294 research outputs found
Intuitionistic fuzzy similarity measures and their role in classification
We present some similarity and distance measures between intuitionistic fuzzy sets (IFSs). Thus, we propose two semi-metric distance measures between IFSs. The measures are applied to classification of shapes and handwritten Arabic sentences described with intuitionistic fuzzy information. The experimental results permitted to do a comparative analysis between intuitionistic fuzzy similarity and distance measures, which can facilitate the selection of such measure in similar applications
Intuitionistic Partition based Conceptual Granulation Topic-Term Modeling
Document Analysis represented in vector space model is often used in information retrieval, topic analysis, and automatic classification. However, it hardly deals with fuzzy information and decision-making problems. To account this, Intuitionistic partition based cosine similarity measure between topic/terms and correlation between document/topic are proposed for evaluation. Conceptual granulation is emphasized in the decision matrix expressed conventionally as tf-idf. A local clustering of topic-terms and document-topics results in comparing dependent terms with membership degree using cosine similarity measure and correlation. A preprocessing of documents with intuitionistic fuzzy sets results in efficient classification of large corpus. But it depends on the datasets chosen. The proposed method effectively works well with large sized categorized corpus
Power of Continuous Triangular Norms with Application to Intuitionistic Fuzzy Information Aggregation
The paper aims to investigate the power operation of continuous triangular
norms (t-norms) and develop some intuitionistic fuzzy information aggregation
methods. It is proved that a continuous t-norm is power stable if and only if
every point is a power stable point, and if and only if it is the minimum
t-norm, or it is strict, or it is an ordinal sum of strict t-norms. Moreover,
the representation theorem of continuous t-norms is used to obtain the
computational formula for the power of continuous t-norms. Based on the power
operation of t-norms, four fundamental operations induced by a continuous
t-norm for the intuitionistic fuzzy (IF) sets are introduced. Furthermore,
various aggregation operators, namely the IF weighted average (IFWA), IF
weighted geometric (IFWG), and IF mean weighted average and geometric (IFMWAG)
operators, are defined, and their properties are analyzed. Finally, a new
decision-making algorithm is designed based on the IFMWAG operator, which can
remove the hindrance of indiscernibility on the boundaries of some classical
aggregation operators. The practical applicability, comparative analysis, and
advantages of the study with other decision-making methods are furnished to
ascertain the efficacy of the designed method
A Unifying Field in Logics: Neutrosophic Logic.
The author makes an introduction to non-standard analysis, then extends the dialectics to Âneutrosophy  which became a new branch of philosophy. This new concept helps in generalizing the intuitionistic, paraconsistent, dialetheism, fuzzy logic to Âneutrosophic logic  which is the first logic that comprises paradoxes and distinguishes between relative and absolute truth. Similarly, the fuzzy set is generalized to Âneutrosophic setÂ. Also, the classical and imprecise probabilities are generalized to Âneutrosophic probabilityÂ
A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS
In 1960s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, which rigorously defines the infinitesimals
A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC PROBABILITY AND STATISTICS - 6th ed.
It was a surprise for me when in 1995 I received a manuscript from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - revealing paradoxes - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) âneutrosophyâ â study of neutralities as an extension of dialectics; b) and its derivative âneutrosophicâ, such as âneutrosophic logicâ, âneutrosophic setâ, âneutrosophic probabilityâ, and âneutrosophic statisticsâ and thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics. It was known to me his setting up in 1980âs of a new literary and artistic avant-garde movement that he called âparadoxismâ, because I received some books and papers dealing with it in order to review them for the German journal âZentralblatt fur Mathematikâ. It was an inspired connection he made between literature/arts and science, philosophy. We started a long correspondence with questions and answers. Because paradoxism supposes multiple value sentences and procedures in creation, antisense and non-sense, paradoxes and contradictions, and itâs tight with neutrosophic logic, I would like to make a small presentation
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