• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.1
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• pp.82-88
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• 2010

In this paper we continue the study of intuitionistic fuzzy groups by introducing the notion of intuitionistic fuzzy normal subgroup based on intuitionistic fuzzy space as a generalization of fuzzy normal subgroup.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.185-190
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• 2022

The aim of this article is to define fuzzy maximal open cover and discuss its few properties. we also defined and study fuzzy m-compact space and discussed its properties. Also we obtain few more results on fuzzy minimal c-regular and fuzzy minimal c-normal spaces. We have proved that a fuzzy Haussdorff m-compact space is fuzzy minimal c-normal.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.3
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• pp.280-285
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• 2001

We introduce the new concepts of some fuzzy continuous and closed mappings and study their properties. Also we investigate the properties of fuzzy mildly normal spaces.

• East Asian mathematical journal
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• v.29 no.3
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• pp.269-278
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• 2013

A fuzzy set A defined on a probability space (${\Omega}$, $\mathfrak{F}$, P) is called a fuzzy event. Zadeh defines the probability of the fuzzy event A using the probability P. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. We calculate the normal fuzzy probability for generalized trapezoidal fuzzy sets and give some examples.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.457-475
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• 2010

In this paper, we have use a fuzzy bitopological space (X, $\tau_1$, $\tau_2$) to create a family $\tau_{ij}^s$ which is a supra fuzzy topology on X. Also, we introduce and study the concepts of r-($\tau_i$, $\tau_j$)-generalized fuzzy regular closed, r-($\tau_i$, $\tau_j$)-generalized fuzzy strongly semi-closed and r-($\tau_i$, $\tau_j$)-generalized fuzzy regular strongly semi-closed sets in fuzzy bitopological space in the sense of $\check{S}$ostak. Also, these classes of fuzzy subsets are applied for constructing several type of fuzzy closed mapping and some type of fuzzy separation axioms called fuzzy binormal, fuzzy mildly binormal and fuzzy almost pairwise normal.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1287-1303
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• 2015

The Hausdorff topology induced by a fuzzy metric space under more weak assumptions is investigated in this paper. Another purpose of this paper is to obtain the Banach contraction theorem in fuzzy metric space based on a natural concept of Cauchy sequence in fuzzy metric space.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.843-856
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• 2009

In possibility framework, we propose two risk measures named Fuzzy Value-at-Risk and Fuzzy Conditional Value-at-Risk, based on Credibility measure. Two portfolio optimization models for fuzzy portfolio selection problems are formulated. Then a chaos genetic algorithm based on fuzzy simulation is designed, and finally computational results show that the two risk measures can play a role in possibility space similar to Value-at-Risk and Conditional Value-at-Risk in probability space.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.05a
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• pp.277-280
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• 2002

In this paper, we characterize the Borel $\sigma$-field generated by the Hausdorff-Skorokhod metric on the space of normal and upper-semicontinuous fuzzy sets with compact support in the Ecleadean space R$\^$n/. As a result. we give a characterization of measurable fuzzy mappings .

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.383-399
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• 2013

In this paper, we establish two types of strong law of large numbers for fuzzy random variables taking values on the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable Banach space. The first result is SLLN for strong-compactly uniformly integrable fuzzy random variables, and the other is the case of that the averages of its expectations converges.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.215-223
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• 2013

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that the weighted averages of expectations of fuzzy random variables converge. Finally, weak laws of large numbers for weighted sums of strongly tight or identically distributed fuzzy random variables are obtained as corollaries.