فهرست مطالب

fuzzy systems - Volume:16 Issue:2, 2019
  • Volume:16 Issue:2, 2019
  • 224 صفحه،
  • تاریخ انتشار: 1397/12/10
  • تعداد عناوین: 15
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  • Vilém Nov?k * Pages 1-16
    This paper is a study of fuzzy type theory (FTT) with partial functions. Out of several possibilities we decided tointroduce a special value ”∗” that represents ”undefined”. In the interpretation of FTT, this value lays outside of thecorresponding domain. In the syntax it can be naturally represented by the description operator acting on the empty(fuzzy) set, because choosing an element from its kernel gives no result. Among many results, we will show that if, in atheory T, ”∗” is defined or provable then T is contradictory. We will also show completeness in the sense any consistenttheory of FTT with partial functions has a model.
    Keywords: Fuzzy type theory, EQ-algebra, partial function, description operator
  • Han&Egrave, Ne Medhaffar *, Moez Feki, Nabil Derbel Pages 17-29
    In this paper, we investigate the stabilization of unstable periodic orbits of continuous time chaotic systems usingfuzzy time-delayed controllers. For this aim, we present a control method that can achieve stabilization of an unstableperiodic orbit (UPO) without any knowledge of the system model. Our proposal is attained progressively. First, wecombine the input-to-state linearizing controller with the fuzzy method to obtain one that achieves UPO stabilization.Then, we use reduced order sliding observer to estimate the necessary state for the controller construction. Finally, theefficiency of the proposed methods is demonstrated using numerical simulations applied to Chua’s system.
    Keywords: Chaos control, Time-delayed state feedback, Fuzzy adaptive systems, Sliding mode observer
  • Sunil Mathew *, John Mordeson, Hai, Long Yang Pages 31-43
    Fuzzy incidence graphs can be used as models for nondeterministic interconnection networks having extra node-edgerelationships. For example, ramps in a highway system may be modeled as a fuzzy incidence graph so that unexpectedflow between cities and highways can be effectively studied and controlled. Like node and edge connectivity in graphs,node connectivity and arc connectivity in fuzzy incidence graphs are introduced in this article. Their relationships withfuzzy connectivity parameters are discussed and results similar to Whitney’s theorems are obtained. Also, the incidenceis used to model flows in human trafficking networks.
    Keywords: Fuzzy incidence graph, Incidence cut, Cutpair, Complete fuzzy incidence, Human trafficking
  • Barbara Pekala * Pages 45-55
    In the paper aspect of comparability alternatives in decision making problem by imprecise or incomplete information isexamined. In particular, new definitions of transitivity based on the measure of the intensity preference between pairsof alternatives in epistemic and ontic case is presented and its application to solve decision making problem is proposed.
    Keywords: Epistemic, ontic order, transitivity, Selection alternatives, Interval-valued fuzzy relations
  • Atefeh Armand *, Tofigh Allahviranloo, Saeid Abbasbandy, Zeinab Gouyandeh Pages 57-72
    In this paper, the generalized Taylor’s expansion is presented for fuzzy-valued functions. To achieve this aim, fuzzyfractional mean value theorem for integral, and some properties of Caputo generalized Hukuhara derivative are necessarythat we prove them in details. In application, the fractional Euler’s method is derived for solving fuzzy fractionaldifferential equations in the sense of Caputo differentiability. The effectiveness of the proposed method is verified bythree examples.
    Keywords: Generalized Hukuhara derivative, Caputo generalized Hukuhara derivative, Fuzzy mean value theorem for Riemann-Liouville integral, Generalized Taylor’s expansion, Fuzzy fractional differential equations, Fuzzy fractional Euler’s method
  • Chuan Yue * Pages 73-86
    Academic libraries play a significant role in providing core services that include research, teaching and learning. Usersatisfaction is an important indicator for evaluating the performance of library service. This paper develops a methodfor measuring the user satisfaction in a group decision-making environment. First, the performance of service isevaluated by using questionnaire survey. The scores are recorded by using some simple symbols. Second, the symbolinformation along with nonresponse items in questionnaires are fused into an intuitionistic fuzzy information. Third, anexperimental analysis is provided to illustrate the validity and effectiveness of introduced method in this paper. Finally,the theoretical and practical implications of current model are discussed, the important limitations are recognized, andsome main advantages and future research directions of current method are shown in conclusions.
    Keywords: User satisfaction, academic digital library, group decision-making, intuitionistic fuzzy information, symbol information
  • Juan Li * Pages 87-96
    The notion of stratified (L, M)-semiuniform convergence tower spaces is introduced, which extends the notions ofprobabilistic semiuniform convergence spaces and lattice-valued semiuniform convergence spaces. The resulting categoryis shown to be a strong topological universe. Besides, the relations between our category and that of stratified (L, M)-filter tower spaces are studied.
    Keywords: Stratified L-filters, Stratified (L, M)-semiuniform convergence tower spaces, Lattice-valued semiuniform convergence spaces, Strong topological universe
  • Chen Yuan *, Yueli Yue Pages 97-106
    In this paper, we give a kind of Cauchy 1-completeness in probabilistic quasi-uniform spaces by using 1-filters. Utilizingthe relationships among probabilistic quasi-uniformities, classical quasi-uniformities and Hutton [0, 1]-quasi-uniformities,we show the relationships between their completeness. In fuzzy quasi-metric spaces, we establish the relationshipsbetween the completeness of induced probabilistic quasi-uniform spaces and both completeness of induced classicalquasi-uniform spaces and induced Hutton [0, 1]-quasi-uniform spaces.
    Keywords: probabilistic quasi-uniformity, classical quasi-uniformity, Hutton [0, 1]-quasi-uniformity, 1-filter, Cauchy 1-completeness
  • Long Hoang *, Nguyen Thi Kim Son, Phuong Thao Pages 107-121
    In this paper, we study the existence of integral solutions of fuzzy fractional differential systems with nonlocal conditions under Caputo generalized Hukuhara derivatives. These models are considered in the framework of completegeneralized metric spaces in the sense of Perov. The novel feature of our approach is the combination of the convergentmatrix technique with Schauder fixed point principle of vector valued operators in semilinear Banach spaces. Somecomputational examples are represented to demonstrate our theoretical results.
    Keywords: Fuzzy fractional differential systems, Caputo gH-derivatives, vector valued metric, generalized metric space
  • Yu, Jie Wang * Pages 123-136
    In this paper, we first use a fuzzy preference relation with a membership function representing preference degree forcomparing two interval-valued fuzzy numbers and then utilize a relative preference relation improved from the fuzzypreference relation to rank a set of interval-valued fuzzy numbers. Since the fuzzy preference relation is a total orderingrelation that satisfies reciprocal and transitive laws on interval-valued fuzzy numbers, the relative preference relation isalso a total ordering relation. Practically, the fuzzy preference relation is more reasonable on ranking interval-valuedfuzzy numbers than defuzzification because defuzzification does not present preference degree between fuzzy numbersand loses messages. However, fuzzy pair-wise comparison for the fuzzy preference relation is more complex and difficultthan defuzzification. To resolve fuzzy pair-wise comparison tie, the relative preference relation takes the strengths ofdefuzzification and the fuzzy preference relation into consideration. The relative preference relation expresses preferencedegrees of interval-valued fuzzy numbers over average as the fuzzy preference relation does, and ranks fuzzy numbersby relative crisp values as defuzzification does. In fact, the application of relative preference relation was shown intraditional fuzzy numbers, such as triangular and trapezoidal fuzzy numbers, for previous approaches. In this paper, weextend and utilize the relative preference relation on interval-valued fuzzy numbers, especially for triangular intervalvalued fuzzy numbers. Obviously, interval-valued fuzzy numbers based on the relative preference relation are easily and quickly ranked, and able to reserve fuzzy information.
    Keywords: Fuzzy preference relation, Interval-valued fuzzy numbers, Ranking, Relative preference relation, Triangular
  • Santosh Desai *, Shrikant Chaudhari Pages 137-146
    In the present paper, we introduce the fuzzy Nehring axiom, fuzzy Sen axiom and weaker form of the weak fuzzycongruence axiom. We establish interrelations between these axioms and their relation with fuzzy Chernoff axiom. Weexpress full rationality of a fuzzy choice function using these axioms along with the fuzzy Chernoff axiom.
    Keywords: Full rationality, New weak fuzzy congruence axiom, fuzzy Nehring axiom, fuzzy Sen axiom, fuzzy Chernoff axiom
  • Indira Debnath *, S. Gupta Pages 147-163
    Fuzziness is ever presented in real life decision making problems. In this paper, we adapt the pessimistic approach tostudy a pair of linear primal-dual problem under intuitionistic fuzzy (I-fuzzy) environment and prove certain dualityresults. We generate the duality results using exponential membership and non-membership functions to represent thedecision maker’s satisfaction and dissatisfaction level. Further, two numerical examples have been given. In each ofthese illustrations, varying the values of the shape variables in the exponential membership functions, various nonlinearoptimization problems have been constructed, analyzed and solved. The duality gaps for all these optimization problemshave been computed and compared with the duality gap under the linear membership function. We found that thesegaps for the I-fuzzy linear primal-dual pair under the exponential membership functions are smaller as compared withthe linear membership functions. The main advantage of using the exponential membership function is that it has theflexibility of altering the values of the shape parameters (as per the decision-maker’s satisfaction). Finally, with thehelp of a suitable ranking defuzzification function, we have extended our approach to the I-fuzzy linear problem withfuzzy parameters and fuzzy constraints.
    Keywords: Fuzzy optimization, Intuitionistic fuzzy set (I-fuzzy set), Primal-dual problems, Fuzzy duality theorems, Duality gaps
  • Mohammad Mohtashami, Mahdi Eftekhari * Pages 165-182
    High dimensional microarray datasets are difficult to classify since they have many features with small number ofinstances and imbalanced distribution of classes. This paper proposes a filter-based feature selection method to improvethe classification performance of microarray datasets by selecting the significant features. Combining the concepts ofrough sets, weighted rough set, fuzzy rough set and hesitant fuzzy sets for developing an effective algorithm is the maincontribution of this paper. The mentioned method has two steps, in the first step, four discretization approaches areapplied to discretize continuous datasets and selects a primary subset of features by combining of weighted rough setdependency degree and information gain via hesitant fuzzy aggregation approach. In the second step, a significancemeasure of features (defined by fuzzy rough concepts) is employed to remove redundant features from primary set.The Wilcoxon Signed Ranked tes (A Non-parametric statistical test) is conducted for comparing the presented methodwith ten feature selection methods across seven datasets. The results of experiments show that the proposed methodis able to select a significant subset of features and it is an effective method in the literature in terms of classificationperformance and simplicity.
    Keywords: Rough set, Weighted Rough set, Information gain, Discretization, Hesitant fuzzy set
  • Alireza Khastan *, S. Hejab Pages 183-196
    In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.
    Keywords: Time scales, Generalized differentiability, First order, Linear fuzzy dynamic equations
  • Madjid Eshaghi, Sadegh Abbaszadeh, Choonkil Park * Pages 197-204
    The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membershipvalue of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is presenthas been well established. Most of the integral inequalities studied in the fuzzy integration context normally considerconditions such as monotonicity or comonotonicity. In this paper, we are trying to extend the fuzzy integrals to theconcept of concavity. It is shown that the Hermite-Hadamard integral inequality for concave functions is not satisfied inthe case of fuzzy integrals. We propose upper and lower bounds on the fuzzy integral of concave functions. We presenta geometric interpretation and some examples in the framework of the Lebesgue measure to illustrate the results.
    Keywords: Sugeno fuzzy integral, Hermite-Hadamard inequality, Concave function, Supergradient