About Nonstandard Neutrosophic Logic (Answers to Imamura 'Note on the Definition of Neutrosophic Logic')

In order to more accurately situate and fit the neutrosophic logic into the framework of nonstandard analysis, we present the neutrosophic inequalities, neutrosophic equality, neutrosophic infimum and supremum, neutrosophic standard intervals, including the cases when the neutrosophic logic standard and nonstandard components T, I, F get values outside of the classical real unit interval [0, 1], and a brief evolution of neutrosophic operators. The paper intends to answer Imamura criticism that we found benefic in better understanding the nonstandard neutrosophic logic, although the nonstandard neutrosophic logic was never used in practical applications.Comment: 16 page

Three-valued logics, uncertainty management and rough sets

This paper is a survey of the connections between three-valued logics and rough sets from the point of view of incomplete information management. Based on the fact that many three-valued logics can be put under a unique algebraic umbrella, we show how to translate three-valued conjunctions and implications into operations on ill-known sets such as rough sets. We then show that while such translations may provide mathematically elegant algebraic settings for rough sets, the interpretability of these connectives in terms of an original set approximated via an equivalence relation is very limited, thus casting doubts on the practical relevance of truth-functional logical renderings of rough sets

Weighted logics for artificial intelligence : an introductory discussion

International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas

An introduction to DSmT

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this introduction, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT), developed for dealing with imprecise, uncertain and conflicting sources of information. We focus our presentation on the foundations of DSmT and on its most important rules of combination, rather than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout this presentation to show the efficiency and the generality of this new approach

The posterity of Zadeh's 50-year-old paper: A retrospective in 101 Easy Pieces – and a Few More

International audienceThis article was commissioned by the 22nd IEEE International Conference of Fuzzy Systems (FUZZ-IEEE) to celebrate the 50th Anniversary of Lotfi Zadeh's seminal 1965 paper on fuzzy sets. In addition to Lotfi's original paper, this note itemizes 100 citations of books and papers deemed “important (significant, seminal, etc.)” by 20 of the 21 living IEEE CIS Fuzzy Systems pioneers. Each of the 20 contributors supplied 5 citations, and Lotfi's paper makes the overall list a tidy 101, as in “Fuzzy Sets 101”. This note is not a survey in any real sense of the word, but the contributors did offer short remarks to indicate the reason for inclusion (e.g., historical, topical, seminal, etc.) of each citation. Citation statistics are easy to find and notoriously erroneous, so we refrain from reporting them - almost. The exception is that according to Google scholar on April 9, 2015, Lotfi's 1965 paper has been cited 55,479 times

Interval-based uncertain reasoning

This thesis examines three interval based uncertain reasoning approaches: reasoning under interval constraints, reasoning using necessity and possibility functions, and reasoning with rough set theory. In all these approaches, intervals are used to characterize the uncertainty involved in a reasoning process when the available information is insufficient for single-valued truth evaluation functions. Approaches using interval constraints can be applied to both interval fuzzy sets and interval probabilities. The notion of interval triangular norms, or interval t-norms for short, is introduced and studied in both numeric and non-numeric settings. Algorithms for computing interval t-norms are proposed. Basic issues on the use of t-norms for approximate reasoning with interval fuzzy sets are studied. Inference rules for reasoning under interval constraints are investigated. In the second approach, a pair of necessity and possibility functions is used to bound the fuzzy truth values of propositions. Inference in this case is to narrow the gap between the pair of the functions. Inference rules are derived from the properties of necessity and possibility functions. The theory of rough sets is used to approximate truth values of propositions and to explore modal structures in many-valued logic. It offers an uncertain reasoning method complementary to the other two