### فهرست مطالب • Volume:17 Issue: 3, 2020
• تاریخ انتشار: 1399/03/12
• تعداد عناوین: 14
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• صفحات 1-18
• صفحات 19-31
• صفحات 33-41
• صفحات 43-49

در این مقاله، روشی را معرفی میکنیم که در آن تبدیلات ابر-و زیر-جمعی توابع انباشتگی با گرفتن سوپرما و اینفیما روی سیمیلکس هایی که بعد آنها امکان افزایش بطور دلخواه دارند، بدست ، میآیند. از این رو امکان تعیین مقادیر دقیق چنین تبدیلاتی درحالت کلی مشکل است. دراین مقاله روش های تقریب الگوریتم چنین تبدیلاتی را مورد بحث قرار میدهیم.

• صفحات 51-68
• صفحات 69-84
• صفحات 85-102
• صفحات 103-116
• صفحات 117-134
• صفحات 135-149
• صفحات 151-161
• صفحات 163-176

در این مقاله، جبرهای مثلثی را با اضافه کردن عملگر یکتایی حالت، توسیع می دهیم. این ساختارهای جبری را جبرهای مثلثی حالت نامیم و برخی ویژگی های اساسی این جبرها را ارایه میدهیم. سپس مفهوم فیلترهای مشبکه مانده بازهای مقدار حالت را معرفی کرده و چند مثال و ویژگی (IVRL) فیلتر توسیع σ هایی از آنها را مورد بررسی قرار می دهیم. در پایان، با استفاده از این مفهوم، دو نوع یافته IVRL از جبرهای مثلثی حالت را معرفی می کنیم.

• صفحات 177-186

مفهوم مجموعه های فازی مختلط، تعمیمی از مجموعه های فازی معمولی است. دراین مقاله، مفهوم زیر ابرگروه های فازی مختلط و همچنین مفهوم زیر ابرگروه های پادفازی مختلط را معرفی می کنیم. ویژگی های آنها و روابط بین آنها و زیر ابرگروه های سنتی را بررسی و برخی نتایج را در این رابطه ثابت میکنیم

• صفحات 187-198

در این مقاله، برای پیشنهاد یک تخصیص توان، توسعه ی کارایی آن و نرمال سازی در چارجوب بازیهای کارایی- قابل انتقال فازی چند معیاره، کارآیی حداکثری را در بین بردارهای (تصمیم) سطح فازی به خدمت میگیریم. همچنین جهت گویایی این قوانین، نتایج اصولی متعددی را فراهم می آوریم. برای توسعه کارایی و نرمالسازی بر اساس نقطه نظرات متفاوت، فرمول های متفاوت و نتایج پویا را به ترتیب با بکار بردن بازی تقلیل یافته و تابع مازاد، معرفی میکنیم.

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• X. Wu *, D. A. Ralescu, Y. Liu Pages 1-18

The aim of this paper is to propose a convex risk measure in the framework of fuzzy random theory and verify its advantage over the conventional variance approach. For this purpose, this paper defines the quadratic deviation (QD) of fuzzy random variable as the mathematical expectation of QDs of fuzzy variables. As a result, the new risk criterion essentially describes the variation of a fuzzy random variable around its expected value. For triangular and trapezoidal fuzzy random variables as well as their linear combinations, we establish the analytical expressions of their QDs, and obtain the desirable convexity about the analytical expressions with respect to critical parameters. To explore the practical value of the proposed QD, we apply it to a portfolio selection problem to quantify the investment risk, and develop three mean-QD models to find the optimal allocation of the fund in different risky securities. Due to the convexity of our QD, the original three mean-QD models can be turned into their equivalent convex parametric quadratic programming problems, which can be solved by conventional optimization methods. The computational results clearly demonstrate that our new QD significantly reduces the computational complexity that cannot be avoided when variance is used as a risk criterion. Finally, the numerical comparison between the proposed mean-QD model and mean-variance model is conducted to show the consistency between the optimal results in both techniques. Meanwhile, the comparison between the proposed QD, variance, spread, and second moment is made to summarize the similarities and differences between them, distinguish these four risk criteria and determine their respective application scopes in decision systems.

Keywords: Risk criterion, hybrid uncertainty, mean-QD model, convexity, computational complexity, portfolio optimization
• R. Osuna-Gomez *, B. Hernandez-Jimenez, Y. Chalco-Cano, G. Ruiz-Garzon Pages 19-31

In this paper we study fuzzy multiobjective optimization problems defined for \$n\$ variables.  Based on a new \$p\$-dimensional fuzzy stationary-point definition,  necessary  efficiency conditions are obtained.  And we prove that these conditions are also sufficient under new fuzzy generalized convexity notions. Furthermore, the results are obtained under general differentiability hypothesis.

Keywords: Multiobjective fuzzy optimization, generalized differentiable fuzzy functions, fuzzy generalized convexity
• X. Pu *, Z. Wang, R. Mesiar, R. R. Yager, J. Qin, X. Feng, L. Jin Pages 33-41

This study discusses some variants of Ordered WeightedAveraging (OWA) operators and related information aggregation methods. Indetail, we define the Extended Ordered Weighted Sum (EOWS) operator and theExtended Ordered Weighted Averaging (EOWA) operator, which are applied inscientometrics evaluation where the preference is over finitely manyrepresentative works. As contrast, we also define the Infinite OrderedWeighted Sum (InOWS) operator and the Infinite Ordered Weighted Averaging(InOWA) operator, which are more suitable for the correspondingscientometrics evaluation where all of works of scholars are considered. Wealso define the family of Infinite Gaussian maxitive OWA weights functionand the family of Infinite Gaussian OWA weights function, and discuss someof their mathematical properties. Some illustrative examples, comparisonsand figures are provided to better expound their applicability inscientometrics evaluation.

Keywords: aggregation function, Decision making, evaluation, Information fusion, ordered weighted averaging operators
• F. Kouchakinejad *, A. Siposova Pages 43-49

The way super- and sub-additive transformations of aggregation functions are introduced involve suprema and infima taken over simplexes whose dimensions may grow arbitrarily. Exact values of such transformations may thus be hard to determine in general. In this note we discuss methods of algorithmic approximation of such transformations.

• B. Farhadinia *, Z. S. Xu Pages 51-68

Throughout the present manuscript, we are going to introduce a novel group emergency decision-making technique in which the application of prospect theory explains the psychological behaviour of the decision maker who is affected by the hesitancy and uncertainty of cognition in decision making problems.\Instead of usual aggregation procedure, we implement here a new fusion technique that is based on modified version of extended hesitant fuzzy set (EHFS), and it definitely keeps possible amount of expert's information more than the existing fusion technique of hesitant fuzzy set (HFS).The main motivation of re-visiting the concept of EHFS comes from its potential role in increasing the richness of numerical appearance in the form of value-groups, and of course its ability in identifying various decision makers in decision making situations. Such a definition further expands the practical applications of HFSs.\Finally, we employ the barrier lake problem to illustrate the feasibility and the validity of the presented technique.

Keywords: Extended hesitant fuzzy set, multiple criteria group decision making, prospect theory, emergency event
• C. Alcalde *, A. Burusco, H. Bustince, M. Sesma-Sara Pages 69-84

Sometimes we have to work with  \$L\$-fuzzy context sequences where one or more values are missing. These sequences can represent, among other things, the evolution in time of an \$L\$-fuzzy context. The studies of tendencies that we have done so far used tools that are not valid when the \$L\$-fuzzy context has unknown values. In this work we address such situations and we propose new methods to tackle the problem. Besides, we use the study of tendencies to analyse relations between the objects and the attributes of \$L\$-fuzzy contexts and to replace the absent values  taking into account the behaviour of the sequence.

Keywords: Trend Analysis, \$L\$-fuzzy context, absent values, \$L\$-fuzzy concept, \$L\$-fuzzy context sequence
• A. Zamzamzadeh *, M. A. Yaghoobi Pages 85-102

This paper considers a biobjective transportation problem with various fuzzy objective functions coefficients. Fuzzy coefficients can be of different types such as triangular, trapezoidal, (semi) \$L-R\$, or flat (semi) \$L-R\$ fuzzy numbers. First, we convert the problem to a parametric interval biobjective transportation problem using \$gamma\$-cuts of fuzzy coefficients. Then, we consider a fix \$gamma\$-cut and obtain a necessarily weak efficient solution to the yielded interval biobjective program by a new algorithm. It uses basic feasible solutions and the parametric simplex algorithm. Furthermore, we suggest another algorithm for finding a reasonable solution, called \$gamma^*\$-necessarily weak efficient, to the main biobjective transportation problem. To illustrate the validity and performance of the proposed algorithms, we present some numerical examples.

Keywords: Biobjective transportation problem, inerval biobjective linear programming problem, necessarily week efficient solution, Fuzzy membership function, \$gamma\$-cut
• X. R. Sun *, H. W. Liu Pages 103-116

Recently the distributive equations involving various classes of aggregation operators have aroused widespread attention because of their importance in the theoretic and applied communities of fuzzy set theory. 2-uninorms and semi-t-operators are two special classes of aggregation operators and have been proved to be useful in many areas such as fuzzy decision making, approximate reasoning and so on. Therefore, the aim of this paper is to investigate the left (right) distributivity of semi-t-operators over 2-uninorms. We consider five subclasses of 2-uninorms and characterize the corresponding left (right) distributive equations of semi-t-operators over 2-uninorms.

Keywords: Fuzzy connective, distributivity, triangular norm, semi-t-operator, 2-uninorm
• A. Hussain *, M. I. Ali, T. Mahmood Pages 117-134

The aim of this manuscript is to present a new concept of hesitant q-rung orthopair fuzzy sets (Hq-ROFSs) by combining the concept of the q-ROFSs as well as Hesitant fuzzy sets. The proposed concept is the generalization of the fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and Pythagorean fuzzy sets as well as intuitionistic hesitant fuzzy sets (IHFSs) and hesitant Pythagorean fuzzy sets (HPFSs).Furthermore some basic operational laws of hesitant q-rung orthopair fuzzy have been investigated. The score and accuracy functions are defined which play a vital role in decision making process for making comparison between the hesitant q-rung orthopair fuzzy numbers (Hq-ROFNs). Under the Hq-ROF environment, Hq-ROF weighted averaging (Hq-ROFWA) and Hq-ROF weighted geometric (Hq-ROFWG) operators are introduced and various properties of these aggregation operators are studied. Additionaly, a numerical application shows that how the proposed operators are utilized to solve multi-criteria decision making (MCDM) problems in which experts added their optimistic and pessimistic preferences. Finally the analysis of proposed method with other methods is presented which show that the method presented in this paper is more flexible and superior than existing methods.

Keywords: Hesitant fuzzy sets, Pythagorean fuzzy sets, q-rung orthopair fuzzy sets, Hesitant q-rung orthopair fuzzy sets, Hesitant q-rung orthopair fuzzy weighted averaging operators, Hesitant q-rung orthopair fuzzy weighted geometric operators, Multi-criteria Decision Making
• M. Yadegari *, S. A. Seyedin Pages 135-149

One of the important challenges in Graphical models is the problem of dealing with the uncertainties in the problem. Among graphical networks, fuzzy cognitive map is only capable of modeling fuzzy uncertainty and the Bayesian network is only capable of modeling probabilistic uncertainty. In many real issues, we are faced with both fuzzy and probabilistic uncertainties. In these cases, the proposed method of this paper can take into account both types of uncertainty with a new and different approach. In this method, we avoid fuzzy transformations to probabilities and vice versa, and fuzzy uncertainties and probabilities are considered jointly. For this purpose, in the original graphical model, first, the type of uncertainty of each node is identified, and accordingly two separate fuzzy and probabilistic networks are constructed. In these networks, relations between nodes are expressed in terms of a set of rules. In each network, fuzzy and probabilistic inference is individually constructed and ultimately the values obtained from each network are combined. This method has been tested on a real problem of localization in wireless sensor networks. In this case, a sensor with uncertain location should be able to predict its location from the received power of its adjacent sensors. In the given scenario, 60 sensors with uncertain locations and 121 sensors with a specific location are considered. Meanwhile, the average location error of sensors has been used to evaluate the methods. The simulation results show the efficiency of the proposed method well.

Keywords: Graphical models, fuzzy cognitive map, Bayesian network, fuzzy, probabilistic uncertainty, rules, Wireless sensor network
• V. V. Tai *, L. D. Nghiep Pages 151-161

This study proposes the model for interpolating time series to use them  to forecast effectively for future. This model is established based on the improved fuzzy clustering analysis problem, which is implemented by the Matlab procedure. The proposed model is illustrated by a data set and tested for many other datasets, especially for 3003 series in  M3-Competition data. Comparing  to the existing models, the proposed model always gives the best result. We also apply  the proposed model in forecasting  the salt peak for a coastal province of Vietnam. Examples and applications show the potential of the studied problem.

Keywords: Cluster analysis, forecast, fuzzy time series model, interpolating data
• S. Zahiri *, A. Borumand Saeid Pages 163-176

In this paper, we enlarge the language of triangle algebra by addinga unary operation that describes properties of a state. Thesestructure algebras are called state triangle algebra. The vitalproperties of these algebras are given. The notion of state interval-valued residuated lattice (IVRL)-filters are introduced and givesome examples and properties of them are given. Using this concept, we definetwo types IVRL-extended \$sigma\$-filters of a state trianglealgebra.

Keywords: Triangle algebra, IVRL-filter, State operator, State IVRL-filter
• M. Al-Tahan *, B. Davvaz Pages 177-186

The concept of complex fuzzy sets is a generalization of ordinary fuzzy sets. In this paper, we introduce the concept of complex fuzzy subhypergroups (\$H_{v}\$-subgroups) as well as the concept of complex anti-fuzzy subhypergroups (\$H_{v}\$-subgroups). We investigate their properties and their relations with the traditional fuzzy (anti-fuzzy) subhypergroups (\$H_{v}\$-subgroups), and we prove some results in this respect.

Keywords: complex fuzzy set, complex fuzzy subhypergroup, complex anti-fuzzy subhypergroup
• Y. H. Liao *, L. Y. Chung Pages 187-198

In this paper, we adopt supreme-utilities among fuzzy level (decision) vectors to propose a power allocation rule, its efficient extension and normalization in the framework of multicriteria fuzzy transferable-utility (TU) games. We also provide several axiomatic results to present the rationality for these rules. Based on different viewpoints, we introduce different formulations and dynamic results for the efficient extension and the normalization by applying the reduced game and the excess function respectively.

Keywords: Multicriteria fuzzy TU game, supreme-utility, reduced game, excess function, dynamic result