Search results for: Fuzzy operator

Authors: Behrouz Fathi-Vajargah, Sara Ghasemalipour

Abstract:

This paper studies a random fuzzy queueing system that the interarrival times of customers arriving at the server and the service times are independent and identically distributed random fuzzy variables. We match the random fuzzy queueing system with the random fuzzy alternating renewal process and we do not use from α-pessimistic and α-optimistic values to estimate the average chance of the event ”random fuzzy queueing system is busy at time t”, we employ the fuzzy simulation method in practical applications. Some theorem is proved and finally we solve a numerical example with fuzzy simulation method.

Keywords: Random fuzzy variables, Fuzzy simulation, Queueing system, Interarrival times.

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Authors: R. Uthayakumar, D. Easwaramoorthy

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This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we analyze some results on intuitionistic fuzzy fractals in the standard intuitionistic fuzzy metric spaces with respect to the Hausdorff intuitionistic fuzzy metrics.

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

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Authors: Amit Kumar, Anila Gupta, Amarpreet Kaur

Abstract:

In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy assignment problems by representing all the parameters as triangular fuzzy numbers. The advantages of the pro-posed method are also discussed. To illustrate the proposed method a fuzzy assignment problem is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy assignment problems occurring in real life situations.

Keywords: Fuzzy assignment problem, Ranking function, Triangular fuzzy numbers.

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Authors: José M. Merigó, Anna M. Gil-Lafuente

Abstract:

We study different types of aggregation operators such as the ordered weighted averaging (OWA) operator and the generalized OWA (GOWA) operator. We analyze the use of OWA operators in the Minkowski distance. We will call these new distance aggregation operator the Minkowski ordered weighted averaging distance (MOWAD) operator. We give a general overview of this type of generalization and study some of their main properties. We also analyze a wide range of particular cases found in this generalization such as the ordered weighted averaging distance (OWAD) operator, the Euclidean ordered weighted averaging distance (EOWAD) operator, the normalized Minkowski distance, etc. Finally, we give an illustrative example of the new approach where we can see the different results obtained by using different aggregation operators.

Keywords: Aggregation operators, Minkowski distance, OWA operators, Selection of strategies.

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Authors: Shaoquan Sun, Qianqian Li

Abstract:

Based on the theory of intuitionistic fuzzy sets, the concepts of intuitionistic fuzzy subalgebras with thresholds (λ, μ) and intuitionistic fuzzy ideals with thresholds (λ, μ) of BCI-algebras are introduced and some properties of them are discussed.

Keywords: BCI-algebra, intuitionistic fuzzy set, intuitionistic fuzzy subalgebra with thresholds (λ, μ), intuitionistic fuzzy ideal with thresholds (λ, μ).

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Authors: Amit Kumar, Manjot Kaur

Abstract:

In this paper, the fuzzy linear programming formulation of fuzzy maximal flow problems are proposed and on the basis of the proposed formulation a method is proposed to find the fuzzy optimal solution of fuzzy maximal flow problems. In the proposed method all the parameters are represented by triangular fuzzy numbers. By using the proposed method the fuzzy optimal solution of fuzzy maximal flow problems can be easily obtained. To illustrate the proposed method a numerical example is solved and the obtained results are discussed.

Keywords: Fuzzy linear programming, Fuzzy maximal flow problem, Ranking function, Triangular fuzzy number

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Authors: Liu Ping

Abstract:

In this paper, for an arbitrary multiplicative functional f from the set of all upper triangular fuzzy matrices to the fuzzy algebra, we prove that there exist a multiplicative functional F and a functional G from the fuzzy algebra to the fuzzy algebra such that the image of an upper triangular fuzzy matrix under f can be represented as the product of all the images of its main diagonal elements under F and other elements under G.

Keywords: Multiplicative functional, triangular fuzzy matrix, fuzzy addition operation, fuzzy multiplication operation.

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Authors: S.K. Sardar, D. Mandal, R. Mukherjee

Abstract:

The notions of intuitionistic fuzzy h-ideal and normal intuitionistic fuzzy h-ideal in Γ-hemiring are introduced and some of the basic properties of these ideals are investigated. Cartesian product of intuitionistic fuzzy h-ideals is also defined. Finally a characterization of intuitionistic fuzzy h-ideals in terms of fuzzy relations is obtained.

Keywords: Γ-hemiring, fuzzy h-ideal, normal, cartesian product.Mathematics Subject Classification[2000] :08A72, 16Y99

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Authors: Shaoquan Sun, Qianqian Li

Abstract:

The aim of this paper is to introduce the notions of intuitionistic T-S fuzzy subalgebras and intuitionistic T-S fuzzy ideals in BCI-algebras, and then to investigate their basic properties.

Keywords: BCI-algebra, intuitionistic T-S fuzzy subalgebra, intuitionistic T-S fuzzy ideal, norm intersection, direct product, epimorphism, isomorphism.

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Authors: Hidehiko Okada

Abstract:

The author proposes an extension of genetic algorithm (GA) for solving fuzzy-valued optimization problems. In the proposed GA, values in the genotypes are not real numbers but fuzzy numbers. Evolutionary processes in GA are extended so that GA can handle genotype instances with fuzzy numbers. The proposed method is applied to evolving neural networks with fuzzy weights and biases. Experimental results showed that fuzzy neural networks evolved by the fuzzy GA could model hidden target fuzzy functions well despite the fact that no training data was explicitly provided.

Keywords: Evolutionary algorithm, genetic algorithm, fuzzy number, neural network, neuroevolution.

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Authors: Mehtap Dursun, E. Ertugrul Karsak, Melis Almula Karadayi

Abstract:

The management of the health-care wastes is one of the most important problems in Istanbul, a city with more than 12 million inhabitants, as it is in most of the developing countries. Negligence in appropriate treatment and final disposal of the healthcare wastes can lead to adverse impacts to public health and to the environment. This paper employs a fuzzy multi-criteria group decision making approach, which is based on the principles of fusion of fuzzy information, 2-tuple linguistic representation model, and technique for order preference by similarity to ideal solution (TOPSIS), to evaluate health-care waste (HCW) treatment alternatives for Istanbul. The evaluation criteria are determined employing nominal group technique (NGT), which is a method of systematically developing a consensus of group opinion. The employed method is apt to manage information assessed using multigranularity linguistic information in a decision making problem with multiple information sources. The decision making framework employs ordered weighted averaging (OWA) operator that encompasses several operators as the aggregation operator since it can implement different aggregation rules by changing the order weights. The aggregation process is based on the unification of information by means of fuzzy sets on a basic linguistic term set (BLTS). Then, the unified information is transformed into linguistic 2-tuples in a way to rectify the problem of loss information of other fuzzy linguistic approaches.

Keywords: Group decision making, health care waste management, multi-criteria decision making, OWA, TOPSIS, 2-tuple linguistic representation

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Authors: M. Hadi Mashinchi, M. Reza Mashinchi, Siti Mariyam H. J. Shamsuddin

Abstract:

In this paper a genetic algorithms approach for solving the linear and quadratic fuzzy equations Ãx̃=B̃ and Ãx̃² + B̃x̃=C̃ , where Ã, B̃, C̃ and x̃ are fuzzy numbers is proposed by genetic algorithms. Our genetic based method initially starts with a set of random fuzzy solutions. Then in each generation of genetic algorithms, the solution candidates converge more to better fuzzy solution x̃_b . In this proposed method the final reached x̃_b is not only restricted to fuzzy triangular and it can be fuzzy number.

Keywords: Fuzzy coefficient, fuzzy equation, genetic algorithms.

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Authors: José M. Merigó, Montserrat Casanovas

Abstract:

We present the induced generalized hybrid averaging (IGHA) operator. It is a new aggregation operator that generalizes the hybrid averaging (HA) by using generalized means and order inducing variables. With this formulation, we get a wide range of mean operators such as the induced HA (IHA), the induced hybrid quadratic averaging (IHQA), the HA, etc. The ordered weighted averaging (OWA) operator and the weighted average (WA) are included as special cases of the HA operator. Therefore, with this generalization we can obtain a wide range of aggregation operators such as the induced generalized OWA (IGOWA), the generalized OWA (GOWA), etc. We further generalize the IGHA operator by using quasi-arithmetic means. Then, we get the Quasi-IHA operator. Finally, we also develop an illustrative example of the new approach in a financial decision making problem. The main advantage of the IGHA is that it gives a more complete view of the decision problem to the decision maker because it considers a wide range of situations depending on the operator used.

Keywords: Decision making, Aggregation operators, OWA operator, Generalized means, Selection of investments.

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Authors: Hesam Mahzoon

Abstract:

By using the two existing operators, we have defined an operator, which is an extension for them. In this paper, first the operator is introduced. Then, using this operator, the subclasses of multivalent functions are defined. These subclasses of multivalent functions are utilized in order to obtain coefficient inequalities, extreme points, and integral means inequalities for functions belonging to these classes.

Keywords: Coefficient inequalities, extreme points, integral means, multivalent functions, Al-Oboudi operator, and Sãlãgean operator.

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Authors: Maslina Darus, Khalifa Al-Shaqsi

Abstract:

In this paper, a generalized derivatives operator n λ,βf introduced by the authors will be discussed. Some subordination and superordination results involving this operator for certain normalized analytic functions in the open unit disk will be investigated. Our results extend corresponding previously known results.

Keywords: Analytic functions, Univalent functions, Derivative operator, Differential subordination, Differential superordination.

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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.

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Authors: José M. Merigó, Anna M. Gil-Lafuente

Abstract:

Different types of aggregation operators such as the ordered weighted quasi-arithmetic mean (Quasi-OWA) operator and the normalized Hamming distance are studied. We introduce the use of the OWA operator in generalized distances such as the quasiarithmetic distance. We will call these new distance aggregation the ordered weighted quasi-arithmetic distance (Quasi-OWAD) operator. We develop a general overview of this type of generalization and study some of their main properties such as the distinction between descending and ascending orders. We also consider different families of Quasi-OWAD operators such as the Minkowski ordered weighted averaging distance (MOWAD) operator, the ordered weighted averaging distance (OWAD) operator, the Euclidean ordered weighted averaging distance (EOWAD) operator, the normalized quasi-arithmetic distance, etc.

Keywords: Aggregation operators, Distance measures, Quasi- OWA operator.

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Authors: Hadi Sadoghi Yazdi, Tahereh Royani, Mehri Sadoghi Yazdi, Sohrab Effati

Abstract:

In this paper, a new version of support vector regression (SVR) is presented namely Fuzzy Cost SVR (FCSVR). Individual property of the FCSVR is operation over fuzzy data whereas fuzzy cost (fuzzy margin and fuzzy penalty) are maximized. This idea admits to have uncertainty in the penalty and margin terms jointly. Robustness against noise is shown in the experimental results as a property of the proposed method and superiority relative conventional SVR.

Keywords: Support vector regression, Fuzzy input, Fuzzy cost.

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Authors: Kavikumar, Azme Khamis, Young Bae Jun,

Abstract:

The purpose of the present paper is to study the concept of fuzzy bi-ideals in ternary semirings. We give some characterizations of fuzzy bi-ideals. Characterizations of regular ternary semirings are provided.

Keywords: Fuzzy ternary subsemiring, fuzzy quasi-ideal, fuzzy bi-ideal, regular ternary semiring

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Authors: N.Subramanian, U.K.Misra

Abstract:

The aim of this paper is to introduce and study a new concept of strong double χ2 (M,A, Δ) of fuzzy numbers and also some properties of the resulting sequence spaces of fuzzy numbers were examined.

Keywords: Modulus function, fuzzy number, metric space.

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Authors: Yuli Hu, Shaoquan Sun

Abstract:

The aim of this paper is to introduce the concepts of (∈, ∈∨q)-fuzzy subalgebras, (∈,∈∨q)-fuzzy ideals and (∈,∈∨q)-fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.

Keywords: BCI-algebras with operators, (∈, ∈∨q)-fuzzy subalgebras, (∈, ∈∨q)-fuzzy ideals, (∈, ∈∨q)-fuzzy quotient algebras.

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Authors: José M. Merigó, Montserrat Casanovas

Abstract:

We study the problem of decision making with Dempster-Shafer belief structure. We analyze the previous work developed by Yager about using the ordered weighted averaging (OWA) operator in the aggregation of the Dempster-Shafer decision process. We discuss the possibility of aggregating with an ascending order in the OWA operator for the cases where the smallest value is the best result. We suggest the introduction of the ordered weighted geometric (OWG) operator in the Dempster-Shafer framework. In this case, we also discuss the possibility of aggregating with an ascending order and we find that it is completely necessary as the OWG operator cannot aggregate negative numbers. Finally, we give an illustrative example where we can see the different results obtained by using the OWA, the Ascending OWA (AOWA), the OWG and the Ascending OWG (AOWG) operator.

Keywords: Decision making, aggregation operators, Dempster- Shafer theory of evidence, Uncertainty, OWA operator, OWG operator.

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Authors: T. Pathinathan, M. Peter

Abstract:

Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: Double layered fuzzy graph, double layered non-cyclic fuzzy graph, strong, order, degree and size.

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Authors: Yuli Hu, Shaoquan Sun

Abstract:

The aim of this paper is to introduce the concepts of generalized fuzzy subalgebras, generalized fuzzy ideals and generalized fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.

Keywords: BCI-algebras with operators, generalized fuzzy subalgebras, generalized fuzzy ideals, generalized fuzzy quotient algebras.

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Authors: Chen-Yuan Chen, Wan-I Lee, Yi-Chaio Sui, Cheng-Wu Chen

Abstract:

This study focuses on the development of triangular fuzzy numbers, the revising of triangular fuzzy numbers, and the constructing of a HCFN (half-circle fuzzy number) model which can be utilized to perform more plural operations. They are further transformed for trigonometric functions and polar coordinates. From half-circle fuzzy numbers we can conceive cylindrical fuzzy numbers, which work better in algebraic operations. An example of fuzzy control is given in a simulation to show the applicability of the proposed half-circle fuzzy numbers.

Keywords: triangular fuzzy number, half-circle fuzzy numbers, predictions, polar coordinates, Lyapunov method

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Authors: Shinoj T. K, Sunil Jacob John

Abstract:

In this paper a new concept named Intuitionistic Fuzzy Multiset is introduced. The basic operations on Intuitionistic Fuzzy Multisets such as union, intersection, addition, multiplication etc. are discussed. An application of Intuitionistic Fuzzy Multiset in Medical diagnosis problem using a distance function is discussed in detail.

Keywords: Intuitionistic Fuzzy set, Multiset, Intuitionistic Fuzzy Multiset

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Authors: D.R Prince Williams

Abstract:

In this paper,we introduce a notion of fuzzy ideals in near-subtraction semigroups and study their related properties.

Keywords: subtraction algebra, subtraction semigroup, an ideal, near-subtraction semigroup, fuzzy level set, fuzzy ideal, fuzzy homomorphism.

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Authors: R. Mechgoug, A. Titaouine

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Fuzzy systems have been successfully used for exchange rate forecasting. However, fuzzy system is very confusing and complex to be designed by an expert, as there is a large set of parameters (fuzzy knowledge base) that must be selected, it is not a simple task to select the appropriate fuzzy knowledge base for an exchange rate forecasting. The researchers often look the effect of fuzzy knowledge base on the performances of fuzzy system forecasting. This paper proposes a genetic fuzzy predictor to forecast the future value of daily US Dollar/Euro exchange rate time’s series. A range of methodologies based on a set of fuzzy predictor’s which allow the forecasting of the same time series, but with a different fuzzy partition. Each fuzzy predictor is built from two stages, where each stage is performed by a real genetic algorithm.

Keywords: Foreign exchange rate, time series forecasting, Fuzzy System, and Genetic Algorithm.

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Authors: Jolly Puri, Shiv Prasad Yadav

Abstract:

Multi-component data envelopment analysis (MC-DEA) is a popular technique for measuring aggregate performance of the decision making units (DMUs) along with their components. However, the conventional MC-DEA is limited to crisp input and output data which may not always be available in exact form. In real life problems, data may be imprecise or fuzzy. Therefore, in this paper, we propose (i) a fuzzy MC-DEA (FMC-DEA) model in which shared and undesirable fuzzy resources are incorporated, (ii) the proposed FMC-DEA model is transformed into a pair of crisp models using α cut approach, (iii) fuzzy aggregate performance of a DMU and fuzzy efficiencies of components are defined to be fuzzy numbers, and (iv) a numerical example is illustrated to validate the proposed approach.

Keywords: Multi-component DEA, fuzzy multi-component DEA, fuzzy resources.

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Authors: Sathinee Malee, Ronnason Chinram

Abstract:

The notion of k-fuzzy ideals of semirings was introduced by Kim and Park in 1996. In 2003, Dutta and Kar introduced a notion of ternary semirings. This structure is a generalization of ternary rings and semirings. The main purpose of this paper is to introduce and study k-fuzzy ideals in ternary semirings analogous to k-fuzzy ideals in semirings considered by Kim and Park.

Keywords: k-ideals, k-fuzzy ideals, fuzzy k-ideals, ternarysemirings

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