### فهرست مطالب

• Volume:15 Issue:6, 2018
• تاریخ انتشار: 1397/09/14
• تعداد عناوین: 10
|
|
• Barbara Pekala* Pages 1-16
The paper introduces a new approach to preference structure, where from a weak preference relation derive the following relations:strict preference, indifference and incomparability, which by aggregations and negations are created and examined. We decomposing a preference relation into a strict preference, an indifference, and an incomparability relation. This approach allows one to quantify different types of uncertainty in selecting alternatives. In presented preference structure we use interval-valued fuzzy relations, which can be interpreted as a tool that may help to model in a better way imperfect information, especially under imperfectly defined facts and imprecise knowledge. Preference structures are of great interest nowadays because of their applications, so we propose at the end the algorithm of decision making by use new preference structure.
Keywords: Interval-valued fuzzy relations, Preference relations, Reciprocity property
• L. Perez, Domnguez* , A. Alvarado, Iniesta, J. L. Garca, Alcaraz, D. J. Valles, Rosales Pages 17-40
Dimensional analysis, for multi-criteria decision making, is a mathematical method that includes diverse heterogeneous criteria into a single dimensionless index. Dimensional Analysis, in its current definition, presents the drawback to manipulate fuzzy information commonly presented in a multi-criteria decision making problem. To overcome such limitation, we propose two dimensional analysis based techniques under intuitionistic fuzzy environments. By the arithmetic operations of intuitionistic fuzzy numbers, we describe the intuitionistic fuzzy dimensional analysis (IFDA) and the aggregated intuitionistic fuzzy dimensional (AIFDA) techniques. In the first technique, we consider only the handling of fuzzy information; and, in the second one we consider both quantitative (crisp) and qualitative (fuzzy) information typically presented together in a decision making problem. To illustrate our approaches, we present some numerical examples and perform some comparisons with other well-known techniques.
Keywords: Dimensional analysis, Intuitionistic fuzzy set, Multi-criteria decision making
• Roya Mastiani, Sohrab Effati * Pages 41-64
In order to more effectively cope with the real world problems of vagueness, imprecise and subjectivity, fuzzy event systems were proposed recently. In this paper, we investigate the controllability and the observability property of two systems that one of them has fuzzy variables and the other one has fuzzy coefficients and fuzzy variables (fully fuzzy system). Also, sufficient conditions for the controllability and the observability of such systems are established. Some examples are given to substantiate the results obtained.
Keywords: Fuzzy dynamical systems, Controllability, Observability, Fuzzy number, Fuzzy state
• Saad M. Darwish* Pages 65-82
Sign language recognition has spawned more and more interest in human–computer interaction society. The major challenge that SLR recognition faces now is developing methods that will scale well with increasing vocabulary size with a limited set of training data for the signer independent application. The automatic SLR based on hidden Markov models (HMMs) is very sensitive to gesture's shape information that makes the accurate parameters of the HMM not capable of characterizing the ambiguous distributions of the observations in gesture's features. This paper presents an extension of the HMMs using interval type-2 fuzzy sets (IT2FSs) to produce interval type-2 fuzzy HMMs to model uncertainties of hypothesis spaces (unknown varieties of parameters of the decision function). The benefit of this enlargement is that it can control both the randomness and fuzziness of traditional HMM mapping. Membership function (MF) of type-2 FS is three-dimensional that provides additional degrees of freedom to evaluate HMM's uncertainties. This system aspires to be a solution to the scalability problem, i.e. has real potential for application on a large vocabulary. Furthermore, it does not rely on the use of data gloves or other means as input devices, and operates in isolated signer-independent modes. Experimental results show that the interval type-2 fuzzy HMM has a comparable performance as that of the fuzzy HMM but is more robust to the gesture variation, while it retains almost the same computational complexity as that of the FHMM.
• Xinxing Wu , Lidong Wang *, Jianhua Liang Pages 83-95
Some characterizations on the chain recurrence, chain transitivity, chain mixing property, shadowing and $h$-shadowing for Zadeh's extension are obtained. Besides, it is proved that a dynamical system is spatiotemporally chaotic provided that the Zadeh's extension is Li-Yorke sensitive.
• Saima Mustafa*, Sobia Asghar, Muhammad Hanif Pages 97-106
Logistic regression is a non-linear modification of the linear regression. The purpose of the logistic regression analysis is to measure the effects of multiple explanatory variables which can be continuous and response variable is categorical. In real life there are situations which we deal with information that is vague in nature and there are cases that are not explained precisely. In this regard, we have used the concept of possiblistic odds and fuzzy approach. Fuzzy logic deals with linguistic uncertainties and extracting valuable information from linguistic terms. In our study, we have developed fuzzy possiblistic logistic model with trapezoidal membership function and fuzzy possiblistic logistic model is a tool that help us to deal with imprecise observations. Comparison fuzzy logistic regression model with classical logistic regression has been done by goodness of fit criteria on real life as an example.
Keywords: Logistic regression, Odd ratio, Goodness of fit, Fuzzy Logic, Trapezoidal number
• A. Khalid* , Ismat Beg Pages 107-120
In this article, we propose a method to deal with incomplete interval-valued hesitant fuzzy preference relations. For this purpose, an additive transitivity inspired technique for interval-valued hesitant fuzzy preference relations is formulated which assists in estimating missing preferences. First of all, we introduce a condition for decision makers providing incomplete information. Decision makers expressing incomplete data are expected to abide by the proposed condition. This ensures that the estimated preferences are well-defined intervals which otherwise may not be possible. Additionally, this condition eliminates the problem of outlying estimated preferences. After resolving the issue of incompleteness, this article proposes a ranking rule for reciprocal and non-reciprocal interval-valued hesitant fuzzy preference relations.
Keywords: Hesitant fuzzy preference relations, Incomplete preference relations, Decision making, Preference modeling
• Jinquan Li *, Dehua Xu, Hongxing Li Pages 121-143
In this paper, a due date assignment scheduling problem with precedence constraints and controllable processing times in uncertain environment is investigated, in which the basic processing time of each job is assumed to be the symmetric trapezoidal fuzzy number, and the linear resource consumption function is used. The objective is to minimize the crisp possibilistic mean (or expected) value of a cost function that includes the costs of earliness, tardiness, makespan and resource consumption jointly by scheduling the jobs under precedence constraints and determining the due date and the resource allocation amount satisfying resource constraints for each job. First, the problem is shown to be NP-hard. Furthermore, an optimal algorithm with polynomial time for the special case of this problem is put forward. Moreover, an efficient 2-approximation algorithm is presented based on solving the relaxation of the problem. Finally, the numerical experiment is given, whose results show that our method is promising.
Keywords: Fuzzy scheduling, Fuzzy number, Possibilistic mean value, variance, Due date assignment scheduling, Precedence constraints, Controllable processing times
• Jiang Yang, Xiao Long Xin *, Peng Fei He Pages 145-158
In this paper, by using a special family of filters $\mathcal{F}$ on an EQ-algebra $E$, we construct a topology $\mathcal{T}_{\mathcal{\mathcal{F}}}$ on $E$ and show that $(E,\mathcal{T}_{\mathcal{F}})$ is a topological EQ-algebra. First of all, we give some properties of topological EQ-algebras and investigate the interaction of topological EQ-algebras and quotient topological EQ-algebras. Then we obtain the form of closure of each subset and show that $(E,\mathcal{T}_{\mathcal{F}})$ is a zero-dimensional space. Finally, we introduce the concept of convergence of sequences on topological EQ-algebras and give a condition under which the limit of a sequence is unique.
Keywords: Topological $EQ$-algebra, System of filters, Cauchy sequence
• Kai Wang, Fu, Gui Shi * Pages 159-174
The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtained from $M$-fuzzifying topological convex spaces.
Keywords: $M$-fuzzifying topological convex space, $M$-fuzzifying topology, $M$-fuzzifying convexity, $M$-fuzzifying weak topology, Compatibility