• Journal of the Korean Society of Safety
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• v.8 no.4
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• pp.91-94
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• 1993

The main purpose of this study was to develop fuzzy models in order to decide system failure rate in industrial accident prevention. The purposed linguistic approach uses the Zadeh's concept of a linguistic variable with value which are not number. The problem of measurement Is the assignment of numbers to reprresnt properties of the involved events, object, or situation. Thus, in this study, part standard compatibility function was used.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.2
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• pp.212-217
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• 2012

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 generalized triangular fuzzy set and apply the extended algebraic operations to these fuzzy sets. A generalized triangular fuzzy set is symmetric and may not have value 1. For two generalized triangular fuzzy sets $A$ and $B$, $A(+)B$ and $A(-)B$ become generalized trapezoidal fuzzy sets, but $A({\cdot})B$ and $A(/)B$ need not to be a generalized triangular fuzzy set or a generalized trapezoidal fuzzy set. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. And we calculate the normal fuzzy probability for generalized triangular fuzzy sets.

• Journal of Digital Convergence
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• v.19 no.10
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• pp.377-382
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• 2021

A fuzzy relation between X and Y as fuzzy subset of X × Y was proposed by Zadeh. Subsequently, several researchers have applied the notion of fuzzy subsets to various branches of mathematics and computer sciences. Murali an Nemitz have studied fuzzy relations connected with fuzzy equivalence relations and fuzzy functions. Ounalli and Jaoua defined a fuzzy difunctional relation on a set. difunctional relations are versatile mathematical tool, which can be used in software design and in database theory. Their work have revealed the usefulness of difunctional relations in program specification and in defining program correctness. The main goal of this paper is to define a fuzzy deterministic relation on a set, characterize the fuzzy deterministic relation as its level subsets and investigate some properties in connection with fuzzy deterministic relation. In particular we prove that a fuzzy relation R is fuzzy deterministic iff R is a fuzzy function.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.73-84
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• 2008

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Aranassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to commutative ideals in BCK-algebras. The notion of an intuitionistic fuzzy commutative ideal of a BCK-algebra is introduced, and some related properties are investigated. Characterizations of an intuitionistic fuzzy commutative ideal are given. Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy commutative ideal are given. Using a collection of commutative ideals, intuitionistic fuzzy commutative ideals are established.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.6
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• pp.804-806
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• 2007

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. Recently, Hong [Fuzzy Sets and Systems 158(2007) 739-746] defined a broader class of bell-shaped fuzzy intervals. Then he study t-norms which are consistent with these particular types of fuzzy intervals as applications of a result proved by Mesiar on a strict f-norm based shape preserving additions of LR-fuzzy intervals with unbounded support. In this note, we give a direct proof of the main results of Hong.

• Journal of the Korean School Mathematics Society
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• v.6 no.1
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• pp.27-43
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• 2003

This paper introduces some theories that can be effectively applied for the development of teaching and learning mathematics using fuzzy theory developed by Zadeh who defined fuzzy set and knowledge space by Doignon and Falmagne. Especially, we expect that two theories mentioned above are expected to solve the situation that could not be taken care of the present evaluation method.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.111-125
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• 1992

Since Zadeh's definition for probability of fuzzy event is presented, alternative definitions for probability of fuzzy event is suggested. Also various properties of these new definitions have been presented. In this paper it is our purpose to show the works continued by finding a natural definition of a fuzzy probability measure on an arbitrary fuzzy measurable space. Thus, the main process is to observe fuzzy probability measure to be qualified by weak axioms of boundary condition, monotonicity and continuity suggested by Klir (1988). Especially, we will show that these axioms are satisfied through in succession of modifications from the Yager's method.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.283-295
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• 2015

The atom-bond connectivity index of a graph G (ABC index for short) is defined as the summation of quantities $\sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}}$ over all edges of G. A cactus graph is a connected graph in which every block is an edge or a cycle. The aim of this paper is to obtain the first and second maximum values of the ABC index among all n vertex cactus graphs.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1215-1227
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• 2012

The membership of the generalized local cohomology modules $H_a^i$(M,N) of two R-modules M and N with respect to an ideal a in certain Serre subcategories of the category of modules is studied from below ($i<t$). Furthermore, the behaviour of the $n$th graded component $H_a^i(M,N)_n$ of the generalized local cohomology modules with respect to an ideal containing the irrelevant ideal as $n{\rightarrow}-{\infty}$ is investigated by using the above result, in certain graded situations.

• Journal of Power Electronics
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• v.9 no.6
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• pp.940-948
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• 2009

The main objective of this a paper is to improve the efficiency of permanent magnet synchronous motors (PMSMs) by using an improved direct torque control (DTC) strategy. The basic idea behind the proposed strategy is to predict the impact of a small change in the stator flux amplitude at each sampling period to decrease electrical loss before the change is applied. Accordingly, at every sampling time, a voltage vector is predicted and applied to the machine to fulfill the flux change. The motor drive simulations confirm a significant improvement in efficiency as well as a very fast and smooth response under the proposed strategy.