Vague Information, p …

The Logica Yearbook, 2004

2011