Iranian Journal of Fuzzy SystemsIranian Journal of Fuzzy Systems
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Sat, 21 Oct 2017 02:46:24 +0100FeedCreatorIranian Journal of Fuzzy Systems
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Feed provided by Iranian Journal of Fuzzy Systems. Click to visit.Cover vol. 14, no. 4, August 2017
http://ijfs.usb.ac.ir/article_3332_410.html
Mon, 31 Jul 2017 19:30:00 +0100SOME COMPUTATIONAL RESULTS FOR THE FUZZY RANDOM VALUE OF LIFE ACTUARIAL LIABILITIES
http://ijfs.usb.ac.ir/article_3323_410.html
The concept of fuzzy random variable has been applied in several papers to model the present value of life insurance liabilities. It allows the fuzzy uncertainty of the interest rate and the probabilistic behaviour of mortality to be used throughout the valuation process without any loss of information. Using this framework, and considering a triangular interest rate, this paper develops closed expressions for the expected present value and its defuzzified value, the variance and the distribution function of several well-known actuarial liabilities structures, namely life insurances, endowments and life annuities.Tue, 29 Aug 2017 19:30:00 +0100CERTAIN TYPES OF EDGE m-POLAR FUZZY GRAPHS
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In this research paper, we present a novel frame work for handling $m$-polar information by combining the theory of $m-$polar fuzzy sets with graphs. We introduce certain types of edge regular $m-$polar fuzzy graphs and edge irregular $m-$polar fuzzy graphs. We describe some useful properties of edge regular, strongly edge irregular and strongly edge totally irregular $m-$polar fuzzy graphs. We discuss the relationship between degree of a vertex and degree of an edge in an $m-$polar fuzzy graph. We investigate edge irregularity on a path on $2n$ vertices and barbell graph $B_{n,n}.$We also present an application of $m-$polar fuzzy graph to decision making.Tue, 29 Aug 2017 19:30:00 +0100ARITHMETIC-BASED FUZZY CONTROL
http://ijfs.usb.ac.ir/article_3325_410.html
Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses $alpha$-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence function via arithmetical operators. Defuzzification is the optimum value of the resultant membership function. The left and right hand sides of the membership function will be handled separately. Here, we present a new ABFC (Arithmetic Based Fuzzy Control) algorithm based on arithmetic operations which use a new defuzzification approach. The solution is much smoother, more accurate, and much faster than the classical Mamdani controller.Tue, 29 Aug 2017 19:30:00 +0100AN OPTIMAL FUZZY SLIDING MODE CONTROLLER DESIGN BASED ON PARTICLE SWARM OPTIMIZATION AND USING ...
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This paper addresses the problems caused by an inappropriate selection of sliding surface parameters in fuzzy sliding mode controllers via an optimization approach. In particular, the proposed method employs the parallel distributed compensator scheme to design the state feedback based control law. The controller gains are determined in offline mode via a linear quadratic regular. The particle swarm optimization is incorporated into the linear quadratic regular technique for determining the optimal weight matrices. Consequently, an optimal sliding surface is obtained using the scalar $sign$ function. This latter is used to design the proposed control law. Finally, the effectiveness of the proposed fuzzy sliding mode controller based on parallel distributed compensator and using particle swarm optimization is evaluated by comparing the obtained results with other reported in literature.Tue, 29 Aug 2017 19:30:00 +0100INTERVAL-VALUED INTUITIONISTIC FUZZY SETS AND SIMILARITY MEASURE
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In this paper, the problem of measuring the degree of inclusion and similarity measure for two interval-valued intuitionistic fuzzy sets is considered. We propose inclusion and similarity measure by using order on interval-valued intuitionistic fuzzy sets connected with lexicographical order. Moreover, some properties of inclusion and similarity measure and some correlation, between them and aggregations are examined. Finally, we have included example of ranking problem in car showrooms.Tue, 29 Aug 2017 19:30:00 +0100TOPOLOGICAL SIMILARITY OF L-RELATIONS
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$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, we introduce the topological similarity of $L$-relations,denote it by T-similarity, and we give intuitive characterization ofT-similarity. Then we introduce the variations of a given $L$-relation andinvestigate the relationship among them. Moreover, we prove that each$L$-relation is uniquely topological similar to an $L$-preorder. Finally,we investigate the related algebraic structures of different sets of$L$-relations on the universe.Tue, 29 Aug 2017 19:30:00 +0100FUZZY INCLUSION LINEAR SYSTEMS
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In this manuscript, we introduce a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between the fuzzy solution set of a fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtaining the unique algebraic solution for a fuzzy linear system. Also, all new concepts are illustrated by numerical examples.Tue, 29 Aug 2017 19:30:00 +0100STONE DUALITY FOR R0-ALGEBRAS WITH INTERNAL STATES
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$Rsb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s.In this paper, we first establish a Stone duality for the category of MV-skeletons of $Rsb{0}$-algebras and the category of three-valued Stone spaces.Then we extend Flaminio-Montagna internal states to $Rsb{0}$-algebras.Such internal states must be idempotent MV-endomorphisms of $Rsb{0}$-algebras.Lastly we present a Stone duality for the category of MV-skeletons of $Rsb{0}$-algebras with Flaminio-Montagna internal states and the category of three-valued Stone spaces with Zadeh type idempotent continuous endofunctions.These dualities provide a topological viewpoint for better understanding of the algebraic structures of $Rsb{0}$-algebras.Tue, 29 Aug 2017 19:30:00 +0100REDUNDANCY OF MULTISET TOPOLOGICAL SPACES
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In this paper, we show the redundancies of multiset topological spaces. It is proved that $(P^star(U),sqsubseteq)$ and $(Ds(varphi(U)),subseteq)$ are isomorphic. It follows that multiset topological spaces are superfluous and unnecessary in the theoretical view point.Tue, 29 Aug 2017 19:30:00 +0100Persian-translation vol. 14, no. 4, August 2017
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Mon, 31 Jul 2017 19:30:00 +0100INFORMATION MEASURES BASED TOPSIS METHOD FOR MULTICRITERIA DECISION MAKING PROBLEM IN ...
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In the fuzzy set theory, information measures play a paramountrole in several areas such as decision making, pattern recognition etc. In thispaper, similarity measure based on cosine function and entropy measures basedon logarithmic function for IFSs are proposed. Comparisons of proposed simi-larity and entropy measures with the existing ones are listed. Numerical resultslimpidly betoken the efficiency of these measures over others. An intuitionisticfuzzy weighted measures (IFWM) with TOPSIS method for multi-criteria de-cision making (MCDM) quandary is introduced to grade the alternatives. Thisapproach is predicated on entropy and weighted similarity measures for IFSs.An authentic case study is discussed to rank the four organizations. To com-pare the different rankings, a portfolio selection problem is considered. Variousportfolios have been constructed and analysed for their risk and return. It hasbeen examined that if the portfolios are developed using the ranking obtainedwith proposed method, the return is increased with slight increment in risk.Sat, 09 Dec 2017 20:30:00 +0100BATHTUB HAZARD RATE DISTRIBUTIONS AND FUZZY LIFE TIMES
http://ijfs.usb.ac.ir/article_2989_0.html
The development of life time analysis started back in the $20^{textit{th}}$ century and since then comprehensive developments have been made to model life time data efficiently. Recent development in measurements shows that all continuous measurements can not be measured as precise numbers but they are more or less fuzzy. Life time is also a continuous phenomenon, and has already been shown that life time observations are not precise measurements but fuzzy. Therefore, the corresponding analysis techniques employed on the data require to consider fuzziness of the observations to obtain appropriate estimates.In this study generalized estimators for the parameters and hazard rates are proposed for bathtub failure rate distributions to model fuzzy life time data effectively.Fri, 17 Feb 2017 20:30:00 +0100GENERAL FUZZY AUTOMATA BASED ON COMPLETE RESIDUATED LATTICE-VALUED
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The present paper has been an attempt to investigate the general fuzzy automata on the basis of complete residuated lattice-valued ($L$-GFAs). The study has been chiefly inspired from the work by Mockor cite{15, 16, 17}. Regarding this, the categorical issue of $L$-GFAs has been studied in more details. The main issues addressed in this research include: (1) investigating the relationship between the category of $L$-GFAs and the category of non-deterministic automata (NDAs); as well as the relationship between the category of generalized $L$-GFAs and the category of NDAs; (2) demonstrating the existence of isomorphism between the category of $L$-GFAs and the subcategory of generalized $L$-GFAs and between the category of $L$-GFAs and the category of sets of NDAs; (3) and further scrutinizing some specific relationship between the output $L$-valued subsets of generalized $L$-GFAs and the output $L$-valued of NDAs.Fri, 17 Feb 2017 20:30:00 +0100K-FLAT PROJECTIVE FUZZY QUANTALES
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In this paper, we introduce the notion of {bf K}-flatprojective fuzzy quantales, and give an elementary characterizationin terms of a fuzzy binary relation on the fuzzy quantale. Moreover,we prove that {bf K}-flat projective fuzzy quantales are preciselythe coalgebras for a certain comonad on the category of fuzzy quantales. Finally, we present two special cases of {bf K} as examples.Sat, 18 Feb 2017 20:30:00 +0100OPTIMAL LOT-SIZING DECISIONS WITH INTEGRATED PURCHASING, MANUFACTURING AND ASSEMBLING FOR ...
http://ijfs.usb.ac.ir/article_3007_0.html
This work applies fuzzy sets to the integration of purchasing, manufacturing and assembling of production planning decisions with multiple suppliers, multiple components and multiple machines in remanufacturing systems. The developed fuzzy multi-objective linear programming model (FMOLP) simultaneously minimizes total costs, total $text{CO}_2$ emissions and total lead time with reference to customer demand, due date, supplier/manufacturer capacity, lot-size release and machine yield. The proposed FMOLP model provides a recoverable remanufacturing framework that facilitates fuzzy decision-making, enabling the decision maker (DM) to adjust interactively the membership function or parameters during the solution procedure to obtain a preferred and satisfactory solution. To test of the model, it was implemented in various scenarios with a remanufacturing production system. The analytical results in this work can help planner by enabling systematic analysis of the cost-effectiveness of remanufacturing systems and their potential for improving $text{CO}_2$ emissions and lead time in terms of remanufacturing planning. Future investigations may apply the related patterns of non-linear membership functions to develop an actual remanufacturing planning decision.Sat, 18 Feb 2017 20:30:00 +0100DISTINGUISHABILITY AND COMPLETENESS OF CRISP DETERMINISTIC FUZZY AUTOMATA
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In this paper, we introduce and study notions like state-linebreak distinguishability, input-distinguishability and output completeness of states of a crisp deterministic fuzzy automaton. We show that for each crisp deterministic fuzzy automaton there corresponds a unique (up to isomorphism), equivalent distinguished crisp deterministic fuzzy automaton. Finally, we introduce two axioms related to output completeness of states and discuss the interrelationship between them.Sat, 18 Feb 2017 20:30:00 +0100L-FUZZY CONVEXITY INDUCED BY L-CONVEX FUZZY SUBLATTICE DEGREE
http://ijfs.usb.ac.ir/article_3013_0.html
In this paper, the notion of $L$-convex fuzzy sublattices is introduced and their characterizations are given. Furthermore, the notion of the degree to which an $L$-subset is an $L$-convex fuzzy sublattice is proposed and its some characterizations are given. Besides, the $L$-convex fuzzy sublattice degrees of the homomorphic image and pre-image of an $L$-subset are studied. Finally, we obtain an $L$-fuzzy convexity, which is induced by the $L$-convex fuzzy sublattice degrees, in the sense of Shi and Xiu.Sat, 18 Feb 2017 20:30:00 +0100SOME COUPLED FIXED POINT RESULTS ON MODIFIED INTUITIONISTIC FUZZY METRIC SPACES AND APPLICATION ...
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In this paper, we introduce fruitful concepts of common limit range and joint common limit range for coupled mappings on modified intuitionistic fuzzy metric spaces. An illustrations are also given to justify the notion of common limit range and joint common limit range property for coupled maps. The purpose of this paper is to prove fixed point results for coupled mappings on modified intuitionistic fuzzy metric spaces. Moreover, we extend the notion of common limit range property and E.A property for coupled maps on modified intuitionistic fuzzy metric spaces. As an application, we extend our main result to integral type contraction condition and also for finite number of mappings on modified intuitionistic fuzzy metric spaces.Sat, 18 Feb 2017 20:30:00 +0100ADAPTIVE FUZZY OUTPUT FEEDBACK TRACKING CONTROL FOR A CLASS OF NONLINEAR TIME-VARYING DELAY ...
http://ijfs.usb.ac.ir/article_3056_0.html
This paper considers the problem of adaptive output feedback tracking control for a class of nonstrict-feedback nonlinear systems with unknown time-varying delays and unknown backlash-like hysteresis. Fuzzy logic systems are used to estimate the unknown nonlinear functions. Based on the Lyapunov–Krasovskii method, the control scheme is constructed by using the backstepping and adaptive technique. The proposed adaptive controller guarantees that all the closed-loop signals are semiglobally uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin. Finally, Simulation results further show the effectiveness of the proposed approach.Sun, 26 Feb 2017 20:30:00 +0100A NOVEL FUZZY-BASED SIMILARITY MEASURE FOR COLLABORATIVE FILTERING TO ALLEVIATE THE SPARSITY PROBLEM
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Memory-based collaborative filtering is the most popular approach to build recommender systems. Despite its success in many applications, it still suffers from several major limitations, including data sparsity. Sparse data affect the quality of the user similarity measurement and consequently the quality of the recommender system. In this paper, we propose a novel user similarity measure based on fuzzy set theory along with default voting technique aimed to provide a valid similarity measurement between users wherever the available ratings are relatively rare. The main idea of this research is to model the rating behaviour of each user by a fuzzy set, and use this model to determine the user's degree of interest on items. Experimental results on the MovieLens and Netflix datasets show the effectiveness of the proposed algorithm in handling data sparsity problem. It also outperforms some state-of-the-art collaborative filtering algorithms in terms of prediction quality.Sun, 26 Feb 2017 20:30:00 +0100FUZZY LOGISTIC DIFFERENCE EQUATION
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In this study, we consider two different inequivalent formulations of the logistic difference equation $x_{n+1}= beta x_n(1- x_n), n=0,1,..., $ where $x_n$ is a sequence of fuzzy numbers and $beta$ is a positive fuzzy number. The major contribution of this paper is to study the existence, uniqueness and global behavior of the solutions for two corresponding equations, using the concept of Hukuhara difference for fuzzy numbers. Finally, some examples are given to illustrate our results.Fri, 03 Mar 2017 20:30:00 +0100TREND-CYCLE ESTIMATION USING FUZZY TRANSFORM OF HIGHER DEGREE
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In this paper, we provide theoretical justification for the application of higher degree fuzzy transform in time series analysis. Under the assumption that a time series can be additively decomposed into a trend-cycle, a seasonal component and a random noise, we demonstrate that the higher degree fuzzy transform technique can be used for the estimation of the trend-cycle, which is one of the basic tasks in time series analysis. We prove that high frequencies appearing in the seasonal component can be arbitrarily suppressed and that random noise, as a stationary process, can be successfully decreased using the fuzzy transform of higher degree with a reasonable adjustment of parameters of a generalized uniform fuzzy partition.Fri, 03 Mar 2017 20:30:00 +0100TRANSPORT EQUATION WITH FUZZY DATA
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In this paper, we use the generalized differentiability concept tostudy the fuzzy transport equation. We consider transport equationin the homogeneous and non-homogeneous cases with fuzzy initialcondition. We present the solution when speed parameter is a fuzzynumber too. Our method is based on the construction of the solutionsby employing Zadeh's extension principle.Fri, 03 Mar 2017 20:30:00 +0100DIAGNOSIS OF BREAST LESIONS USING THE LOCAL CHAN-VESE MODEL, HIERARCHICAL FUZZY PARTITIONING ...
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Breast cancer is one of the leading causes of death among women. Mammography remains today the best technology to detect breast cancer, early and efficiently, to distinguish between benign and malignant diseases. Several techniques in image processing and analysis have been developed to address this problem. In this paper, we propose a new solution to the problem of computer aided detection and interpretation for breast cancer. In the proposed approach, a Local Chan-Vese (LCV) model is used for the mass lesion segmentation step to isolate a suspected abnormality in a mammogram. In the classification step, we propose a two-step process: firstly, we use the hierarchical fuzzypartitioning (HFP) to construct fuzzy partitions from data, instead of using the only human information, available from expert knowledge, which are not sufficiently accurate and confronted to errors or inconsistencies. Secondly,fuzzy decision tree induction are proposed to extract classification knowledge from a set of feature-based examples. Fuzzy decision trees are first used todetermine the class of the abnormality detected (well-defined mass, ill-defined mass, architectural distortion, or speculated masses), then, to identify the Severity of the abnormality, which can be benign or malignant. The proposed system is tested by using the images from Mammographic Image AnalysisSociety[MIAS] database. Experimental results show the efficiency of the proposed approach, resulting in an accuracy rate of 87, a sensitivity of 82.14%, and good specificity of 91.42%.Sat, 24 Jun 2017 19:30:00 +0100MULTIPERIOD CREDIBILITIC MEAN SEMI-ABSOLUTE DEVIATION PORTFOLIO SELECTION
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In this paper, we discuss a multiperiod portfolio selection problem with fuzzy returns. We present a new credibilitic multiperiod mean semi- absolute deviation portfolio selection with some real factors including transaction costs, borrowing constraints, entropy constraints, threshold constraints and risk control. In the proposed model, we quantify the investment return and risk associated with the return rate on a risky asset by its credibilitic expected value and semi- absolute deviation. Since the proposed model is a nonlinear dynamic optimization problem with path dependence, we design a novel forward dynamic programming method to solve it. Finally, we provide a numerical example to demonstrate the performance of the designed algorithm and the application of the proposed model.Sat, 24 Jun 2017 19:30:00 +0100CREDIBILITY THEORY ORIENTED PREFERENCE INDEX FOR RANKING FUZZY NUMBERS
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This paper suggests a novel approach for ranking the most applicable fuzzy numbers, i.e. $LR$-fuzzy numbers. Applying the $alpha$-optimistic values of a fuzzy number, a preference criterion is proposed for ranking fuzzy numbers using the Credibility index. The main properties of the proposed preference criterion are also studied. Moreover, the proposed method is applied for ranking fuzzy numbers using target-rank-based methods. Some numerical examples are used to illustrate the proposed ranking procedure. The proposed preference criterion is also examined in order to compare with some common methods and the feasibility and effectiveness of the proposed ranking method is cleared via some numerical comparisons.Sat, 24 Jun 2017 19:30:00 +0100ON CONVERGENCE THEOREMS FOR FUZZY HENSTOCK INTEGRALS
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The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which the point-wise limit of a sequence of fuzzy Henstock integrable functions is fuzzy Henstock integrable has been established.Sat, 24 Jun 2017 19:30:00 +0100ROBUSTNESS OF THE TRIPLE IMPLICATION INFERENCE METHOD BASED ON THE WEIGHTED LOGIC METRIC
http://ijfs.usb.ac.ir/article_3270_0.html
This paper focuses on the robustness problem of full implication triple implication inference method for fuzzy reasoning. First of all, based on strong regular implication, the weighted logic metric for measuring distance between two fuzzy sets is proposed. Besides, under this metric, some robustness results of the triple implication method are obtained, which demonstrates that the triple implication method possesses a good behavior of robustness.Sat, 24 Jun 2017 19:30:00 +0100A NEW APPROACH FOR PARAMETER ESTIMATION IN FUZZY LOGISTIC REGRESSION
http://ijfs.usb.ac.ir/article_3271_0.html
Logistic regression analysis is used to model categorical dependent variable. It is usually used in social sciences and clinical research. Human thoughts and disease diagnosis in clinical research contain vagueness. This situation leads researchers to combine fuzzy set and statistical theories. Fuzzy logistic regression analysis is one of the outcomes of this combination and it is used in situations where the classical logistic regression assumptions' are not satisfied. Also it can be used if the observations or their relations are vague. In this study, a model called “Fuzzy Logistic Regression Based on Revised Tanaka's Fuzzy Linear Regression Model” is proposed. In this regard, the methodology and formulation of the proposed model is explained in detail and the revised Tanaka's regression model is used to estimate the parameters. The Revised Tanaka’s Regression model is an extension of Tanaka's Regression Model in which the objection function is developed. An application is performed on birth weight data set. Also, an application of diabetes data set used in Pourahmad et al.'s study was conducted via our proposed data set. The validity of the model is shown by the help of goodness – of –fit criteria called Mean Degree Memberships (MDM).Sat, 24 Jun 2017 19:30:00 +0100SOME SIMILARITY MEASURES FOR PICTURE FUZZY SETS AND THEIR APPLICATIONS
http://ijfs.usb.ac.ir/article_3273_0.html
In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similarity measure, weighted set-theoretic cosine similarity measure, grey similarity measure and weighted grey similarity measure. Then, we apply these similarity measures between picture fuzzy sets to building material recognition and minerals field recognition. Finally, two illustrative examples are given to demonstrate the efficiency of the similarity measures for building material recognition and minerals field recognition.Sat, 24 Jun 2017 19:30:00 +0100ON SOMEWHAT FUZZY AUTOMATA CONTINUOUS FUNCTIONS IN FUZZY AUTOMATA TOPOLOGICAL SPACES
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In this paper, the concepts of somewhat fuzzy automata continuous functions and somewhat fuzzy automata open functions in fuzzy automata topological spaces are introduced and some interesting properties of these functions are studied. In this connection, the concepts of fuzzy automata resolvable spaces and fuzzy automata irresolvable spaces are also introduced and their properties are studied.Sat, 24 Jun 2017 19:30:00 +0100INTERVAL ANALYSIS-BASED HYPERBOX GRANULAR COMPUTING CLASSIFICATION ALGORITHMS
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Representation of a granule, relation and operation between two granules are mainly researched in granular computing. Hyperbox granular computing classification algorithms (HBGrC) are proposed based on interval analysis. Firstly, a granule is represented as the hyperbox which is the Cartesian product of $N$ intervals for classification in the $N$-dimensional space. Secondly, the relation between two hyperbox granules is measured by the novel positive valuation function induced by the two endpoints of an interval, where the operations between two hyperbox granules are designed so as to include granules with different granularity. Thirdly, hyperbox granular computing classification algorithms are designed on the basis of the operations between two hyperbox granules, the fuzzy inclusion relation between two hyperbox granules, and the granularity threshold. We demonstrate the superior performance of the proposed algorithms compared with the traditional classification algorithms, such as, Random Forest (RF), Support Vector Machines (SVMs), and Multilayer Perceptron (MLP).Sat, 24 Jun 2017 19:30:00 +0100ON STRATIFIED LATTICE-VALUED CONVERGENCE SPACES
http://ijfs.usb.ac.ir/article_3282_0.html
In this paper we provide a common framework for different stratified $LM$-convergence spaces introduced recently. To this end, we slightly alter the definition of a stratified $LMN$-convergence tower space. We briefly discuss the categorical properties and show that the category of these spaces is a Cartesian closed and extensional topological category. We also study the relationship of our category to the categories of stratified $L$-topological spaces and of enriched $LM$-fuzzy topological spaces.Sat, 01 Jul 2017 19:30:00 +0100F-TRANSFORM FOR NUMERICAL SOLUTION OF TWO-POINT BOUNDARY VALUE PROBLEM
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We propose a fuzzy-based approach aiming at finding numerical solutions to some classical problems. We use the technique of F-transform to solve a second-order ordinary differential equation with boundary conditions. We reduce the problem to a system of linear equations and make experiments that demonstrate applicability of the proposed method. We estimate the order of accuracy of the proposed method. We show that the F-transform-based approach does not only extend the set of its applications, but has a certain advantage in the solution of ill-posed problems.Sat, 01 Jul 2017 19:30:00 +0100POINTWISE CONVERGENCE TOPOLOGY AND FUNCTION SPACES IN FUZZY ANALYSIS
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We study the space of all continuous fuzzy-valued functions from a space $X$ into the space of fuzzy numbers $(mathbb{E}sp{1},dsb{infty})$ endowed with the pointwise convergence topology. Our results generalize the classical ones for continuous real-valued functions. The field of applications of this approach seems to be large, since the classical case allows many known devices to be fitted to general topology, functional analysis, coding theory, Boolean rings, etc.Sat, 01 Jul 2017 19:30:00 +0100BASES AND CIRCUITS OF FUZZIFYING MATROIDS
http://ijfs.usb.ac.ir/article_3286_0.html
In this paper, as an application of fuzzy matroids, the fuzzifying greedy algorithm is proposed and an achievableexample is given. Basis axioms and circuit axioms of fuzzifying matroids, which are the semantic extension for the basis axioms and circuit axioms of crisp matroids respectively, are presented. It is proved that a fuzzifying matroid is equivalent to a mapping which satisfies the basis axioms or circuit axioms.Sat, 01 Jul 2017 19:30:00 +0100BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES
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Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbases can be used to characterize CP mappings and CC mappings between $M$-fuzzifying convex spaces.Sat, 01 Jul 2017 19:30:00 +0100QUANTALE-VALUED GAUGE SPACES
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We introduce a quantale-valued generalization of approach spaces in terms of quantale-valued gauges. The resulting category is shown to be topological and to possess an initially dense object. Moreover we show that the category of quantale-valued approach spaces defined recently in terms of quantale-valued closures is a coreflective subcategory of our category and, for certain choices of the quantale, is even isomorphic to our category. Finally, the category of quantale-valued metric spaces is shown to be coreflectively embedded in our category.Sat, 01 Jul 2017 19:30:00 +0100ON THE MATCHING NUMBER OF AN UNCERTAIN GRAPH
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Uncertain graphs are employed to describe graph models with indeterministicinformation that produced by human beings. This paper aims to study themaximum matching problem in uncertain graphs.The number of edges of a maximum matching in a graph is called matching numberof the graph. Due to the existence of uncertain edges, the matching number of an uncertain graph is essentially an uncertain variable.Different from that in a deterministic graph, it is more meaningful to investigate theuncertain measure that an uncertain graph is $k$-edge matching (i.e., the matching number is greater than or equal to $k$).We first study the properties of the matching number of an uncertain graph,and then give a fundamental formula for calculating the uncertain measure. We further prove that the fundamental formula can be transformed into a simplified form. What is more, a polynomial time algorithmto numerically calculate the uncertain measure is derived from the simplified form.Finally, some numerical examples are illustrated to show the application and efficiency of the algorithm.Sat, 01 Jul 2017 19:30:00 +0100RESOLUTION OF NONLINEAR OPTIMIZATION PROBLEMS SUBJECT TO BIPOLAR MAX-MIN FUZZY RELATION ...
http://ijfs.usb.ac.ir/article_3290_0.html
This paper studies the nonlinear optimization problems subject to bipolar max-min fuzzy relation equation constraints. The feasible solution set of the problems is non-convex, in a general case. Therefore, conventional nonlinear optimization methods cannot be ideal for resolution of such problems. Hence, a Genetic Algorithm (GA) is proposed to find their optimal solution. This algorithm uses the structure of the feasible domain of the problems and lower and upper bound of the feasible solution set to choose the initial population. The GA employs two different crossover operations: 1- N-points crossover and 2- Arithmetic crossover. We run the GA with two crossover operations for some test problems and compare their results and performance to each other. Also, their results are compared with the results of other authors' works.Sat, 01 Jul 2017 19:30:00 +0100SOME PROPERTIES OF UNCERTAIN INTEGRAL
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Uncertainty theory is a mathematical methodology for dealing withnon-determinate phenomena in nature. As we all know, uncertainprocess and uncertain integral are important contents of uncertaintytheory, so it is necessary to have deep research. This paperpresents the definition and discusses some properties of strongcomonotonic uncertain process. Besides, some useful formulas ofuncertain integral such as nonnegativity, monotonicity, intermediateresults are studied.Sat, 01 Jul 2017 19:30:00 +0100ADMISSIBLE PARTITION FOR BL-GENERAL FUZZY AUTOMATON
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In this note, we define the concepts of admissible relation and admissible partition for an arbitrary BL-general fuzzy automaton.In particular, a connection between the admissible partition and the quotient BL-general fuzzy automaton is presented.It is shown that if we use the maximal admissible partition, then we obtain a quotient BL-general fuzzy automaton and this quotient is minimal. Finally, we present some examples to clarify the notions and results of this paper.Sat, 01 Jul 2017 19:30:00 +0100AN INVESTIGATION ON THE CO-ANNIHILATORS IN TRIANGLE ALGEBRAS
http://ijfs.usb.ac.ir/article_3293_0.html
In this paper, we introduce the notion of co-annihilator of a subsetin a triangle algebra. It is shown that the co-annihilator of asubset is an interval valued residuated lattice (IVRL)-filter. Also, aspecial set of a triangle algebra is defined and the relationshipbetween this set and co-annihilator of a subset in triangle algebrais considered. Finally, co-annihilators preserving congruencerelation, or $CP$-congruence are defined and some results of themare given.Sat, 01 Jul 2017 19:30:00 +0100ON TRUNCATED MEASURES OF INCOME INEQUALITY FROM A FUZZY PERSPECTIVE
http://ijfs.usb.ac.ir/article_3294_0.html
In most statistical analysis, inequality or extent of variation in income isrepresented in terms of certain summary measures. But some authors arguedthat the concept of inequality is vague and thus cannot be measured as anexact concept. Therefore, fuzzy set theory provides naturally a useful toolfor such circumstances. In this paper we have introduced a real-valued fuzzymethod of illustrating the measures of income inequality in truncated randomvariables based on the case where the conditional events are vague. Toguarantee certain relevant properties of these measures, we first selectedthree main families of measures and obtained their closed formulas, thenused two simulated and real data set to illustrate the usefulness of derivedresults.Sat, 01 Jul 2017 19:30:00 +0100L-CONVEX SYSTEMS AND THE CATEGORICAL ISOMORPHISM TO SCOTT-HULL OPERATORS
http://ijfs.usb.ac.ir/article_3296_0.html
The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.Sun, 02 Jul 2017 19:30:00 +0100ITERATIVE METHOD FOR SOLVING TWO-DIMENSIONAL NONLINEAR FUZZY INTEGRAL EQUATIONS USING FUZZY ...
http://ijfs.usb.ac.ir/article_3297_0.html
In this paper, we propose an iterative procedure based on two dimensionalfuzzy block-pulse functions for solving nonlinear fuzzy Fredholm integralequations of the second kind. The error estimation and numerical stabilityof the proposed method are given in terms of supplementary Lipschitz condition.Finally, illustrative examples are included in order to demonstrate the accuracyand convergence of the proposed method.Mon, 03 Jul 2017 19:30:00 +0100(1612-3379) POWERSET OPERATORS OF EXTENSIONAL FUZZY SETS
http://ijfs.usb.ac.ir/article_3318_0.html
Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theory there exists a strong relation, which can be represented as a homomorphism. Analogical results are also proved for new powerset theories of extensional fuzzy sets.Sun, 27 Aug 2017 19:30:00 +0100(1601-2661) SOME PROBABILISTIC INEQUALITIES FOR FUZZY RANDOM VARIABLES
http://ijfs.usb.ac.ir/article_3319_0.html
In this paper, the concepts of positive dependence and linearly positive quadrant dependence are introduced for fuzzy random variables.Also, an inequality is obtained for partial sums of linearly positive quadrant dependent fuzzy random variables.Moreover, a weak law of large numbers is established for linearly positive quadrant dependent fuzzy random variables.We extend some well known inequalities to independent fuzzy random variables.Furthermore, a weak law of large numbers for independent fuzzy random variables is stated and proved.Sun, 27 Aug 2017 19:30:00 +0100(1603-2831) INVENTORY MODEL WITH DEMAND AS TYPE-2 FUZZY NUMBER: A FUZZY DIFFERENTIAL EQUATION ...
http://ijfs.usb.ac.ir/article_3321_0.html
An inventory model is formulated with type-2 fuzzy parameters under trade credit policy and solved by using Generalized Hukuhara derivative approach. Representing demand parameter of each expert's opinion is a membership function of type-1 and thus, this membership function again becomes fuzzy. The final opinion of all experts is expressed by a type-2 fuzzy variable. For this present problem, to get corresponding defuzzified values of the triangular type-2 fuzzy demand parameters, first critical value (CV)-based reduction methods are applied to reduce corresponding type-1 fuzzy variables which becomes pentagonal in form. After that $alpha$- cut of a pentagonal fuzzy number is used to construct the upper $alpha$- cut and lower $alpha$- cut of the fuzzy differential equation. Different cases are considered for fuzzy differential equation: gH-(i) differentiable and gH-(ii) differentiable systems. The objective of this paper is to find out the optimal time so as to minimize the total inventory cost. The considered problem ultimately reduces to a multi-objective problem which is solved by weighted sum method and global criteria method. Finally the model is solved by generalised reduced gradient method using LINGO (13.0) software. The proposed model and technique are lastly illustrated by providing numerical examples. Results from two methods are compared and some sensitivity analyses both in tabular and graphical forms are presented and discussed. The effects of total cost with respect to the change of demand related parameter ($beta$), holding cost parameter ($r$), unit purchasing cost parameter ($p$), interest earned $(i_e)$ and interest payable $(i_p)$ are discussed. We also find the solutions for type-1 and crisp demand as particular cases of type-2 fuzzy variable. This present study can be applicable in many aspects in many real life situations where type-1 fuzzy set is not sufficient to formulate the mathematical model. From the numerical studies, it is observed that under both gH-(i) and gH-(ii) cases, total cost of the system gradually reduces for the sub-cases - 1.1, 1.2 and 1.3 depending upon the positions of N(trade credit for customer) and M (trade credit for retailer) with respect to T (time period).Fri, 01 Sep 2017 19:30:00 +0100(1606-3013) SHAPLEY FUNCTION BASED INTERVAL-VALUED INTUITIONISTIC FUZZY VIKOR TECHNIQUE FOR ...
http://ijfs.usb.ac.ir/article_3322_0.html
Interval-valued intuitionistic fuzzy set (IVIFS) has developed to cope with the uncertainty of imprecise human thinking. In the present communication, new entropy and similarity measures for IVIFSs based on exponential function are presented and compared with the existing measures. Numerical results reveal that the proposed information measures attain the higher association with the existing measures, which demonstrate their efficiency and reliablity. To deal with the interactive characteristics among the elements in a set, Shapley weighted similarity measure based on proposed similarity measure for IVIFSs is discussed via Shapley function. Thereafter, the linear programming model for optimal fuzzy measure is originated for incomplete information about the weights of the criteria and thus, the optimal weight vector is obtained in terms of Shapley values. Further, the VIKOR technique is discussed for correlative multi-criteria decision making problems under interval-valued intuitionistic fuzzy environment. Finally, an example of investment problem is presented to exemplify the application of the proposed technique under incomplete and uncertain information situation.Fri, 01 Sep 2017 19:30:00 +0100(1604-2940) A NEW APPROACH IN FAILURE MODES AND EFFECTS ANALYSIS BASED ON COMPROMISE SOLUTION ...
http://ijfs.usb.ac.ir/article_3339_0.html
Failure modes and effects analysis (FMEA) is a well-known risk analysis approach that has been conducted to distinguish, analyze and mitigate serious failure modes. It demonstrates the effectiveness and the ability of understanding and documenting in a clear manner; however, the FMEA has weak points and it has been criticized by some authors. For example, it does not consider relative importance among three risk factors (i.e., $ O, S $ and $ D $). Different sequences of $ O $, $ S $ and $ D $ may result in exactly the same value of risk priority number (RPN), but their semantic risk implications may be totally different and these three risk factors are difficult to be precisely expressed. This study introduces a new interval-valued intuitionistic fuzzy (IVIF)-decision approach based on compromise solution concept that defeats the above weak points and improves the traditional FMEA's results. This study firstly employs both subjective and objective weights in the decision process simultaneously. Secondly, there are two kinds of subjective weights performed in the study: aggregated weights obtained by experts' assessments as well as entropy measure. Thirdly, this approach is defined under an IVIF-environment to ensure that the evaluation information would be preserved, and the uncertainties could be handled during the computations. Hence, it considers uncertainty in experts' judgments as well as reduces the probability of obtaining two ranking orders with the same value. Finally, the alternatives are ranked with a new collective index according to the compromise solution concept. To show the effectiveness of the proposed approach, two practical examples are solved from the recent literature in engineering applications. The proposed decision approach has an acceptable performance. Also, its advantages have been mentioned in comparison with other decision approaches.Tue, 05 Sep 2017 19:30:00 +0100(1704-3609) A NEW SECRET SHARING SCHEME ADVERSARY FUZZY STRUCTURE BASED ON AUTOMATA
http://ijfs.usb.ac.ir/article_3340_0.html
In this paper, we introduce a new verifiable multi-use multi-secretsharing scheme based on automata and one-way hash function. The scheme has theadversary fuzzy structure and satisfy the following properties:1) The dealer can change the participants and the adversary fuzzy structure without refreshing any participants' real-shadow. 2) The scheme is based on the inversion of weakly invertible finite automata and its security depends on the properties of the one-way hash functions.3) The scheme does not encounter time-consuming computationslike discrete logarithm problem.4) The validity of the transmitted data can be verified by the combiner and participants.5) Every participant has only one reusable real-shadow,whereas the most of other existing schemes have more than one shadow.In addition, the proposed scheme which is based on automata has all the properties of a perfect scheme.Finally, the comparisons among other schemes and our scheme prove the efficiency of our scheme.Tue, 05 Sep 2017 19:30:00 +0100(1702-3470) TOPOLOGICAL CHARACTERIZATION FOR FUZZY REGULAR LANGUAGES
http://ijfs.usb.ac.ir/article_3341_0.html
We present a topological characterization for fuzzy regular languages:we show that there is a bijective correspondence between fuzzy regular languagesand the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular languages.Moreover, we prove that the induced fuzzy topological space has a basis consisting of leveled characteristic functions of the closure of cut languages of fuzzy regular languages.Sat, 09 Sep 2017 19:30:00 +0100(1512-2657) GENERALIZED RESIDUATED LATTICES BASED F-TRANSFORM
http://ijfs.usb.ac.ir/article_3342_0.html
The aim of the present work is to study the $F$-transform over a generalized residuated lattice. We discuss the properties that are common with the $F$-transform over a residuated lattice. We show that the $F^{uparrow}$-transform can be used in establishing a fuzzy (pre)order on the set of fuzzy sets.Sat, 09 Sep 2017 19:30:00 +0100(1704-3631) SOLUTION AND STABILITY OF QUATTUORVIGINTIC FUNCTIONAL EQUATION IN INTUITIONISTIC ...
http://ijfs.usb.ac.ir/article_3360_0.html
In this paper, we investigate the general solution and the generalized Hyers-Ulam stability of a new functional equation which is called quattuorvigintic functional equation in intuitionistic fuzzy normed spaces by using the fixed point method.These results can be regarded as an important extension of stability results corresponding to functional equations on normed spaces.Fri, 15 Sep 2017 19:30:00 +0100(1611-3294) Testing statistical hypotheses under fuzzy data and based on a new signed distance
http://ijfs.usb.ac.ir/article_3361_0.html
This paper deals with the problem of testing statisticalhypotheses when the available data are fuzzy. In this approach, wefirst obtain a fuzzy test statistic based on fuzzy data, and then,based on a new signed distance between fuzzy numbers, we introducea new decision rule to accept/reject the hypothesis of interest.The proposed approach is investigated for two cases: the casewithout nuisance parameters and the case with nuisance parameters.This method is employed to test the hypotheses for the mean of anormal distribution with known/unknown variance, the variance of anormal distribution, the difference of means of two normaldistributions with known/unknown variances, and the ratio ofvariances of two normal distributions.Fri, 15 Sep 2017 19:30:00 +0100(1611-3292) FURTHER RESULTS OF CONVERGENCE OF UNCERTAIN RANDOM SEQUENCES
http://ijfs.usb.ac.ir/article_3362_0.html
Convergence is an issue being widely concerned about. Thus, in this paper, we mainly put forward two types of concepts of convergence in mean and convergence in distribution for the sequence of uncertain random variables. Then some of theorems are proved to show the relations among the three convergence concepts that are convergence in mean, convergence in measure and convergence in distribution. Furthermore, several examples are given to illustrate how we use the theorems to make sure the uncertain random sequence being convergent. Finally, several counterexamples are taken to explain the relations between these different types of convergence.Fri, 15 Sep 2017 19:30:00 +0100(1510-2544) SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS
http://ijfs.usb.ac.ir/article_3372_0.html
In this paper, we study fuzzy calculus in two main branches differential and integral. Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating $gH$-derivative of a composite function. Two techniques namely, Leibniz's rule and integration by parts are introduced for fuzzy integrals. Furthermore, we prove three essential theorems such as a fuzzy intermediate value theorem, fuzzy mean value theorem for integral and mean value theorem for $gH$-derivative. We derive a Bolzano's theorem, Rolle's theorem and some properties for $gH$-differentiable functions. To illustrate and explain these rules and theorems, we have provided several examples in details.Tue, 19 Sep 2017 19:30:00 +0100(1606-2986) TREE AUTOMATA BASED ON COMPLETE RESIDUATED LATTICE-VALUED LOGIC: REDUCTION ...
http://ijfs.usb.ac.ir/article_3392_0.html
In this paper, at first we define the concepts of response function and accessible states of a complete residuated lattice-valued (for simplicity we write $mathcal{L}$-valued) tree automaton with a threshold $c.$ Then, related to these concepts, we prove some lemmas and theorems that are applied in considering some decision problems such as finiteness-value and emptiness-value of recognizable tree languages. Moreover, we propose a reduction algorithm for $mathcal{L}$-valued tree automata with a threshold $c.$ The goal of reducing an $ mathcal{L}$-valued tree automaton is to obtain an $mathcal{L}$-valued tree automaton with reduced number of states %that all of its states are accessible all of which are accessible, in addition it recognizes the same language as the first one given. We compare our algorithm with some other algorithms in the literature. Finally, utilizing the obtained results, we consider some fundamental decision problems for $mathcal{L}$-valued tree automata including the membership-value, the emptiness-value, the finiteness-value, the intersection-value and the equivalence-value problems.Tue, 03 Oct 2017 20:30:00 +0100(1606-3016) CONTROL OF FLEXIBLE JOINT ROBOT MANIPULATORS
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A flexible-joint robot manipulator is a complex system because it is nonlinear, multivariable, highly coupled along with joint flexibility and uncertainty. To overcome flexibility, several methods have been proposed based on flexible model. This paper presents a novel method for controlling flexible-joint robot manipulators. A novel control law is presented by compensating flexibility to form a rigid robot and then control methods for rigid robots are applied. Feedback linearization and direct adaptive fuzzy control, based on rigid model, are designed with torque control strategy. A decentralized adaptive fuzzy controller is designed because of simplicity and ease of implementation. Effectiveness of the proposed control approach is demonstrated by simulations, using a three-joint articulated flexible-joint robot, driven by permanent magnet dc motors.Fri, 06 Oct 2017 20:30:00 +0100(1611-3300) A NEW MULTIPLE CRITERIA DECISION-MAKING METHOD BASED ON BIPOLAR FUZZY SOFT GRAPHS
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In this research study, we present a novel frame work for handling bipolar fuzzy soft information by combining bipolar fuzzy soft sets with graphs. We introduce several basic notions concerning bipolar fuzzy soft graphs and investigate some related properties. We also consider the application of the bipolar fuzzy soft graphs. In particular, three efficient algorithms are developed to solve multiple criteria decision-making problems regarding social network, investment in shares and detection of bipolar disorder in children.Sat, 07 Oct 2017 20:30:00 +0100(1605-2930) INTEGRABILITY OF AN INTERVAL-VALUED MULTIFUNCTION WITH RESPECT TO AN ...
http://ijfs.usb.ac.ir/article_3406_0.html
Intervals are related to the representation of uncertainty. In this sense, we introduce an integral of Gould type for an interval-valued multifunction relative to an interval-valued set multifunction, withrespect to Guo and Zhang order relation. Classical and specific properties of this new type of integral are established and several examples and applications from multicriteria decision makingproblems are provided.Fri, 13 Oct 2017 20:30:00 +0100(1603-2816) A NEW WAY TO EXTEND FUZZY IMPLICATIONS
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The main purpose of this paper is to use a new way to extendfuzzy implications $I$ from a generalized sublattice $M$ to a bounded lattice$L$, such that the extended implications preserve many of the considered properties of fuzzy implications on $M$.Furthermore, as a special case, we investigate the extension of $(S,N)-$implications. Results indicate that the extended implications preserve many of the considered properties of $(S,N)$-implications.Fri, 13 Oct 2017 20:30:00 +0100