26 research outputs found
A Geometric Interpretation of the Neutrosophic Set - A Generalization of the Intuitionistic Fuzzy Set
In this paper we generalize the intuitionistic fuzzy set (IFS),
paraconsistent set, and intuitionistic set to the neutrosophic set (NS).
Several examples are presented. Also, a geometric interpretation of the
Neutrosophic Set is given using a Neutrosophic Cube. Many distinctions between
NS and IFS are underlined.Comment: 9 pages. Presented at the 2003 BISC FLINT-CIBI International Workshop
on Soft Computing for Internet and Bioinformatics, University of Berkeley,
California, December 15-19, 2003, under the title "Generalization of the
Intuitionistic Fuzzy Set to the Neutrosophic Set
NEUTROSOPHIC SET – A GENERALIZATION OF THE INTUITIONISTIC FUZZY SET
In this paper one generalizes the intuitionistic fuzzy set (IFS),paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined
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
Interval-valued algebras and fuzzy logics
In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter
About t-norms on type-2 fuzzy sets.
Walker et al. defined two families of
binary operations on M (set of functions of [0,1]
in [0,1]), and they determined that, under certain
conditions, those operations are t-norms (triangular
norm) or t-conorms on L (all the normal and convex
functions of M). We define binary operations
on M, more general than those given by Walker et
al., and we study many properties of these general
operations that allow us to deduce new t-norms and
t-conorms on both L, and M
A new fuzzy multi-attribute group decision-making method based on TOPSIS and optimization models
In this paper, a new method based on TOPSIS and optimization models is
proposed for multi-attribute group decision-making in the environment of
interval-valued intuitionistic fuzzy sets.Firstly, by minimizing the sum of
differences between individual evaluations and the overallconsistent
evaluations of all experts, a new optimization model is established for
determining expert weights. Secondly, based on TOPSIS method, the improved
closeness index for evaluating each alternative is obtained. Finally, the
attribute weight is determined by establishing an optimization model with the
goal of maximizing the closeness of each alternative, and it is brought into
the closeness index so that the alternatives can be ranked. Combining all these
together, the complete fuzzy multi-attribute group decision-making algorithm is
formulated, which can give full play to the advantages of subjective and
objective weighting methods. In the end, the feasibility and effectiveness of
the provided method are verified by a real case study
Thirty years of the international journal of intelligent systems: a bibliometric review
The International Journal of Intelligent Systems was created in 1986. Today, the journal is 30 years old. To celebrate this anniversary, this study develops a bibliometric review of all of the papers published in the journal between 1986 and 2015. The results are largely based on the Web of Science Core Collection, which classifies leading bibliographic material by using several indicators including total number of publications and citations, the h-index, cites per paper, and citing articles. Thework also uses theVOS viewer software for visualizing the main results through bibliographic coupling and co-citation. The results show a general overview of leading trends that have influenced the journal in terms of highly cited papers, authors, journals, universities and countries. C 2016 Wiley Periodicals, Inc