• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Aggregation Operators for Interval-Valued Pythagorean Fuzzy SoftSet with Their Application to Solve Multi-Attribute Group Decision Making Problem

    2022-07-02 07:43:54RanaMuhammadZulqarnainImranSiddiqueAiyaredIampanandDumitruBaleanu

    Rana Muhammad Zulqarnain,Imran Siddique,Aiyared Iampan and Dumitru Baleanu

    1Department of Mathematics,University of Management and Technology,Sialkot Campus,Lahore,54770,Pakistan

    2Department of Mathematics,University of Management and Technology,Lahore,54000,Pakistan

    3Department of Mathematics,School of Science,University of Phayao,Mae Ka,Mueang,Phayao,56000,Thailand

    4Department of Mathematics,Cankaya University,Balgat Ankara,06530,Turkey

    5Institute of Space Sciences,Magurele-Bucharest,077125,Romania

    6Department of Medical Research,China Medical University Hospital,China Medical University,Taichung,40447,Taiwan

    ABSTRACT Interval-valued Pythagorean fuzzy softset(IVPFSS)is a generalization of the interval-valued intuitionistic fuzzy softset (IVIFSS) and interval-valued Pythagorean fuzzy set (IVPFS).The IVPFSS handled more uncertainty comparative to IVIFSS;it is the most significant technique for explaining fuzzy information in the decision-making process.In this work,some novel operational laws for IVPFSS have been proposed.Based on presented operational laws,two innovative aggregation operators(AOs)have been developed such as interval-valued Pythagorean fuzzy softweighted average (IVPFSWA) and interval-valued Pythagorean fuzzy softweighted geometric (IVPFSWG)operators with their fundamental properties.A multi-attribute group decision-making(MAGDM)approach has been established utilizing our developed operators.A numerical example has been presented to ensure the validity of the proposed MAGDM technique.Finally,comparative studies have been given between the proposed approach and some existing studies.The obtained results through comparative studies show that the proposed technique is more credible and reliable than existing approaches.

    KEYWORDS Interval-valued Pythagorean fuzzy softset;IVPFSWA operator;IVPFSWG operator;MAGDM

    1 Introduction

    MAGDM is considered as the most appropriate technique to find the finest alternative from all possible alternatives,following criteria or attributes.Conventionally,it is supposed that all information that accesses the alternative in terms of attributes and their corresponding weights are articulated in the form of crisp numbers.On the other hand,in real-life circumstances,most of the decisions are taken in situations where the objectives and limitations are usually indefinite or ambiguous.To overcome such ambiguities and anxieties,Zadeh offered the notion of the fuzzy set (FS) [1],a prevailing tool to handle the obscurities and uncertainties in decision making (DM).Such a set allocates to all objects a membership value ranging from 0 to 1.Mostly,experts consider membership and a non-membership value in the DM process which cannot be handled by FS.Atanassov [2] introduced the idea of the intuitionistic fuzzy set (IFS) to overcome the aforementioned limitation.In 2011,Wang et al.[3] presented numerous operations on IFS,such as Einstein product,Einstein sum,etc.,and constructed some novel AOs.They also discussed some important properties of these operators and utilized their proposed operators to resolve multi-attribute decision making (MADM).Atanassov [4] presented a generalized form of IFS in the light of ordinary interval values,called interval-valued intuitionistic fuzzy set (IVIFS).Garg et al.[5] extended the concept of IFS and presented a novel concept of the cubic intuitionistic fuzzy set (CIFS) which is a successful tool to represent vague data by embedding both IFS and IVIFS directly.They also discussed several desirable properties of CIFS.

    The above-mentioned models have been well-recognized by the specialists but the existing IFS is unable to handle the inappropriate and vague data because it is considered to envision the linear inequality between the membership and non-membership grades.For example,if decision-makers choose membership and non-membership values 0.9 and 0.6 respectively,then the above-mentioned IFS theory is unable to deal with it because 0.9 + 0.6≥1.To resolve the aforesaid limitation,Yager [6] presented the idea of the Pythagorean fuzzy set (PFS) by amending the basic conditionκ+δ≤1 toκ2+δ2≤1 and developed some results associated with score function and accuracy function.Rahman et al.[7] developed the Pythagorean fuzzy Einstein weighted geometric operator and presented a MAGDM methodology utilizing their proposed operator.Zang et al.[8] developed some basic operational laws and prolonged the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method to resolve multi-criteria decision-making (MCDM) complications for PFS information.Wei et al.[9] offered the Pythagorean fuzzy power AOs along with basic characteristics,they also established a DM technique to resolve MADM difficulties based on presented operators.Wang et al.[10] offered the interaction operational laws for Pythagorean fuzzy numbers (PFNs) and developed power Bonferroni mean operators.To assess the professional health risk,IIbahar et al.[11] offered the Pythagorean fuzzy proportional risk assessment technique.Zhang [12] proposed a novel DM approach based on similarity measures to resolve multi-criteria group decision making (MCGDM)difficulties for the PFS.

    All of the aforementioned techniques have a wide range of applications,but owing to their ineffectiveness,they have several restrictions with the parameterization tool.Presenting a solution to this type of uncertainty and obfuscation Molodtsov [13] established the idea of soft sets (SS)and described some basic operations with their characteristics to handle the above-mentioned confusion and ambiguity.Maji et al.[14] expanded the concept of SS and developed many basic and binary operations for it.Maji et al.[15] developed the fuzzy soft set with some desirable properties by merging two existing notions FS and SS.Maji et al.[16] developed the notion of the intuitionistic fuzzy soft set (IFSS) and some fundamental operations with their necessary properties.Garg et al.[5] presented the cubic IFSS and established some AOs for cubic IFSS.They also planned a DM technique based on their developed operators.Zulqarnain et al.[17]planned the TOPSIS method based on the correlation coefficient for interval-valued IFSS to solve MADM problems.Jiang et al.[18] introduced the notion of the interval-valued intuitionistic fuzzy soft set (IVIFSS) and discussed some of their basic properties.Narayanamoorthy et al.[19]proposed the score function for a normal wiggly hesitant fuzzy set and utilized it to expose the deepest ideas hidden in the thought-level of the decision-makers.Narayanamoorthy et al.[20]introduced the hesitant fuzzy subjective and objective weight integrated method to find weights under hesitant fuzzy information.They also presented a novel ranking methodology for hesitant fuzzy sets.Ramya et al.[21] developed the interval-valued hesitant Pythagorean fuzzy set under the normal wiggly mathematical methodology and used it to solve the MCDM problem.Peng et al.[22] merged two well-known theories PFS and SS and offered the concept of Pythagorean fuzzy soft set (PFSS).Zulqarnain et al.[23] developed the AOs for PFSS with their application for the green supplier chain management.Zulqarnain et al.[24] introduced an advanced form of AOs considering the interaction and construct a DM approach based on their developed interactive AOs.Smarandache [25] prolonged the idea of SS to hypersoft sets (HSS) by substituting the single-parameter functionfwith a multi-parameter (sub-attribute) function.He privileges that HSS proficiently contracts with inexact data comparative to SS.

    MAGDM is a very effective and well-known tool to examine fuzzy data more effectively.Therefore,it is obvious from the published literature that the interval-valued structures are more general and increase more consideration in decision-making difficulties.The choice of vehicle is a key part of real-life and will advise on complications of MAGDM.Lack of thinking about the ambiguity of alternative associations will be the core motivation for some MAGDM concerns about the undesirable consequences.By using a wealth of existing content,it contains previous criticisms and suppressed sensitivities.Many logical and scientific tools/procedures are offended in the literature for choosing the most suitable vehicle.As far as we know,there is currently no work on the AOs of IVPFSS.Therefore,this article proposes some operational laws for interval-valued Pythagorean fuzzy soft numbers (IVPFSN).The presented IVPFSN is well worth observing the inaccurate information that occurs in the complications of daily life.Therefore,the main purpose of this work is to propose new IVPFSWA and IVPFSWG operators based on the established operational laws.An algorithm based on the proposed operators to solve the decision-making problem is proposed.To prove the effectiveness of the proposed decision-making method,we use a numerical example to illustrate it.The main benefit of the proposed operator is that the proposed operator can reduce to IVIFSS and IVFSS operators under some specific conditions of unconfidence.The organization of this paper is given as follows: Section 2 of this paper consists of some basic concepts which help us to develop the structure of the following research.In Section 3,some novel operational laws for IVPFSN have been proposed.Also,in the same section,IVPFSWA and IVPFSWG operators have been introduced based on our developed operators with their basic properties.In Section 4,a MAGDM approach has been constructed based on the proposed AOs.To ensure the practicality of the developed approach a numerical example has been presented for the selection of the best vehicle in Section 5.

    2 Preliminaries

    This section consists of some basic definitions which will provide a structure to form the following work.

    Definition 2.1[1]

    LetUbe a collection of objects then a fuzzy set (FS)AoverUis defined as

    A={(t,κ(t))|t∈U}

    where,κA(t):X→[0,1] is a membership grade function.

    Definition 2.2[26]

    LetUbe a collection of objects then an interval-valued fuzzy set (IVFS)AoverUis defined as

    where,κl(t),κu(t)∈[0,1] and represents the lower and upper bounds of the membership value.

    Definition 2.3[4]

    LetUbe a collection of objects then an interval-valued intuitionistic fuzzy set (IVIFS)AoverUis defined as

    Definition 2.4[27]

    LetUbe a collection of objects then an interval-valued Pythagorean fuzzy set (IVPFS)AoverUis defined as

    Definition 2.5[13]

    LetUbe a universal set and N={t1,t2,t3,...,tm} be set of attributes then a pair (F,N)is called a soft set (SS) overUwhereF: N→KUis a mapping andKUis known as a collection of all subsets of universal setU.

    Definition 2.6[19]

    LetUbe a universal set and N be a set of attributes then a pair (Ω,N)is called an intervalvalued intuitionistic fuzzy soft set (IVIFSS) overU.WhereΩ: N→IKUis a mapping andIKUis known as a collection of all interval-valued intuitionistic fuzzy subsets of universal setUandA?N.

    Definition 2.7

    LetUbe a universal set and N be set of attributes then a pair ((Ω,N)is called an intervalvalued Pythagorean fuzzy soft set (IVPFSS) overUwhereΩ: N→?KUis a mapping and?KUis known as the collection of all interval-valued Pythagorean fuzzy subsets of universal setU.

    Definition 2.8

    Definition 2.9

    3 Aggregation Operators for Interval Valued Pythagorean Fuzzy Soft Sets

    In this section,we are going to define operational laws under IVPFSNs.Based on these operational laws,we shall also present interval-valued Pythagorean fuzzy soft weighted average(IVPFSWA) and interval-valued Pythagorean fuzzy soft geometric (IVPFSWG) operators.

    3.1 Operational Laws for Interval Valued Pythagorean Fuzzy Soft Numbers

    3.2 Interval Valued Pythagorean Fuzzy Soft Weighted Average Operator

    Theorem 3.1

    where ωiandνjare weight vector for expert’s and attributes respectively with given conditions

    Proof.We shall prove the IVPFSWA operator by utilizing the principle of mathematical induction:

    Forn=1,we getω1=1.Then,we have

    Form=1,we getν1=1.Then,we have

    This shows that the above theorem holds forn=1 andm=1.Now,consider the above theorem also holds form=α1+1,n=α2andm=α1,n=α2+1,such as

    Form=α1+1 andn=α2+1,we have

    Therefore,it holds form=α1+1 andn=α2+1.So,we can judge that the above theorem also holds for all values ofmandn.

    Example 3.1

    Letχ={x1,x2,x3} be the set of specialists with weightsωi=(0.38,0.45,0.17)Twho wants to choose a bike under some defined set of propertiesφ={e1=Resale Value,e2=Mileage,e3=Cost of bike} with weightsνj=(0.25,0.45,0.3)T.We suppose the rating values of the specialists for each property in the form of IVPFSNsis given as

    By using the above theorem,we have

    3.3 Properties of PFSWA Operator

    3.3.1 Idempotency

    Proof: As we know that allthen,we have

    Hence proved.

    3.3.2 Boundedness

    LetMeijbe a collection of PFSNs whereandthen

    Proof.As we know thatbe an IVPFSN,then

    Similarly,we can prove that

    Let IVPFSWA (Me11,Me12,...,Menm)=then inequalities (a) and(b) can be transferred into the form:andrespectively.

    So,by using the score function,we have

    Then,by order relation between two IVPFSNs,we have

    Hence proved.

    3.3.3 Shift Invariance

    IVPFSWA(Me11⊕Me,Me12⊕Me,...,Menm⊕Me)=IVPFSWA(Me11,Me12,...,Menm)⊕Me

    Proof.ConsiderMeandMeijbe two IVPFSNs.Then,by operational laws defined under IVPFSNs defined above,we have

    Hence proved.

    3.3.4 Homogeneity

    Prove that IVPFSWA(βMe11,βMe12,...,βMenm)=βIVPFSWA(Me11,Me12,...,Menm)for any positive real numberβ.

    Proof.LetMeijbe an IVPFSN andβ>0,then by using the operational laws mentioned above,we have

    So,

    which completes the proof.

    3.4 Interval Valued Pythagorean Fuzzy Soft Weighted Geometric Operator

    Theorem 3.2

    where ωiandνjare weight vector for expert’s and attributes respectively with given conditions

    Proof.We can prove the IVPFSWG operator by using the principle of mathematical induction as follows:

    Forn=1,we getω1=1.Then,we have

    Form=1,we getν1=1.Then,we have

    This shows that the above theorem holds forn=1 andm=1.Now,consider the above theorem also holds form=α1+1,n=α2andm=α1,n=α2+1,such as

    Form=α1+1 andn=α2+1,we have

    It is clarified from the above equation that the theorem holds form=α1+1 andn=α2+1.So,we can say that the theorem holds for all values ofmandn.

    Example 3.2

    Again,consider Example 3.1 with rating values of the specialists for each property in the form of IVPFSNsis given as

    By using the above theorem,we have

    3.5 Properties of IVPFSWG

    3.5.1 Idempotency

    Proof.As we know that allthen,we have

    Hence proved.

    3.5.2 Boundedness

    LetMeijbe a collection of PFSNs whereandthen

    Proof.As we know thatbe an IVPFSN,then

    Similarly,we can prove that

    Let IVPFSWG(Me11,Me12,...,Menm)=then inequalities (c) and(d) can be transferred into the form:

    respectively.

    So,by using the score function,we have

    Then,by order relation between two IVPFSNs,we have

    Hence proved.

    3.5.3 Shift Invariance

    IVPFSWG (Me11⊕Me,Me12⊕Me,...,Menm⊕Me)=IVPFSW(Me11,Me12,...,Menm)⊕Me

    Proof.ConsiderMeandMeijbe two IVPFSNs.Then,by operational laws defined under IVPFSNs defined above,we have

    Hence proved.

    3.5.4 Homogeneity

    Prove that IVPFSWG(βMe11,βMe12,...,βMenm)=βIVPFSWA(Me11,Me12,...,Menm)for any positive real numberβ.

    Proof: LetMeijbe an IVPFSN andβ>0,then by using the operational laws mentioned above,we have

    So,

    which completes the proof.

    4 Multi-Attribute Group Decision-Making Approach Based on Proposed Operators

    In this section,a decision-making (DM) approach for solving multi-attribute group decisionmaking (MAGDM) problems based on proposed IVPFSWA and IVPFSWG operators has been developed along with numerical examples.

    4.1 Proposed Approach

    The procedure to apply proposed IVPFSWG and IVPFSWA operators for solving the MAGDM problem is summarized in the following steps:

    Step-1: Obtain a decision matrix in the form of PFSNs for alternatives relative to experts.

    Step-2: By using the normalization formula,normalize the decision matrix to convert the rating value of cost type parameters into benefit type parameters.

    Step-3: Use the developed IVPFSWG and IVPFSWA operators to aggregate the IVPFSNsMeijfor each alternativeinto the decision matrixMij.

    Step-4: Calculate the score values ofMfor all alternatives.

    Step-5: Select the alternative having maximum score value and examine the ranking.

    4.2 Numerical Example

    Suppose a person wants to buy a car and he has four alternatives such as I1,I2,I3and I4.There are four considered attributes according to which the person has to take the decision such ase1;price of the car,e2;comfortability,e3;resale value,and,e4;growth rate with the weighted vectorν=(0.3,0.1,0.2,0.4)T.Heree1,e3are cost type parameters ande2,e4are benefit type parameters.The person hires a team of four expertsXr(r=1,2,3,4)for decision making with the weighted vectorω=(0.1,0.2,0.4,0.3)T.

    4.2.1 By IVPFSWA Operator

    Step-1: Obtain Pythagorean fuzzy soft decision matrices (Tables 1–4).

    Table 1:IVPFS decision matrix for I1

    Table 2:IVPFS decision matrix for I2

    Table 3:IVPFS decision matrix for I3

    Table 4:IVPFS decision matrix for I4

    Step-2: Becausee1,e3are cost type parameters,so utilized the normalization formula to obtain normalized Pythagorean fuzzy soft decision matrices are given in the following Tables 5–8.

    Table 5:Normalized IVPFS decision matrix for I1

    Table 6:Normalized IVPFS decision matrix for I2

    Table 7:Normalized IVPFS decision matrix for I3

    Table 8:Normalized IVPFS decision matrix for I4

    Step-3: Apply the proposed IVPFSWA operator on the acquired data,we will obtain an opinion of the decision-makers.

    Step-4: Use the score functionS=for the interval-valued Pythagorean fuzzy soft set to calculate the score values for all alternatives.S(Θ1)=0.0377,S(Θ2)=0.0834,S(Θ3)=0.0113,andS(Θ4)=0.0141.

    Step-5: From the above calculation,we getS(Θ2)>S(Θ1)>S(Θ4)>S(Θ3),which shows that I2is the best alternative.So,I2>I1>I4>I3.

    4.2.2 By IVPFSWG Operator

    Step-1: Obtain PFS decision matrices (Tables 1–4).

    Step-2: Use the normalization formula to normalize the obtained PFS decision matrices(Tables 5–8).

    Step-3: Apply the proposed IVPFSWG operator on the acquired data,we will obtain an opinion of the decision-makers

    Step-4: Use the score functionS=interval-valued for the Pythagorean fuzzy soft set to calculate the score values for all alternatives such asS(Θ1)=0.0524,S(Θ2)=0.0754,S(Θ3)=0.0241,andS(Θ4)=0.0114.

    Step-5: From the above calculation,we get the ranking of alternativesS(Θ2)>S(Θ1)>S(Θ3)>S(Θ4),which shows that I2is the best alternative.So,I2>I1>I3>I4.

    5 Comparative Studies

    To highlight the effectiveness of the presented method,a comparison between the proposed model and prevailing methods is proposed in the following section.

    5.1 Comparative Analysis with Interval-Valued Pythagorean Fuzzy Weighted Average Operator[28]

    Step-1: Obtain an IVPF decision matrices (Tables 1–4).

    Step-2: Use normalization formula to normalize the obtained IVPF decision matrices(Tables 5–8).

    Step-3: Apply the IVPFWA operator on the acquired data,then we get the opinion of decision-makers.

    As we have

    Step-4: Use the score functionfor IVPFS to calculate the score values for all alternatives.

    Step-5: Ranking of alternativesS(Θ2)>S(Θ4)>S(Θ3)>S(Θ1).So,I2>I4>I3>I1.Hence,the best alternative is I2.

    5.2 Comparison with Interval-Valued Pythagorean Fuzzy Weighted Geometric Operator[28]

    Step-1: Obtain an IVPF decision matrices (Tables 1–4).

    Step-2: Use normalization formula to normalize the obtained IVPF decision matrices(Tables 5–8).

    Step-3: Apply the IVPFWG operator on the acquired data,then we get the opinion of decision-makers.

    As we have

    Step-4: Use the score functionfor IVPFS to calculate the score values for all alternatives.

    Step-5: Ranking of alternatives,S(Θ2)>S(Θ3)>S(Θ4)>S(Θ1).So,I2>I3>I1>I4.Hence,the best alternative is I2.

    Similarly,we can get the outcomes utilizing several other existing operators for comparative studies.

    5.3 Comparative Analysis

    To verify the effectiveness of the proposed method,we compare the obtained results with some existing methods under the environment of IVPFS and IVIFSS.A summary of all results is given in Table 9.Zulqarnain et al.[17] developed aggregation operators for IVIFSS that are unable to accommodate the decision-makers choices when the sum of upper membership and nonmembership values of the parameters exceeds one.Peng et al.[27] interval-valued Pythagorean fuzzy weighted average operator and Rahman et al.[28] interval-valued Pythagorean fuzzy weighted geometric operator cannot handle the parametrized values of the alternatives.Furthermore,if only one parameter is supposed rather than more than one parameter,the interval-valued Pythagorean fuzzy soft set reduces to the interval-valued Pythagorean fuzzy set.Similarly,if the sum of upper values of membership and nonmembership degree is less or equal to 1.Then,IVPFSS reduced to IVIFSS.Thus,IVPFSS is the most generalized form of interval-valued Pythagorean fuzzy set.Hence,based on the above-mentioned facts,admittedly,the proposed operators in this paper are more powerful,reliable,and successful.

    Table 9:Comparison of proposed operators with some existing operators

    6 Conclusion

    In this work,we have introduced two novel aggregation operators such as IVPFSWA and IPFSWG operators.Firstly,we defined operational laws under an interval-valued Pythagorean fuzzy soft environment.Based on these operational laws,we developed the aggregation operators for IVPFSS such as IVPFSWA and IVPFSWG operators with their desirable properties.Furthermore,a DM approach has been established to resolve multi-attribute group decision-making (MAGDM)problems based on presented aggregation operators.To ensure the validity of the established technique,a comprehensive numerical example has been presented.To verify the effectiveness of the proposed method,a comparative analysis with some existing methods is presented.Finally,based on obtained results,it has been concluded that the proposed method in this research is the most feasible and successful method for the MAGDM problem.

    Funding Statement: The authors received no specific funding for this study.

    Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

    久热爱精品视频在线9| 亚洲少妇的诱惑av| 国产一区二区 视频在线| 视频在线观看一区二区三区| 久久鲁丝午夜福利片| 国产日韩欧美亚洲二区| 午夜精品国产一区二区电影| 久久久久久人人人人人| 久久久久精品性色| 黑人欧美特级aaaaaa片| 久久久精品94久久精品| 日韩大码丰满熟妇| 人成视频在线观看免费观看| 伊人久久国产一区二区| 女性被躁到高潮视频| 亚洲国产欧美网| 激情五月婷婷亚洲| 国产成人免费无遮挡视频| 美女福利国产在线| 超碰成人久久| 亚洲欧美精品综合一区二区三区| 水蜜桃什么品种好| 精品国产超薄肉色丝袜足j| 免费黄网站久久成人精品| 无遮挡黄片免费观看| 精品人妻在线不人妻| 亚洲,欧美精品.| 日韩视频在线欧美| 欧美激情 高清一区二区三区| 一区二区日韩欧美中文字幕| 欧美黑人精品巨大| 亚洲,欧美,日韩| 久久亚洲国产成人精品v| 久久亚洲国产成人精品v| 看免费成人av毛片| 男女之事视频高清在线观看 | 不卡av一区二区三区| 免费在线观看视频国产中文字幕亚洲 | 国产成人av激情在线播放| 亚洲,一卡二卡三卡| 亚洲欧美一区二区三区久久| a 毛片基地| 麻豆精品久久久久久蜜桃| 亚洲国产成人一精品久久久| 天天躁狠狠躁夜夜躁狠狠躁| 久久毛片免费看一区二区三区| 91精品三级在线观看| 最近中文字幕2019免费版| 欧美精品人与动牲交sv欧美| 日本av免费视频播放| 国产一区二区在线观看av| 2018国产大陆天天弄谢| 人人澡人人妻人| 久久精品国产综合久久久| 下体分泌物呈黄色| 亚洲精品一区蜜桃| 在线精品无人区一区二区三| 精品国产一区二区三区久久久樱花| 欧美在线一区亚洲| 亚洲精品,欧美精品| 精品久久久久久电影网| 亚洲国产中文字幕在线视频| 中文字幕最新亚洲高清| xxxhd国产人妻xxx| 一区二区三区乱码不卡18| 麻豆乱淫一区二区| 国产亚洲精品第一综合不卡| 欧美黄色片欧美黄色片| 日本黄色日本黄色录像| 久久狼人影院| 十八禁网站网址无遮挡| 亚洲av电影在线进入| 免费高清在线观看日韩| 18在线观看网站| 中文字幕人妻熟女乱码| 国产片内射在线| 精品久久久精品久久久| 少妇被粗大的猛进出69影院| 激情五月婷婷亚洲| 黑人欧美特级aaaaaa片| 中文字幕av电影在线播放| 久久国产亚洲av麻豆专区| 国产免费一区二区三区四区乱码| 99久国产av精品国产电影| 在线观看www视频免费| 欧美在线黄色| 看免费成人av毛片| 麻豆av在线久日| 一本—道久久a久久精品蜜桃钙片| 久久综合国产亚洲精品| 亚洲综合精品二区| 一二三四中文在线观看免费高清| 国产女主播在线喷水免费视频网站| 国产成人精品久久久久久| 汤姆久久久久久久影院中文字幕| 亚洲熟女精品中文字幕| 亚洲美女视频黄频| √禁漫天堂资源中文www| 亚洲成人手机| 妹子高潮喷水视频| 久久精品熟女亚洲av麻豆精品| 国产精品一区二区在线观看99| 国产精品久久久久久人妻精品电影 | a级毛片在线看网站| 日本一区二区免费在线视频| 午夜老司机福利片| 大片电影免费在线观看免费| 亚洲av电影在线观看一区二区三区| 中文乱码字字幕精品一区二区三区| 熟妇人妻不卡中文字幕| 人人妻人人爽人人添夜夜欢视频| 这个男人来自地球电影免费观看 | 国产日韩欧美在线精品| 男人添女人高潮全过程视频| 在线看a的网站| 十分钟在线观看高清视频www| 久久青草综合色| av不卡在线播放| 久久精品国产a三级三级三级| 亚洲在久久综合| 亚洲av欧美aⅴ国产| 熟女少妇亚洲综合色aaa.| 大片免费播放器 马上看| 国产亚洲av高清不卡| 久久久精品免费免费高清| 成年美女黄网站色视频大全免费| 男人操女人黄网站| 日韩一卡2卡3卡4卡2021年| av网站在线播放免费| 国产成人a∨麻豆精品| 少妇人妻精品综合一区二区| 一个人免费看片子| 美女高潮到喷水免费观看| 在线观看免费日韩欧美大片| 黄片播放在线免费| 亚洲图色成人| 亚洲一区二区三区欧美精品| 日韩成人av中文字幕在线观看| 自线自在国产av| 欧美日韩一区二区视频在线观看视频在线| 国产精品一区二区在线不卡| 晚上一个人看的免费电影| 波野结衣二区三区在线| 中文字幕最新亚洲高清| 精品人妻一区二区三区麻豆| 交换朋友夫妻互换小说| 久久久久久久精品精品| 免费少妇av软件| 亚洲一区二区三区欧美精品| 精品少妇久久久久久888优播| 老熟女久久久| 汤姆久久久久久久影院中文字幕| 精品久久久精品久久久| 亚洲人成网站在线观看播放| 日日撸夜夜添| 久久人人爽人人片av| 国产在线免费精品| 国产激情久久老熟女| 国产日韩欧美视频二区| 99国产综合亚洲精品| 男女边吃奶边做爰视频| 精品亚洲乱码少妇综合久久| 十八禁人妻一区二区| 亚洲,一卡二卡三卡| 天天躁狠狠躁夜夜躁狠狠躁| 国产精品国产三级专区第一集| 一二三四中文在线观看免费高清| 亚洲国产毛片av蜜桃av| 国产免费福利视频在线观看| 大香蕉久久成人网| 男女床上黄色一级片免费看| 永久免费av网站大全| 中文字幕色久视频| 日日摸夜夜添夜夜爱| 久久久精品区二区三区| 欧美老熟妇乱子伦牲交| 国产成人精品无人区| 日韩不卡一区二区三区视频在线| 国产一区二区 视频在线| 97精品久久久久久久久久精品| 免费少妇av软件| 狠狠婷婷综合久久久久久88av| 国产麻豆69| 国产成人av激情在线播放| 欧美成人午夜精品| 午夜免费观看性视频| 亚洲国产精品一区二区三区在线| 成人国语在线视频| 欧美日韩国产mv在线观看视频| 亚洲精品国产av蜜桃| 久久久久精品人妻al黑| 香蕉国产在线看| 亚洲av电影在线观看一区二区三区| 最近2019中文字幕mv第一页| 国产精品香港三级国产av潘金莲 | 精品国产一区二区三区久久久樱花| 亚洲欧洲国产日韩| 91精品伊人久久大香线蕉| 男女床上黄色一级片免费看| 亚洲精品aⅴ在线观看| av又黄又爽大尺度在线免费看| 亚洲国产最新在线播放| 久久精品国产a三级三级三级| 波野结衣二区三区在线| 久久99精品国语久久久| 国产精品欧美亚洲77777| 亚洲综合精品二区| 十八禁高潮呻吟视频| 色网站视频免费| 免费人妻精品一区二区三区视频| 蜜桃在线观看..| 欧美激情极品国产一区二区三区| 波多野结衣一区麻豆| 免费在线观看黄色视频的| 欧美在线一区亚洲| 欧美日韩一级在线毛片| 免费观看性生交大片5| 老司机靠b影院| 日韩,欧美,国产一区二区三区| 亚洲熟女精品中文字幕| 亚洲 欧美一区二区三区| 男女午夜视频在线观看| 久久精品久久久久久噜噜老黄| 欧美日韩精品网址| 中文字幕另类日韩欧美亚洲嫩草| 少妇猛男粗大的猛烈进出视频| 亚洲精品久久成人aⅴ小说| 免费在线观看黄色视频的| 777久久人妻少妇嫩草av网站| 久久精品人人爽人人爽视色| 日本爱情动作片www.在线观看| 国产免费又黄又爽又色| 日韩精品有码人妻一区| 97精品久久久久久久久久精品| 成人亚洲欧美一区二区av| 两个人看的免费小视频| 青春草视频在线免费观看| 欧美日韩福利视频一区二区| 精品国产超薄肉色丝袜足j| 男女之事视频高清在线观看 | 免费av中文字幕在线| 亚洲图色成人| av福利片在线| 久久久精品区二区三区| 亚洲精品自拍成人| a级毛片黄视频| 国产在线免费精品| 色视频在线一区二区三区| 亚洲国产看品久久| 久久久精品国产亚洲av高清涩受| 晚上一个人看的免费电影| 日韩人妻精品一区2区三区| 午夜91福利影院| 中文字幕人妻丝袜一区二区 | 亚洲在久久综合| 欧美中文综合在线视频| 亚洲伊人色综图| 黄片无遮挡物在线观看| 最近的中文字幕免费完整| 欧美日韩亚洲综合一区二区三区_| 久久综合国产亚洲精品| 久久毛片免费看一区二区三区| 日韩大片免费观看网站| 国产乱人偷精品视频| 久久性视频一级片| 亚洲精品第二区| 香蕉丝袜av| 日日爽夜夜爽网站| 老汉色av国产亚洲站长工具| 国产成人av激情在线播放| 在线观看免费视频网站a站| 99热网站在线观看| 亚洲美女搞黄在线观看| 日本午夜av视频| 一级a爱视频在线免费观看| 香蕉丝袜av| 日日摸夜夜添夜夜爱| 18禁国产床啪视频网站| 伦理电影免费视频| 午夜免费观看性视频| 日韩大片免费观看网站| 涩涩av久久男人的天堂| 99热网站在线观看| 人人妻,人人澡人人爽秒播 | 又粗又硬又长又爽又黄的视频| 人人妻,人人澡人人爽秒播 | 男女国产视频网站| 一区福利在线观看| 一边亲一边摸免费视频| 无遮挡黄片免费观看| 国产极品粉嫩免费观看在线| 亚洲国产成人一精品久久久| 久久免费观看电影| 综合色丁香网| 蜜桃国产av成人99| 日本黄色日本黄色录像| 99热国产这里只有精品6| 欧美国产精品va在线观看不卡| 秋霞伦理黄片| 99精品久久久久人妻精品| 日韩欧美精品免费久久| 日韩精品免费视频一区二区三区| 久久精品亚洲av国产电影网| 一二三四中文在线观看免费高清| 波多野结衣av一区二区av| 午夜日本视频在线| 综合色丁香网| 纯流量卡能插随身wifi吗| 成人亚洲欧美一区二区av| 国产一区亚洲一区在线观看| 一二三四在线观看免费中文在| 欧美黑人欧美精品刺激| 亚洲av男天堂| 日韩 亚洲 欧美在线| 欧美日韩一区二区视频在线观看视频在线| 美国免费a级毛片| 久久精品国产亚洲av涩爱| 在线观看国产h片| 日韩电影二区| 国产男女内射视频| 久久狼人影院| √禁漫天堂资源中文www| 国产免费又黄又爽又色| 啦啦啦在线观看免费高清www| 国产乱人偷精品视频| 久久精品久久久久久噜噜老黄| 狂野欧美激情性bbbbbb| 看十八女毛片水多多多| 天天影视国产精品| 亚洲视频免费观看视频| 国产黄频视频在线观看| 婷婷色综合www| 欧美变态另类bdsm刘玥| 日韩中文字幕视频在线看片| 久久久久久久大尺度免费视频| 久久精品人人爽人人爽视色| 成人国产av品久久久| 最近2019中文字幕mv第一页| 亚洲av在线观看美女高潮| 中文天堂在线官网| 亚洲精品久久午夜乱码| 99热全是精品| 久热这里只有精品99| 国产黄色免费在线视频| 亚洲婷婷狠狠爱综合网| 国产野战对白在线观看| 这个男人来自地球电影免费观看 | 国产成人午夜福利电影在线观看| 可以免费在线观看a视频的电影网站 | 亚洲精华国产精华液的使用体验| 日本av免费视频播放| 日韩免费高清中文字幕av| 午夜福利一区二区在线看| 如日韩欧美国产精品一区二区三区| 欧美日韩国产mv在线观看视频| 免费在线观看完整版高清| √禁漫天堂资源中文www| 男人舔女人的私密视频| 国产av码专区亚洲av| 啦啦啦在线免费观看视频4| 一区福利在线观看| 最新的欧美精品一区二区| 久久人人爽av亚洲精品天堂| 国产精品嫩草影院av在线观看| 久久狼人影院| av在线观看视频网站免费| 毛片一级片免费看久久久久| 免费少妇av软件| 男人操女人黄网站| 一级a爱视频在线免费观看| 你懂的网址亚洲精品在线观看| 桃花免费在线播放| 国产亚洲一区二区精品| 国产免费又黄又爽又色| 制服诱惑二区| 五月天丁香电影| 精品国产一区二区三区久久久樱花| 亚洲精品久久午夜乱码| 丝袜在线中文字幕| 亚洲av国产av综合av卡| 久久久久网色| 欧美日本中文国产一区发布| 亚洲国产欧美在线一区| 热re99久久精品国产66热6| 色精品久久人妻99蜜桃| www日本在线高清视频| 黄色视频不卡| av网站在线播放免费| 女的被弄到高潮叫床怎么办| 国产成人精品无人区| 亚洲国产精品一区三区| 亚洲精品一区蜜桃| 国产 一区精品| 男男h啪啪无遮挡| 国产伦理片在线播放av一区| 欧美日韩亚洲国产一区二区在线观看 | 精品福利永久在线观看| 精品国产国语对白av| 捣出白浆h1v1| 欧美日韩亚洲国产一区二区在线观看 | 欧美精品人与动牲交sv欧美| 毛片一级片免费看久久久久| 国产探花极品一区二区| 成年女人毛片免费观看观看9 | 国产男女内射视频| 人人妻,人人澡人人爽秒播 | 久久精品国产亚洲av涩爱| 日本猛色少妇xxxxx猛交久久| 亚洲一区中文字幕在线| 久久精品人人爽人人爽视色| 搡老乐熟女国产| 精品亚洲成国产av| 18在线观看网站| 老司机影院成人| 美女脱内裤让男人舔精品视频| 天堂8中文在线网| 国产日韩欧美在线精品| 性少妇av在线| 少妇人妻精品综合一区二区| 纵有疾风起免费观看全集完整版| 精品卡一卡二卡四卡免费| 久久久欧美国产精品| av又黄又爽大尺度在线免费看| 激情视频va一区二区三区| 大话2 男鬼变身卡| xxx大片免费视频| 高清在线视频一区二区三区| 日本av免费视频播放| 一边摸一边做爽爽视频免费| 亚洲精品aⅴ在线观看| av国产久精品久网站免费入址| 99re6热这里在线精品视频| 国产精品 欧美亚洲| 免费黄频网站在线观看国产| 如日韩欧美国产精品一区二区三区| 欧美日韩精品网址| 精品少妇黑人巨大在线播放| 女人精品久久久久毛片| 欧美亚洲日本最大视频资源| 国产免费福利视频在线观看| 亚洲精品av麻豆狂野| 黄片小视频在线播放| 中文字幕最新亚洲高清| 人妻 亚洲 视频| 中国三级夫妇交换| 久久精品久久久久久久性| 叶爱在线成人免费视频播放| 国产成人免费无遮挡视频| 性高湖久久久久久久久免费观看| 国精品久久久久久国模美| 熟女av电影| 成人国语在线视频| av线在线观看网站| 制服诱惑二区| 日本欧美国产在线视频| 波野结衣二区三区在线| 中文字幕av电影在线播放| 捣出白浆h1v1| 黄色怎么调成土黄色| 亚洲欧美成人精品一区二区| 中文字幕色久视频| 国产亚洲精品第一综合不卡| 十八禁人妻一区二区| 9热在线视频观看99| 亚洲av欧美aⅴ国产| 五月天丁香电影| 亚洲七黄色美女视频| 亚洲四区av| 黑丝袜美女国产一区| 91老司机精品| 午夜福利一区二区在线看| 日韩大片免费观看网站| 乱人伦中国视频| 天天躁夜夜躁狠狠久久av| 一区二区三区乱码不卡18| 国产在线视频一区二区| 久久久久久久精品精品| 久久久久精品人妻al黑| 校园人妻丝袜中文字幕| 99re6热这里在线精品视频| 欧美最新免费一区二区三区| 午夜91福利影院| 99精国产麻豆久久婷婷| 99久久99久久久精品蜜桃| 国产成人精品在线电影| 午夜福利视频精品| 成人免费观看视频高清| 91精品伊人久久大香线蕉| 看免费成人av毛片| 一二三四中文在线观看免费高清| 中文字幕人妻丝袜一区二区 | 日韩一区二区视频免费看| 亚洲国产中文字幕在线视频| 久久久欧美国产精品| 国产日韩一区二区三区精品不卡| 热99久久久久精品小说推荐| 久久综合国产亚洲精品| 尾随美女入室| 精品一区在线观看国产| 赤兔流量卡办理| 中国国产av一级| 日韩欧美一区视频在线观看| 成人18禁高潮啪啪吃奶动态图| 国产精品国产av在线观看| 国产日韩一区二区三区精品不卡| 国产淫语在线视频| 日韩av免费高清视频| 男女无遮挡免费网站观看| 自拍欧美九色日韩亚洲蝌蚪91| 巨乳人妻的诱惑在线观看| 国产一区二区在线观看av| 国产欧美日韩一区二区三区在线| 在线观看免费午夜福利视频| 久久久久久人妻| 亚洲国产av影院在线观看| 伊人久久国产一区二区| 成人国产av品久久久| 黄色一级大片看看| 色播在线永久视频| 99精国产麻豆久久婷婷| 免费在线观看视频国产中文字幕亚洲 | 天天躁日日躁夜夜躁夜夜| 国产福利在线免费观看视频| 侵犯人妻中文字幕一二三四区| 欧美精品一区二区大全| 国产精品熟女久久久久浪| 国产成人精品久久二区二区91 | 1024香蕉在线观看| 成人影院久久| 久久鲁丝午夜福利片| 毛片一级片免费看久久久久| 色网站视频免费| 人妻人人澡人人爽人人| 肉色欧美久久久久久久蜜桃| 国产精品嫩草影院av在线观看| 国产成人精品无人区| 狂野欧美激情性bbbbbb| 18在线观看网站| 999精品在线视频| 十八禁人妻一区二区| 国产亚洲av高清不卡| 汤姆久久久久久久影院中文字幕| 一区二区三区激情视频| 十八禁人妻一区二区| 在线观看www视频免费| 如日韩欧美国产精品一区二区三区| 蜜桃国产av成人99| 少妇被粗大猛烈的视频| 国产亚洲午夜精品一区二区久久| 亚洲五月色婷婷综合| 欧美最新免费一区二区三区| 精品国产国语对白av| 日韩,欧美,国产一区二区三区| 国产成人免费无遮挡视频| 国产av精品麻豆| 国产老妇伦熟女老妇高清| 欧美精品人与动牲交sv欧美| 亚洲精品第二区| 香蕉国产在线看| 中文字幕亚洲精品专区| 别揉我奶头~嗯~啊~动态视频 | 国产一区二区三区av在线| 国产一级毛片在线| 99精品久久久久人妻精品| 97在线人人人人妻| 大码成人一级视频| 一区二区日韩欧美中文字幕| 制服人妻中文乱码| 欧美激情 高清一区二区三区| 亚洲精品av麻豆狂野| 最近中文字幕2019免费版| 高清欧美精品videossex| 久久免费观看电影| 999精品在线视频| 少妇人妻久久综合中文| 成年av动漫网址| 精品久久蜜臀av无| 成人午夜精彩视频在线观看| 91老司机精品| 人人妻人人澡人人爽人人夜夜| 又黄又粗又硬又大视频| 电影成人av| 性色av一级| 日韩不卡一区二区三区视频在线| 日本91视频免费播放| 男女高潮啪啪啪动态图| 捣出白浆h1v1| 欧美乱码精品一区二区三区| 国产成人精品无人区| 日韩中文字幕欧美一区二区 | 成人国语在线视频| 日韩一区二区视频免费看| 久久影院123| 亚洲国产日韩一区二区| 午夜福利影视在线免费观看| 欧美精品一区二区大全| 少妇 在线观看| 欧美日韩成人在线一区二区| 亚洲av综合色区一区| 国产欧美日韩综合在线一区二区| 国产深夜福利视频在线观看| 一本色道久久久久久精品综合| 少妇精品久久久久久久| 自拍欧美九色日韩亚洲蝌蚪91| 午夜免费观看性视频| 搡老乐熟女国产| 亚洲成av片中文字幕在线观看| 免费观看性生交大片5| 国产免费现黄频在线看| 天天躁日日躁夜夜躁夜夜| 欧美日韩亚洲综合一区二区三区_| 2021少妇久久久久久久久久久| 亚洲精品aⅴ在线观看| 99热全是精品| 91国产中文字幕|