• Honam Mathematical Journal
• /
• v.26 no.1
• /
• pp.17-41
• /
• 2004

In this paper, we obtain the intuitionistic fuzzy subgroups generated by intuitionistic fuzzy sets and some properties preserved by a ring homomorphism. Furthermore, we introduce the concept of intuitionistic fuzzy coset and study some of it's properties.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.19 no.4
• /
• pp.556-561
• /
• 2009

In this paper, we propose new method to calculate the distance between intuitionistic fuzzy sets(IFSs) based on the three dimensional representation of IFSs and analyze the relations of similarity measure and distance measure of IFSs. Finally, we apply the proposed measures to pattern recognitions.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.359-367
• /
• 2007

We consider the intuitionistic fuzzification of the concept of several ${\Gamma}$-ideals in a ${\Gamma}$-semigroup S, and investigate some properties of such ${\Gamma}$-ideals.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.11 no.2
• /
• pp.71-76
• /
• 2011

The problem of decision making under imprecise environments are widely spread in real life decision situations. We present a method of object recognition from imprecise multi observer data, which extends the work of Roy and Maji [J Compu. Appl. Math. 203(2007) 412-418] to generalized intuitionistic fuzzy soft set theory. The method involves the construction of a comparison table from a generalized intuitionistic fuzzy soft set in a parametric sense for decision making.

• Korean Journal of Mathematics
• /
• v.28 no.4
• /
• pp.753-774
• /
• 2020

We introduce the notion of interval valued intuitionistic fuzzy hyperideals, bi-hyperideals and quasi-hyperideals of an ordered semihypergroup. We characterize an interval valued intuitionistic fuzzy hyperideal of an ordered semihypergroup in terms of its level subset. Moreover, we show that interval valued intuitionistic fuzzy bi-hyperideals and quasi-hyperideals coincide only in a particular class of ordered semihypergroups. Finally, we show that every interval valued intuitionistic fuzzy quasi-hyperideal is the intersection of an interval valued intuitionistic fuzzy left hyperideal and an interval valued intuitionistic fuzzy right hyperideal.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2008.04a
• /
• pp.311-312
• /
• 2008

Fuzzy logic is introduced by Zadeh in 1965. It has been continuously developed by many mathematicians and knowledge engineers all over the world. A lot of papers concerning with the history of mathematics and the mathematical education related with fuzzy logic, but there is no paper concerning with Zadeh. In this article, we investigate his life and papers about fuzzy logic. We also compare two-valued logic, three-valued logic, fuzzy logic, intuisionistic logic and intuitionistic fuzzy sets. Finally we discuss about the expression of intuitionistic fuzzy sets.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.22 no.1
• /
• pp.126-134
• /
• 2012

By using the concept of intuitionistic interval-valued fuzzy sets, we introduce the notion of intuitionistic interval-valued fuzzy topology. And we study some fundamental properties of intuitionistic interval-valued fuzzy topological spaces: First, we obtain analogues[see Theorem 3.11 and 3.12] of neighborhood systems in ordinary topological spaces. Second, we obtain the result[see Theorem 4.9] corresponding to "the 14-set Theorem" in ordinary topological spaces. Finally, we give the initial structure on intuitionistic interval-valued fuzzy topologies[see Theorem 5.9].

• The Pure and Applied Mathematics
• /
• v.12 no.1
• /
• pp.33-45
• /
• 2005

We introduce the category ISet(H) of intuitionistic H-fuzzy sets and show that ISet(H) satisfies all the conditions of a topological universe except the terminal separator property. And we study the relation between Set(H) and ISet(H).

• Journal of the Korean Institute of Intelligent Systems
• /
• v.19 no.2
• /
• pp.265-272
• /
• 2009

Fuzzy number intuitionistic fuzzy sets (FNIFSs), each of which is characterized by a membership function and a non-membership function whose values are trigonometric fuzzy number rather than exact numbers, are a very useful means to describe the decision information in the process of decision making. Wang [10] developed some arithmetic aggregation operators, such as the fuzzy number intuitionistic fuzzy weighted averaging (FIFWA) operator, the fuzzy number intuitionistic fuzzy ordered weighted averaging (FIFOWA) operator and the fuzzy number intuitionistic fuzzy hybrid aggregation (FIFHA) operator. In this paper, based on the FIFHA operator and the FIFWA operator, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as fuzzy number intuitionistic fuzzy decision matrices where each of the elements is characterized by fuzzy number intuitionistic fuzzy numbers, and the information about attribute weights is partially known. An example is used to illustrate the applicability of the proposed approach.

• Journal of applied mathematics & informatics
• /
• v.35 no.3_4
• /
• pp.331-347
• /
• 2017

Soft sets are fantastic mathematical tools to handle imprecise and uncertain information in complicated situations. In this paper, we defined the hybrid structure which is the combination of soft set and complex number representation of intuitionistic fuzzy set. We defined basic set theoretic operations such as complement, union, intersection, restricted union, restricted intersection etc. for this hybrid structure. Moreover, we developed this theory to establish some more set theoretic operations like Disjunctive sum, difference, product, conjugate etc.