University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
10
1
2013
03
02
Cover vol. 10, no. 1, February 2013
0
EN
10.22111/ijfs.2013.2723
http://ijfs.usb.ac.ir/article_2723.html
http://ijfs.usb.ac.ir/article_2723_3ee3c7840b0dd11f70a6f651d5237cbc.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
10
1
2013
02
04
A CONSTRAINED SOLID TSP IN FUZZY ENVIRONMENT:
TWO HEURISTIC APPROACHES
1
28
EN
Chiranjit
Changdar
Department of Computer Science, Raja N.L. Khan Women's
College, Midnapore, Paschim- Medinipur, West Bengal, India-721102
chiranjit changdar@yahoo.co.in
Manas Kumar
Maiti
Department of Mathematics, Mahishadal Raj College, Mahishadal,
Purba- Medinipur, West Bengal, India-721628
manasmaiti@yahoo.co.in
Manoranjan
Maiti
Department of Mathematics, Vidyasagar University, Midnapore,
Paschim- Medinipur, West Bengal, India-721102
mmaiti2005@yahoo.co.in
10.22111/ijfs.2013.153
A solid travelling salesman problem (STSP) is a travelling salesman problem (TSP) where the salesman visits all the cities only once in his tour using dierent conveyances to travel from one city to another. Costs and environmental eect factors for travelling between the cities using dierent conveyances are dierent. Goal of the problem is to nd a complete tour with minimum cost that damages the environment least. An ant colony optimization (ACO) algorithm is developed to solve the problem. Performance of the algorithm for the problem is compared with another soft computing algorithm, Genetic Algorithm(GA). Problems are solved with crisp as well as fuzzy costs. For fuzzy cost and environmental eect factors, cost function as well as environment constraints become fuzzy. As optimization of a fuzzy objective function is not well de ned, fuzzy possibility approach is used to get optimal decision. To test the eciency of the algorithm, the problem is solved considering only one conveyance facility ignoring the environmental eect constraint, i.e., a classical two dimensional TSP (taking standard data sets from TSPLIB for solving the problem). Dierent numerical examples are used for illustration.
Solid travelling salesman problem,Fuzzy possibility,Ant colony optimization,Genetic Algorithm
http://ijfs.usb.ac.ir/article_153.html
http://ijfs.usb.ac.ir/article_153_100415578c754927aaf8d608b87dfdd1.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
10
1
2013
02
04
A COGNITIVE STYLE AND AGGREGATION OPERATOR
MODEL: A LINGUISTIC APPROACH FOR CLASSIFICATION
AND SELECTION OF THE AGGREGATION OPERATORS
29
60
EN
Kevin Kam Fung
Yuen
Department of Computer science and Software Engineering,
Xi'an Jiaotong-Liverpool University, 111 Ren Ai Road, Suzhou Industrial Park, Suzhou,
Jiangsu Province, 215123, P. R. China
kevinkf.yuen@gmail.com
10.22111/ijfs.2013.154
Aggregation operators (AOs) have been studied by many schol- ars. As many AOs are proposed, there is still lacking approach to classify the categories of AO, and to select the appropriate AO within the AO candidates. In this research, each AO can be regarded as a cognitive style or individual dierence. A Cognitive Style and Aggregation Operator (CSAO) model is pro- posed to analyze the mapping relationship between the aggregation operators and the cognitive styles represented by the decision attitudes. Four algorithms are proposed for CSAO: CSAO-1, CSAO-2 and two selection strategies on the basis of CSAO-1 and CSAO-2. The numerical examples illustrate how the choice of the aggregation operators on the basis of the decision attitudes can be determined by the selection strategies of CSAO-1 and CSAO-2. The CSAO model can be applied to decision making systems with the selection problems of the appropriate aggregation operators with consideration of the cognitive styles of the decision makers.
Cognitive styles,Aggregation operators,Information fusion,Decision
attitudes,Decision making
http://ijfs.usb.ac.ir/article_154.html
http://ijfs.usb.ac.ir/article_154_6135966bcbefde837de8dc2560d927ba.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
10
1
2013
02
04
FUZZY GOAL PROGRAMMING TECHNIQUE TO SOLVE
MULTIOBJECTIVE TRANSPORTATION PROBLEMS WITH
SOME NON-LINEAR MEMBERSHIP FUNCTIONS
61
74
EN
Maryam
Zangiabadi
Department of Applied Mathematics, Faculty of Mathematical
Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran
zangiabadi-m@sci.sku.ac.ir
Hamid Reza
Maleki
Department of Basic Sciences, Shiraz University of Technology,
Shiraz, Iran
maleki@sutech.ac.ir
10.22111/ijfs.2013.155
The linear multiobjective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conicting in nature. This paper presents an application of fuzzy goal programming to the linear multiobjective transportation problem. In this paper, we use a special type of nonlinear (hyperbolic and exponential) membership functions to solve multiobjective transportation problem. It gives an optimal compromise solution. The obtained result has been compared with the solution obtained by using a linear membership function. To illustrate the methodology some numerical examples are presented.
Multiobjective decision making,Goal programming,Transportation
problem,Membership function,Fuzzy programming
http://ijfs.usb.ac.ir/article_155.html
http://ijfs.usb.ac.ir/article_155_3287502ac100353886714e75cecddc84.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
10
1
2013
02
05
MINIMIZATION OF DETERMINISTIC FINITE AUTOMATA
WITH VAGUE (FINAL) STATES AND INTUITIONISTIC
FUZZY (FINAL) STATES
75
88
EN
Alka
Choubey
Mathematics Department, Jaypee Institute of Information Technol-
ogy, A-10, Sector-62, Noida-201307 (U. P.), India
alka.choubey@jiit.ac.in, alka.choubey@gmail.com
K. M.
Ravi
Department of Mathematics, JSS Academy of Technical Education, C-
20/1, Sector-62, Noida-201301 (U. P), India
rv.km19@gmail.com, rv km@yahoo.com
10.22111/ijfs.2013.164
In this paper, relations among the membership values of gener- alized fuzzy languages such as intuitionistic fuzzy language, interval-valued fuzzy language and vague language are studied. It will aid in studying the properties of one language when the properties of another are known. Further, existence of a minimized nite automaton with vague ( final) states for any vague regular language recognized by a nite automaton with vague ( final) states is shown in this paper. Finally, an ecient algorithm is given for minimizing the nite automaton with vague ( final) states. Similarly, it can be shown for intuitionistic fuzzy regular language. These may contribute to a better understanding of the role of nite automaton with vague ( final) states or the nite automaton with intuitionistic fuzzy ( final) states while studying lexical analysis, decision making etc.
Intuitionistic fuzzy regular language,Interval-valued fuzzy regular
language,Vague regular language,Finite automaton with vague (final) states,Finite automaton
with intuitionistic fuzzy (nal) states,Myhill-Nerode theorem
http://ijfs.usb.ac.ir/article_164.html
http://ijfs.usb.ac.ir/article_164_8f88d3102db5acd9349513069a44355a.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
10
1
2013
02
05
On the Diagram of One Type Modal Operators on Intuitionistic fuzzy
sets: Last expanding with $Z_{alpha ,beta }^{omega ,theta
89
106
EN
g.
cuvalcioglu
department of mathematics, university of mersin, ciftlikkoy, 33016,
mersin turkey
gcuvalcioglu@mersin.edu.tr
10.22111/ijfs.2013.166
Intuitionistic Fuzzy Modal Operator was defined by Atanassov in cite{at3}in 1999. In 2001, cite{at4}, he introduced the generalization of thesemodal operators. After this study, in 2004, Dencheva cite{dencheva} definedsecond extension of these operators. In 2006, the third extension of thesewas defined in cite{at6} by Atanassov. In 2007,cite{gc1}, the authorintroduced a new operator over Intuitionistic Fuzzy Sets which is ageneralization of Atanassov's and Dencheva's operators. At the same year,Atanassov defined an operator which is an extension of all the operatorsdefined until 2007. The diagram of One Type Modal Operators onIntuitionistic Fuzzy Sets was introduced first in 2007 by Atanassovcite{at10}. In 2008, Atanassov defined the most general operator and in2010 the author expanded the diagram of One Type Modal Operators onIntuitionistic Fuzzy Sets with the operator $Z_{alpha ,beta }^{omega }$.Some relationships among these operators were studied by several researchers%cite{at5}-cite{at8} cite{gc1}, cite{gc3}, cite{dencheva}- cite%{narayanan}.The aim of this paper is to expand the diagram of one type modal operatorsover intuitionistic fuzzy sets . For this purpose, we defined a new modaloparator $Z_{alpha ,beta }^{omega ,theta }$ over intuitionistic fuzzysets. It is shown that this oparator is the generalization of the operators$Z_{alpha ,beta }^{omega },E_{alpha ,beta },boxplus _{alpha ,beta},boxtimes _{alpha ,beta }.$
Modal operator,$Z_{alpha,beta }^{omega,theta }$ operator,Modal operator diagram
http://ijfs.usb.ac.ir/article_166.html
http://ijfs.usb.ac.ir/article_166_54fe632cc30a351a943cae82a4dd7742.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
10
1
2013
02
06
FUZZY INTEGRO-DIFFERENTIAL EQUATIONS: DISCRETE
SOLUTION AND ERROR ESTIMATION
107
122
EN
Masoumeh
Zeinali
Faculty of mathematical sciences, University of Tabriz, Tabriz,
Iran
zeynali@tabrizu.ac.ir
Sedaghat
Shahmorad
0000-0002-2476-1176
Faculty of mathematical sciences, University of Tabriz, Tabriz,
Iran
shahmorad@tabrizu.ac.ir
Kamal
Mirnia
Faculty of mathematical sciences, University of Tabriz, Tabriz, Iran
mirnia-kam@tabrizu.ac.ir
10.22111/ijfs.2013.169
This paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. Then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. Finally an example is given to illustrate the performance of the methods.
Fuzzy integro-differential equation,Discrete solution,Fuzzy quadrature
rule
http://ijfs.usb.ac.ir/article_169.html
http://ijfs.usb.ac.ir/article_169_4d7ef7b69c85251841a56ba41099c819.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
10
1
2013
02
06
SET-NORM EXHAUSTIVE SET MULTIFUNCTIONS
123
134
EN
Anca
Croitoru
Faculty of Mathematics, "A.I. Cuza" University, Bd. Carol I, no 11,
Iasi-700506, Romania
croitoru@uaic.ro
Alina
Gavrilut
Faculty of Mathematics, "A.I. Cuza" University, Bd. Carol I, no
11, Iasi-700506, Romania
gavrilut@uaic.ro
10.22111/ijfs.2013.170
In this paper we present some properties of set-norm exhaustive set multifunctions and also of atoms and pseudo-atoms of set multifunctions taking values in the family of non-empty subsets of a commutative semigroup with unity.
Set-norm,Exhaustive,Continuous,Null-null-additive,Atom,Pseudo-
atom
http://ijfs.usb.ac.ir/article_170.html
http://ijfs.usb.ac.ir/article_170_2bb1c36480ee857421fd93fd71dde045.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
10
1
2013
02
06
APPROXIMATE FIXED POINT IN FUZZY NORMED SPACES
FOR NONLINEAR MAPS
135
142
EN
S. A. M.
Mohseniailhosseini
Faculty of Mathematics, Vali-e-Asr University of Raf-
senjan, Rafsenjan, Iran
amah@vru.ac.ir
H.
Mazaheri
Faculty of Mathematics, Yazd University, Yazd, Iran
hmazaheri@yazduni.ac.ir
M. A.
Dehghan
Faculty of Mathematics, Vali-e-Asr University of Rafsenjan, Raf-
senjan, Iran
dehghan@vru.ac.ir
10.22111/ijfs.2013.173
We de ne approximate xed point in fuzzy norm spaces and prove the existence theorems, we also consider approximate pair constructive map- ping and show its relation with approximate fuzzy xed point.
Fuzzy norm space,$F^z-$approximate
fixed point,Diameter $F^z$-approximate fixed point
http://ijfs.usb.ac.ir/article_173.html
http://ijfs.usb.ac.ir/article_173_1b3c8fc3ea44800472a6b09a730cd34d.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
10
1
2013
02
06
WEAK AND STRONG DUALITY THEOREMS FOR FUZZY
CONIC OPTIMIZATION PROBLEMS
143
152
EN
B.
Farhadinia
Department of Mathematics, Quchan Institute of Engineering and
Technology, Iran,
bfarhadinia@yahoo.com.au
A. V.
Kamyad
Department of Mathematics, Ferdowsi University of Mashhad, Iran,
kamyad@math.um.ac.ir
10.22111/ijfs.2013.174
The objective of this paper is to deal with the fuzzy conic program- ming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. Un- der this setting, duality theorems are extended from crisp conic optimization problems to fuzzy ones.
Fuzzy conic optimization problem,Fuzzy number,Weak and strong
duality theorems
http://ijfs.usb.ac.ir/article_174.html
http://ijfs.usb.ac.ir/article_174_7ccb2ebf7e64971e3e0a4c7c1dd909f7.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
10
1
2013
03
02
Persian-translation vol. 10, no. 1, February 2013
155
163
EN
10.22111/ijfs.2013.2724
http://ijfs.usb.ac.ir/article_2724.html
http://ijfs.usb.ac.ir/article_2724_70b945a70f7f7d14a5f622dc8b8f9e14.pdf