**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2696

# Search results for: ordered fuzzy point

##### 2696 On Completely Semiprime, Semiprime and Prime Fuzzy Ideals in Ordered Semigroups

**Authors:**
Jian Tang

**Abstract:**

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semigroups. Furthermore, we introduce the notion of semiprime fuzzy ideals of ordered semigroup S and establish the relations between completely semiprime fuzzy ideals and semiprime fuzzy ideals of S. Finally, we give a characterization of prime fuzzy ideals of an ordered semigroup S and show that a nonconstant fuzzy ideal f of an ordered semigroup S is prime if and only if f is twovalued, and max{f(a), f(b)} = inf f((aSb]), ∀a, b ∈ S.

**Keywords:**
Ordered fuzzy point,
fuzzy left (right) ideal of anordered semigroup,
completely semiprime fuzzy ideal,
semiprimefuzzy ideal,
prime fuzzy ideal.

##### 2695 On Weakly Prime and Weakly Quasi-Prime Fuzzy Left Ideals in Ordered Semigroups

**Authors:**
Jian Tang

**Abstract:**

In this paper, we first introduce the concepts of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S. Furthermore, we give some characterizations of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S by the ordered fuzzy points and fuzzy subsets of S.

**Keywords:**
Ordered semigroup,
ordered fuzzy point,
weakly prime
fuzzy left ideal,
weakly quasi-prime fuzzy left ideal.

##### 2694 Characterizations of Ordered Semigroups by (∈,∈ ∨q)-Fuzzy Ideals

**Authors:**
Jian Tang

**Abstract:**

Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈,∈ ∨q)-fuzzy ideals, (∈,∈ ∨q)-fuzzy bi-ideals and (∈,∈ ∨q)-fuzzy generalized bi-ideals of an ordered semigroup S, and investigate their related properties. Furthermore, we also define the upper and lower parts of fuzzy subsets of an ordered semigroup S, and investigate the properties of (∈,∈ ∨q)-fuzzy ideals of S. Finally, characterizations of regular ordered semigroups and intra-regular ordered semigroups by means of the lower part of (∈ ,∈ ∨q)-fuzzy left ideals, (∈,∈ ∨q)-fuzzy right ideals and (∈,∈ ∨q)- fuzzy (generalized) bi-ideals are given.

**Keywords:**
Ordered semigroup,
regular ordered semigroup,
intraregular
ordered semigroup,
(∈,
∈ ∨q)-fuzzy left (right) ideal of an
ordered semigroup,
(∈,
∈ ∨q)-fuzzy (generalized) bi-ideal of an
ordered semigroup.

##### 2693 Using Fuzzy Numbers in Heavy Aggregation Operators

**Authors:**
José M. Merigó,
Montserrat Casanovas

**Abstract:**

**Keywords:**
Aggregation operators,
Fuzzy numbers,
Fuzzy OWAoperator,
Heavy OWA operator.

##### 2692 The Intuitionistic Fuzzy Ordered Weighted Averaging-Weighted Average Operator and its Application in Financial Decision Making

**Authors:**
Shouzhen Zeng

**Abstract:**

**Keywords:**
Intuitionistic fuzzy numbers,
Weighted average,
OWA operator,
Financial decision making

##### 2691 On Tarski’s Type Theorems for L-Fuzzy Isotone and L-Fuzzy Relatively Isotone Maps on L-Complete Propelattices

**Authors:**
František Včelař,
Zuzana Pátíková

**Abstract:**

**Keywords:**
Fixed point,
L-complete propelattice,
L-fuzzy
(relatively) isotone map,
residuated lattice,
transitivity.

##### 2690 A Further Study on the 4-Ordered Property of Some Chordal Ring Networks

**Authors:**
Shin-Shin Kao,
Hsiu-Chunj Pan

**Abstract:**

Given a graph G. A cycle of G is a sequence of vertices of G such that the first and the last vertices are the same. A hamiltonian cycle of G is a cycle containing all vertices of G. The graph G is k-ordered (resp. k-ordered hamiltonian) if for any sequence of k distinct vertices of G, there exists a cycle (resp. hamiltonian cycle) in G containing these k vertices in the specified order. Obviously, any cycle in a graph is 1-ordered, 2-ordered and 3- ordered. Thus the study of any graph being k-ordered (resp. k-ordered hamiltonian) always starts with k = 4. Most studies about this topic work on graphs with no real applications. To our knowledge, the chordal ring families were the first one utilized as the underlying topology in interconnection networks and shown to be 4-ordered. Furthermore, based on our computer experimental results, it was conjectured that some of them are 4-ordered hamiltonian. In this paper, we intend to give some possible directions in proving the conjecture.

**Keywords:**
Hamiltonian cycle,
4-ordered,
Chordal rings,
3-regular.

##### 2689 Intuitionistic Fuzzy Points in Semigroups

**Authors:**
Sujit Kumar Sardar Manasi Mandal Samit Kumar Majumder

**Abstract:**

**Keywords:**
Semigroup,
Regular(intra-regular) semigroup,
Intuitionistic fuzzy point,
Intuitionistic fuzzy subsemigroup,
Intuitionistic fuzzy ideal,
Intuitionistic fuzzy interior ideal,
Intuitionistic fuzzy semiprime ideal,
Intuitionistic fuzzy prime ideal.

##### 2688 Fixed Point Theorems for Set Valued Mappings in Partially Ordered Metric Spaces

**Authors:**
Ismat Beg,
Asma Rashid Butt

**Abstract:**

Let (X,) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X, then xn x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F(x), F(y)) ≤ κd(x, y), for all x y, (ii) if d(x, y) < ε < 1 for some y ∈ F(x) then x y, (iii) there exists x0 ∈ X, and some x1 ∈ F(x0) with x0 x1 such that d(x0, x1) < 1. It is shown that F has a fixed point. Several consequences are also obtained.

**Keywords:**
Fixed point,
partially ordered set,
metric space,
set
valued mapping.

##### 2687 Maximum Power Point Tracking Using FLC Tuned with GA

**Authors:**
Mohamed Amine Haraoubia,
Abdelaziz Hamzaoui,
Najib Essounbouli

**Abstract:**

The pursuit of the MPPT has led to the development of many kinds of controllers, one of which is the Fuzzy Logic controller, which has proven its worth. To further tune this controller this paper will discuss and analyze the use of Genetic Algorithms to tune the Fuzzy Logic Controller. It will provide an introduction to both systems, and test their compatibility and performance.

**Keywords:**
Fuzzy logic controller (FLC),
fuzzy logic (FL),
genetic algorithm (GA),
maximum power point (MPP),
maximum power point tracking (MPPT).

##### 2686 Comparison Results of Two-point Fuzzy Boundary Value Problems

**Authors:**
Hsuan-Ku Liu

**Abstract:**

This paper investigates the solutions of two-point fuzzy boundary value problems as the form x = f(t, x(t)), x(0) = A and x(l) = B, where A and B are fuzzy numbers. There are four different solutions for the problems when the lateral type of H-derivative is employed to solve the problems. As f(t, x) is a monotone function of x, these four solutions are reduced to two different solutions. As f(t, x(t)) = λx(t) or f(t, x(t)) = -λx(t), solutions and several comparison results are presented to indicate advantages of each solution.

**Keywords:**
Fuzzy derivative,
lateral type of H-derivative,
fuzzy differential equations,
fuzzy boundary value problems,
boundary value problems.

##### 2685 Analysis on Fractals in Intuitionistic Fuzzy Metric Spaces

**Authors:**
R. Uthayakumar,
D. Easwaramoorthy

**Abstract:**

**Keywords:**
Fractal Analysis,
Fixed Point,
Contraction,
Iterated Function System,
Intuitionistic Fuzzy Metric Space.

##### 2684 Order Penetration Point Location using Fuzzy Quadratic Programming

**Authors:**
Hamed Rafiei,
Masoud Rabbani

**Abstract:**

**Keywords:**
Fuzzy sets theory,
Hybrid MTS/MTO,
Order penetration point,
Quadratic programming.

##### 2683 Determination of Adequate Fuzzy Inequalities for their Usage in Fuzzy Query Languages

**Authors:**
Marcel Shirvanian,
Wolfram Lippe

**Abstract:**

**Keywords:**
Fuzzy Databases,
Fuzzy Inequalities,
Fuzzy QueryLanguages,
Fuzzy Ranking.

##### 2682 On the Fuzzy Difference Equation xn+1 = A +

**Authors:**
Qianhong Zhang,
Lihui Yang,
Daixi Liao,

**Abstract:**

In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.

**Keywords:**
Fuzzy difference equation,
boundedness,
persistence,
equilibrium point,
asymptotic behaviour.

##### 2681 Fuzzy Shortest Paths Approximation for Solving the Fuzzy Steiner Tree Problem in Graphs

**Authors:**
Miloš Šeda

**Abstract:**

**Keywords:**
Steiner tree,
single shortest path problem,
fuzzyranking,
binary heap,
priority queue.

##### 2680 Sensitizing Rules for Fuzzy Control Charts

**Authors:**
N. Pekin Alakoç,
A. Apaydın

**Abstract:**

**Keywords:**
Fuzzy set theory,
Quality control charts,
Run Rules,
Unnatural patterns.

##### 2679 Ranking Fuzzy Numbers Based On Epsilon-Deviation Degree

**Authors:**
Vincent F. Yu,
Ha Thi Xuan Chi

**Abstract:**

Nejad and Mashinchi (2011) proposed a revision for ranking fuzzy numbers based on the areas of the left and the right sides of a fuzzy number. However, this method still has some shortcomings such as lack of discriminative power to rank similar fuzzy numbers and no guarantee the consistency between the ranking of fuzzy numbers and the ranking of their images. To overcome these drawbacks, we propose an epsilon-deviation degree method based on the left area and the right area of a fuzzy number, and the concept of the centroid point. The main advantage of the new approach is the development of an innovative index value which can be used to consistently evaluate and rank fuzzy numbers. Numerical examples are presented to illustrate the efficiency and superiority of the proposed method.

**Keywords:**
Ranking fuzzy numbers,
Centroid,
Deviation degree.

##### 2678 On Fuzzy Weakly-Closed Sets

**Authors:**
J. Mahanta,
P.K. Das

**Abstract:**

A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets. Alongwith the study of fundamental results of such closed sets, we define and characterize fuzzy weakly compact space and fuzzy weakly closed space.

**Keywords:**
Fuzzy weakly-closed set,
fuzzy weakly-closed
space,
fuzzy weakly-compactness,
MSC: 54A40,
54D30.

##### 2677 Fuzzy Rules Generation and Extraction from Support Vector Machine Based on Kernel Function Firing Signals

**Authors:**
Prasan Pitiranggon,
Nunthika Benjathepanun,
Somsri Banditvilai,
Veera Boonjing

**Abstract:**

**Keywords:**
Fuzzy Rule Base,
Rule Extraction,
Rule Generation,
Support Vector Machine.

##### 2676 A Centroid Ranking Approach Based Fuzzy MCDM Model

**Abstract:**

This paper suggests ranking alternatives under fuzzy MCDM (multiple criteria decision making) via an centroid based ranking approach, where criteria are classified to benefit qualitative, benefit quantitative and cost quantitative ones. The ratings of alternatives versus qualitative criteria and the importance weights of all criteria are assessed in linguistic values represented by fuzzy numbers. The membership function for the final fuzzy evaluation value of each alternative can be developed through α-cuts and interval arithmetic of fuzzy numbers. The distance between the original point and the relative centroid is applied to defuzzify the final fuzzy evaluation values in order to rank alternatives. Finally a numerical example demonstrates the computation procedure of the proposed model.

**Keywords:**
Fuzzy MCDM,
Criteria,
Fuzzy number,
Ranking,
Relative centroid.

##### 2675 Fuzzy Logic Based Maximum Power Point Tracking Designed for 10kW Solar Photovoltaic System with Different Membership Functions

**Authors:**
S. Karthika,
K. Velayutham,
P. Rathika,
D. Devaraj

**Abstract:**

The electric power supplied by a photovoltaic power generation systems depends on the solar irradiation and temperature. The PV system can supply the maximum power to the load at a particular operating point which is generally called as maximum power point (MPP), at which the entire PV system operates with maximum efficiency and produces its maximum power. Hence, a Maximum power point tracking (MPPT) methods are used to maximize the PV array output power by tracking continuously the maximum power point. The proposed MPPT controller is designed for 10kW solar PV system installed at Cape Institute of Technology. This paper presents the fuzzy logic based MPPT algorithm. However, instead of one type of membership function, different structures of fuzzy membership functions are used in the FLC design. The proposed controller is combined with the system and the results are obtained for each membership functions in Matlab/Simulink environment. Simulation results are decided that which membership function is more suitable for this system.

**Keywords:**
MPPT,
DC-DC Converter,
Fuzzy logic controller,
Photovoltaic (PV) system.

##### 2674 The Analysis of Different Classes of Weighted Fuzzy Petri Nets and Their Features

**Authors:**
Yurii Bloshko,
Oksana Olar

**Abstract:**

This paper presents the analysis of six different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.

**Keywords:**
Fuzzy petri net,
intelligent computational techniques,
knowledge representation,
triangular norms.

##### 2673 Normalization and Constrained Optimization of Measures of Fuzzy Entropy

**Authors:**
K.C. Deshmukh,
P.G. Khot,
Nikhil

**Abstract:**

**Keywords:**
Fuzzy set,
Uncertainty,
Fuzzy entropy,
Normalization,
Membership function

##### 2672 Compromise Ratio Method for Decision Making under Fuzzy Environment using Fuzzy Distance Measure

**Authors:**
Debashree Guha,
Debjani Chakraborty

**Abstract:**

The aim of this paper is to adopt a compromise ratio (CR) methodology for fuzzy multi-attribute single-expert decision making proble. In this paper, the rating of each alternative has been described by linguistic terms, which can be expressed as triangular fuzzy numbers. The compromise ratio method for fuzzy multi-attribute single expert decision making has been considered here by taking the ranking index based on the concept that the chosen alternative should be as close as possible to the ideal solution and as far away as possible from the negative-ideal solution simultaneously. From logical point of view, the distance between two triangular fuzzy numbers also is a fuzzy number, not a crisp value. Therefore a fuzzy distance measure, which is itself a fuzzy number, has been used here to calculate the difference between two triangular fuzzy numbers. Now in this paper, with the help of this fuzzy distance measure, it has been shown that the compromise ratio is a fuzzy number and this eases the problem of the decision maker to take the decision. The computation principle and the procedure of the compromise ratio method have been described in detail in this paper. A comparative analysis of the compromise ratio method previously proposed [1] and the newly adopted method have been illustrated with two numerical examples.

**Keywords:**
Compromise ratio method,
Fuzzy multi-attributesingle-expert decision making,
Fuzzy number,
Linguistic variable

##### 2671 On Strong(Weak) Domination in Fuzzy Graphs

**Authors:**
C.Natarajan,
S.K.Ayyaswamy

**Abstract:**

Let G be a fuzzy graph. Then D Ôèå V is said to be a strong (weak) fuzzy dominating set of G if every vertex v ∈ V -D is strongly (weakly) dominated by some vertex u in D. We denote a strong (weak) fuzzy dominating set by sfd-set (wfd-set). The minimum scalar cardinality of a sfd-set (wfd-set) is called the strong (weak) fuzzy domination number of G and it is denoted by γsf (G)γwf (G). In this paper we introduce the concept of strong (weak) domination in fuzzy graphs and obtain some interesting results for this new parameter in fuzzy graphs.

**Keywords:**
Fuzzy graphs,
fuzzy domination,
strong (weak) fuzzy domination number.

##### 2670 Financing Decision and Productivity Growth for the Venture Capital Industry Using High-Order Fuzzy Time Series

**Authors:**
Shang-En Yu

**Abstract:**

Human society, there are many uncertainties, such as economic growth rate forecast of the financial crisis, many scholars have, since the the Song Chissom two scholars in 1993 the concept of the so-called fuzzy time series (Fuzzy Time Series)different mode to deal with these problems, a previous study, however, usually does not consider the relevant variables selected and fuzzy process based solely on subjective opinions the fuzzy semantic discrete, so can not objectively reflect the characteristics of the data set, in addition to carrying outforecasts are often fuzzy rules as equally important, failed to consider the importance of each fuzzy rule. For these reasons, the variable selection (Factor Selection) through self-organizing map (Self-Organizing Map, SOM) and proposed high-end weighted multivariate fuzzy time series model based on fuzzy neural network (Fuzzy-BPN), and using the the sequential weighted average operator (Ordered Weighted Averaging operator, OWA) weighted prediction. Therefore, in order to verify the proposed method, the Taiwan stock exchange (Taiwan Stock Exchange Corporation) Taiwan Weighted Stock Index (Taiwan Stock Exchange Capitalization Weighted Stock Index, TAIEX) as experimental forecast target, in order to filter the appropriate variables in the experiment Finally, included in other studies in recent years mode in conjunction with this study, the results showed that the predictive ability of this study further improve.

**Keywords:**
Heterogeneity,
residential mortgage loans,
foreclosure.

##### 2669 Fuzzy Logic Approach to Robust Regression Models of Uncertain Medical Categories

**Authors:**
Arkady Bolotin

**Abstract:**

Dichotomization of the outcome by a single cut-off point is an important part of various medical studies. Usually the relationship between the resulted dichotomized dependent variable and explanatory variables is analyzed with linear regression, probit regression or logistic regression. However, in many real-life situations, a certain cut-off point dividing the outcome into two groups is unknown and can be specified only approximately, i.e. surrounded by some (small) uncertainty. It means that in order to have any practical meaning the regression model must be robust to this uncertainty. In this paper, we show that neither the beta in the linear regression model, nor its significance level is robust to the small variations in the dichotomization cut-off point. As an alternative robust approach to the problem of uncertain medical categories, we propose to use the linear regression model with the fuzzy membership function as a dependent variable. This fuzzy membership function denotes to what degree the value of the underlying (continuous) outcome falls below or above the dichotomization cut-off point. In the paper, we demonstrate that the linear regression model of the fuzzy dependent variable can be insensitive against the uncertainty in the cut-off point location. In the paper we present the modeling results from the real study of low hemoglobin levels in infants. We systematically test the robustness of the binomial regression model and the linear regression model with the fuzzy dependent variable by changing the boundary for the category Anemia and show that the behavior of the latter model persists over a quite wide interval.

**Keywords:**
Categorization,
Uncertain medical categories,
Binomial regression model,
Fuzzy dependent variable,
Robustness.

##### 2668 Novel and Different Definitions for Fuzzy Union and Intersection Operations

**Authors:**
Aarthi Chandramohan,
M. V. C. Rao

**Abstract:**

**Keywords:**
Centroid,
fuzzy set operations,
intersection,
triangular norms ,
triangular S-norms,
union.

##### 2667 Reliability Evaluation using Triangular Intuitionistic Fuzzy Numbers Arithmetic Operations

**Authors:**
G. S. Mahapatra,
T. K. Roy

**Abstract:**

**Keywords:**
Fuzzy set,
Intuitionistic fuzzy number,
Systemreliability,
Triangular intuitionistic fuzzy number.