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The purpose of this article is to present a novel biobjective biform game framework for optimizing strategy selection of nodes (agents) in bilateral link network formation under dual objectives of profit and link security. First, in the first part of the noncooperative game, we construct various possible strategy combinations (situations) of all players (nodes) in the network, which define the competitive environment in the second part of the cooperative game. Second, in the second part, we derive coalitions’ payoffs under the two objectives of profit and link security and propose the biobjective Banzhaf values to allocate the corresponding cooperative games in all strategy situations. Then, a biobjective noncooperative game is formed on the basis of the obtained biobjective Banzhaf values. Third, we redefine Pareto–Nash equilibriums (in the sense of pure strategies) and obtain the Pareto–Nash equilibriums of the biobjective noncooperative game in the first part. Subsequently, the choice of the obtained Pareto–Nash equilibriums is regarded as a biobjective group decision-making problem, which is solved by employing the redefined Borda choice function method with objective weights. Hence, we can obtain the optimal strategy choices of all the nodes (players) for the entire bilateral link network formation. Finally, numerical examples and comparative analysis are given to verify the validity and applicability of the proposed models and methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several improved Shapley values for cooperative transferable utility (TU) games depending on the players' least square contributions instead of their marginal contributions. This work is mainly enlightened by the Shapley value and the player's productivity-based excess (usually called the excess of the player). Based on the player's contribution-based excess, two quadratic programming models for obtaining the players' (weighted) least square contributions are constructed. The efficient weighted Shapley-like value proposed in this paper as an extension of the Shapley value can be characterized by four independent axioms such as the symmetry, the efficiency, the additivity, and the quasi-null player, which are almost similar to the Shapley value's four axioms except that the anonymity is replaced with the quasi-null player. The four axioms are proven to uniquely determine the efficient weighted Shapley-like value. Finally, the advantages of the proposed values are illustrated with a real case about the collaborative profit sharing of the rural e-commerce. [ABSTRACT FROM AUTHOR]

Then, a series of group consensus cost robust optimization models are constructed under asymmetric unit adjustment cost constraints and the aforesaid four uncertainty sets. Sensitivity analysis shows that the proposed group consensus cost robust optimization models are superior to the existing minimum cost consensus models. Finally, data-driven group consensus cost robust optimization models are developed based on the uncertainty set of asymmetric unit adjustment costs calibrated by using the pricing information of the new product MACUBE 550 in the DEEPCOOL company. [Extracted from the article]

In this paper, we investigate the equal surplus division value for cooperative games with a level structure, which is a sequence of coalition structures becoming coarser and coarser. We propose three axiomatizations of the value. Among them, the first two use different variations of the recent population solidarity axiom, and the third one invokes a special reduced game consistency axiom. Due to the existence of a level structure, our axioms impose special restrictions on the players we focus. We show that our value can be characterized with these axioms and other variations of well-known axioms, such as efficiency, standardness, and quotient game property. Besides characterizing the value, we also connect it to the recent field of ordered tree cooperative games, wherein we find that the iterative value can be viewed as a special case of our value. [ABSTRACT FROM AUTHOR]

The score functions are often used to rank the interval-valued intuitionistic fuzzy sets (IVIFSs) in multiattribute decision making (MADM). The purpose of this paper is to develop an information-based score function of the IVIFS and apply it to MADM. Considering the information amount, the reliability, the certainty information, and the relative closeness degree, we propose an information-based score function of the IVIFS. Comparing the information-based score function with existing ranking methods, we find that the information-based score function can overcome the drawbacks of the existing ranking methods and can rank the IVIFSs well. Three illustrative examples of MADM with linear programming are examined to demonstrate the applicability and feasibility of the information-based score function. It is shown that the information-based score function is well defined and can be applied to MADM. [ABSTRACT FROM AUTHOR]

The interval complex single-valued neutrosophic fuzzy set (ICSVNFS) and hesitant fuzzy set (HFS) are two important different generalizations of the fuzzy set (FS) to cope with unreliable and unpredictable information in the real world. The ICSVNHFS is characterized by interval complex-valued membership, interval complex-valued abstinence, and interval complex-valued non-membership grades, whose ranges are restricted to a unit disc in a complex plane instead of real numbers. In this paper, the notions of interval-valued complex single-valued neutrosophic hesitant fuzzy sets (IVCSVNHFSs) are initiated and also their operational laws are described with examples. Further, based on IVCSVNHFSs, we develop the notions of the interval-valued complex single-valued neutrosophic fuzzy generalized weighted (IVCSVNHFGW) operator, interval-valued complex single-valued neutrosophic fuzzy generalized ordered weighted (IVCSVNHFGOW) operator, and interval-valued complex single-valued neutrosophic fuzzy generalized hybrid weighted (IVCSVNHFGHW) operator to cope with decision information and also study their properties. Further, a new multi-attribute group decision making (MAGDM) problem is initiated based on the proposed operators. Finally, we provide some numerical examples to illustrate the reliability and superiority of the proposed methods by comparison with other existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the hesitant fuzzy multi-attribute decision-making method based on entropy and prioritization relationship. Considering the double impact of priority levels of attributes and the dispersion degree of hesitant fuzzy elements, we propose a prioritized level weighted method based on entropy. The weighted method can guarantee a constant priority level of the attributes and distinguish the unity degree of expert opinions effectively. Then, we put forward the hesitant fuzzy prioritized level average (HFPLA) and hesitant fuzzy prioritized level geometric (HFPLG) operators based on the prioritized level weighted method. Furthermore, we discuss some desirable properties of the proposed operators. Finally, the practicability and effectiveness of the proposed methods are verified by numerical examples. [ABSTRACT FROM AUTHOR]

With the development of modern property service industry, the property perceived service quality (PPSQ) evaluation data is characterized by multiple evaluation subjects, complicated data structure and large scale data. Since the traditional decision-making methods are difficult to solve the above similar problems, this paper proposes a large group decision-making (LGDM) method of generalized multi-attribute and multi-scale (MAMS) based on the linear programming technique for multidimensional analysis of preference (LINMAP). In this method, the large-scale heterogeneous data of expert preference and user evaluation is fused. The decision matrix of generalized MAMS is used to process user evaluation information. The positive ideal solution (PIS) and the attribute weights are determined by the LINMAP model. The comprehensive evaluation values are calculated and hereby the alternatives are ranked order. According to the relation between attribute weights and preset values, a mechanism for identifying invalid data is designed. This paper analyzes a set of survey data of PPSQ for the four public construction projects in the same city. The analysis results show the validity and rationality of the proposed method, and develop the property service evaluation theory. [ABSTRACT FROM AUTHOR]

• This paper considers fairness in coordinating a closed-loop supply chain. • Based on the classic Shapley value, we propose an weighted coordination approach. • Consider a supply chain consisting a manufacturer, a retailer and a remanufacturer. • Given fairness concerns, we focus on how to allocate the centralized-setting profit. • We prove that our model conditionally outperforms the classic Shapley value. This paper considers a closed-loop supply chain (CLSC) structure in which a manufacturer allows a retailer and a third-party remanufacturer to sell and remanufacture his products, respectively. Given the retailer's distributional fairness concerns, we investigate the optimal/equilibrium decisions and profits under five non-cooperative and cooperative game models, and focus on how to allocate maximum profit in a centralized setting. Based on the classic Shapley value, we propose an innovative weighted allocation approach-namely, the variable-weighted Shapley value-to coordinate this CLSC. Numerical studies demonstrate that when remanufactured products are lowly accepted by consumers, our model outperforms the classic Shapley value. [ABSTRACT FROM AUTHOR]

Through adding a discounted factor, Shapley values of cooperative games are extended to interval-valued (IV) cooperative games. The main purpose of this paper is to propose the concept of IV discounted Shapley values and hereby develop a simplified method for computing IV discounted Shapley values for a class of IV cooperative games. In this method, we introduce the concept of discounted Shapley values of -cooperative games associated with IV cooperative games for any attitude factor and find a weaker coalition monotonicity-like condition so that the defined discounted Shapley values possess the monotonicity. Hence we can obtain the analytical formula of IV discounted Shapley value of any IV cooperative game with the coalition monotonicity-like through utilizing only the lower and upper bounds of coalitions’ IV values. The proposed method utilizes the weaker coalition monotonicity-like condition rather than the irreversible interval subtraction and hereby can effectively overcome some irrational issues. [ABSTRACT FROM AUTHOR]

The aim of this paper is to extend the concept of the solidarity value to interval-valued (IV) cooperative games and develop a fast and simplified method for computing the IV solidarity values for a special class of IV cooperative games under some weaker conditions. In the method, we find a size (or coalition) monotonicity-like condition so that we can compute the IV solidarity values of a special class of IV cooperative games via determining their lower and upper bounds by utilizing the lower and upper bounds of the IV coalitions' values, respectively. In addition, some important and useful properties of IV solidarity values are discussed and the feasibility and applicability of the method proposed in this paper are verified with numerical examples as well as comparison analysis with existing methods is conducted. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop a method for solving multi-attribute group decision making (MAGDM)problems with intuitionistic uncertain 2-tuple linguistic (IU2TL) variables (IU2TLVs). Firstly, operational laws and similarity degrees of IU2TLVs are introduced. Secondly, a new aggregation operator called IU2TL continuous chi-deviation ordered weighted quasi-averaging (IU2TLC-CDOWQA) is proposed. Then, to deal with heterogeneous relationships, the IU2TL continuous extend Bonferroni mean (IU2TLC-EBM) operator is developed, and hereby a method for MAGDM problems with IU2TLVs is proposed. Finally, an illustrated example and comparing analysis show that the proposed method is practical and effective. [ABSTRACT FROM AUTHOR]

The Mesoproterozoic Kawabulake Group, which is unconformably overlain by the Lower Cambrian Huangshan Formation and conformably overlies the Mesoproterozoic Xingxingxia Group in the Eastern Tianshan area, NW China, is comprised mainly of siltstone, slate, sandstone and phyllite. New geochemical data for the clastic rocks from the Kawabulake Group were investigated to constrain the provenance and weathering history of the source rocks, in order to evaluate the tectonic evolution of the Eastern Tianshan area. Kawabulake Group rocks are compositionally similar to PAAS (average Post-Archean Australian Shale), indicating derivation from a felsic source that is characterized by depletion in some HFSEs such as Nb, Ta and Ti. The Chemical Index of Alteration (CIA) for the sandstone, siltstone and slate samples (CIA = 60 on average) suggests intensely weathered sources. Light REE-enrichment patterns ((La/Yb) = 4-20) coupled with negative Eu anomalies (Eu/Eu* between 0.44 and 0.89 with an average of 0.62) are similar to those of PAAS, consistent with cratonic sources. The major and trace element compositions imply a dominantly Precambrian felsic source region with a minor contribution from mafic materials. The Sr-Nd isotopic compositions and the ages of T (~3.4, 2.5-1.8, 1.2 and 1.0 Ga) are consistent with the evolutionary history of Kuluketage in the northern Tarim, suggesting that the Tarim Craton was the main source area for the Kawabulake Group. [ABSTRACT FROM AUTHOR]

The Caixiashan giant carbonate-hosted Zn–Pb deposit (~ 131 Mt@ 3.95% Zn + Pb) formed by replacement of dolomitized marble, with stratiform massive and breccia bodies is located near the base of the Proterozoic Kawabulake Group limestone and marble. It is one of the largest carbonated-hosted massive sulfides Zn–Pb ore deposits in Northwest China to have been discovered in recent years. Abundant pyrite occurs in dolomitized marble, along fractures in dolomitized clasts in the host rocks and filling cracks in the host rock. Locally, colloform or framboidal pyrites are observed in the early period and sometimes replaced by the later sphalerite. The sulfide assemblage of the main ore stage is characterized by massive or disseminated sphalerite and galena, with less pyrite than the earlier stage, and minor pyrrhotite. Galena occurs as small veins cutting the early-formed sphalerite. Dolomite and calcite are the main gangue minerals that co-precipitated with these sulfides. Tremolite and quartz alteration commonly overprints the orebodies. According to the crosscutting relationships and the different mineral associations within the host rocks and ore bodies, three stages are recognized at Caixiashan, i.e., syn-sedimentary pyrite (stage I), pyrite alteration, sphalerite–carbonate and galena–pyrite–carbonate (stage II-1, stage II-2 and stage II-3, respectively) and magmatic/metamorphic reworking (stage III). Calcite and quartz crystals are important host minerals among the three hypogene stages (stages I–III, although quartz mainly occurred in stage III). Stage I contains only aqueous inclusions (W-type), which were homogenized from 110 to 236 °C (main range of 138–198 °C and average at 168 °C; main range = average ± σ) and the salinities are from 0.5 to 16.5 (main range of 5.1–15.1 with average of 10.1) wt.% NaCl eqv. In the pyrite alteration of stage II-1 the W-type fluid inclusions homogenized from 175 to 260 °C (main range of 210–260 with average of 235) and the salinities range from 8.5 to 22.4 (main range of 16.7–20.1 with average of 18.4) wt.% NaCl eqv. In the main Zn–Pb mineralization stage (stage II-2–3), four types of fluid inclusions were identified an aqueous phase (W-type), a pure carbon phase (PC-type), a carbon phase containing (C-type) and mineral bearing inclusions (S-type). The W-type fluid inclusions of stage II-2–3 homogenized at 210 to 370 °C (main range of 253–323 and average at 270) and the salinities range from 5.9 to 23.1 (main range of 13.3–20.3 with average at 16.8) wt.% NaCl eqv.; C-type homogenized at 237 °C to 371 °C and the salinities range from 6.4–19.7 wt.% NaCl eqv.; S-type fluid inclusions homogenized at 211 to 350 °C and daughter minerals melted between 340 and 374 °C during heating, indicating a salinity range of 42 to 44 wt.% NaCl eqv. PC-type fluid inclusions with homogenization temperatures of CO 2 phase show large variation from 7.4 °C to 21.2 °C. Laser Raman analyses show that CH 4 , CO 2 and SO 4 2 − coexist in the main mineralization stage fluids. The magmatic/metamorphic reworking stage only contains W-type fluid inclusions which yield homogenized between 220 and 360 °C (main range of 251–325 and average at 288), with salinities ranging from 1.7 to 23.0 (main range of 14.3–20.0 and average at 18.8) wt.% NaCl eqv. The textural features, mineral assemblages and fluid geochemistry suggest that the Zn–Pb ores were formed through hydrothermal convection of hot marine waters along the faults and fractures resulting in metal (Zn, Pb and Fe) enriched stratiform orebodies. Subsequent rapid precipitation of sulfides was triggered by sulfate (SO 4 2 − ) thermal reduction with the CH 4 preserved in sedimentary rocks and early stage I pyrite bodies. This process occurred at moderate temperatures ( ca . 270 °C). Higher-temperature magmatic hydrothermal alteration overprinted the orebodies, but only provided a minor contribution to the mineralization. [ABSTRACT FROM AUTHOR]

Zircon U–Pb ages of high Mg dioritic dikes in the Mesoproterozoic Kawabulake Group in the Eastern Tianshan area, NW China indicate that they were emplaced in the Early Carboniferous at 353–348 Ma. The dikes consist of medium-grained plagioclase and hornblende with minor clinopyroxene and trace quartz. They are characterized by intermediate SiO 2 (60–62 wt.%), low TiO 2 (0.63–0.71 wt.%), relatively high Al 2 O 3 (15.1–15.8 wt.%) and MgO contents (3.45–4.15 wt.%) with Mg# generally higher than 56 (56–59). The geochemistry of the high Mg diorites suggest they were formed by similar magmatic processes to sanukitoid high Mg Andesites such as those of the Setouchi volcanic belt, Japan. Zircons from the high Mg dioritic dikes have ε Hf( t ) values of −6.8 to +14.5. The dominantly positive values suggest a juvenile source, whereas the small number of negative values suggests mature components were also incorporated into the source. Similarly, the positive ε Nd( t ) values (0 to +2.2) are interpreted to reflect a juvenile source whereas the negative values of (−5.2 to 0) suggest participation of old crustal rocks in the petrogenesis of the diorites. The variable ε Hf( t ) and ε Nd( t ) values suggest that the mature material was assimilated during magma ascent rather than in the mantle wedge which would result in more uniform values. Mass balance calculations suggest that the dioritic dikes were derived from sources composed of approximately 97% juvenile mantle-derived material and 3% sediment. Petrographic, elemental, and isotopic evidence suggest that the dioritic dikes were generated by partial melting of depleted mantle that migrated into the shallow crust where it assimilated older sedimentary rocks of the Mesoproterozoic Kawabulake Group. [ABSTRACT FROM AUTHOR]

Imprecision and vagueness often occur in practical multi-attribute decision making (MADM) problems. Intuitionistic fuzzy (IF) sets are flexible to simulate these situations. The aim of this paper is to develop an effective method for solving MADM problems in which the attribute values are expressed with IF sets. Inspired by TOPSIS, we propose a new ranking function of IF sets, which takes into the amount and the reliability of an IF set. Hereby we develop a new MADM method. An example of the investment selection problem is examined to demonstrate applicability and feasibility of the proposed method. It is shown that the proposed method has some advantages over other methods. [ABSTRACT FROM AUTHOR]

The Talate ore field is located in the Abagong polymetallic metallogenic belt of the Altay Orogen, NW China. Lenticular ore bodies occur in the Kangbutiebao Formation, a package of intermediate-felsic marine volcanic rocks and terrigenous clastic sedimentary-carbonate rocks. Skarn alteration (mainly garnet) is present in both ore and wall rocks, especially the carbonate rocks. The mineral assemblages and cross-cutting relationships of veins allow the alteration and mineralization process to be divided into four stages. From early to late, these are the early skarn (E-skarn), the late skarn with quartz-magnetite veins (QM), the quartz-sulphide (QS) and the quartz-carbonate (QC) assemblages. Quartz crystals are important gangue minerals in the latter three stages, in which four distinct compositions of fluid inclusions are identified based on petrography, microthermometry and laser Raman microspectroscopy, namely aqueous inclusions (W-type), pure CO2 inclusions (PC-type), CO2-rich inclusions (C-type) and daughter mineral-bearing inclusions (S-type). Microthermometric data and laser Raman analyses show that the quartz crystals from the QM stage contain all four inclusion types, with the W-type being predominant. Homogenization temperatures range between 271 and 426 °C. The salinities of the W- and C-type fluid inclusions range from 0.5 to 22.4 wt.% NaCl eqv., whereas the S-type fluid inclusions in the QM stage range from 31 to 41 wt.% NaCl eqv. Daughter minerals in the fluid inclusions include halite, sylvite, pyrite and calcite. Quartz from the QS stage (main mineralization stage) contains the W-, C- and PC-type inclusions, which are homogenized at temperatures of 204-269 °C, with salinities of 0.2-15.6 wt.% NaCl eqv. Only W-type fluid inclusions have been identified in the QC stage. These yielded homogenizing temperatures of 175-211 °C and salinities of 1.1-9.9 wt.% NaCl eqv. The C-type fluid inclusions of the main (QS) mineralization stage yield trapping pressures of 107-171 MPa, corresponding to a depth of 4-6 km. The sulphur isotope values (−1.7‰ and −6.6‰) imply that the QS stage may not be directly associated with the early skarn (−7.4‰) and quartz-magnetite stages (−4.8‰ and −5.0‰), though the QS stage is probably dominated by magmatic-hydrothermal fluids. 40Ar/39Ar isotope plateau ages of 227.6 and 214.1 Ma for biotite separated from the QM and QS stages are significantly younger than the host Kangbutiebao Formation ( ca. 410 Ma). The Talate Pb-Zn(-Fe) deposit is interpreted to be an unusual skarn-type system formed in a continental collision orogeny. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The dual hesitant fuzzy set is an efficient mathematical approach to study imprecise, uncertain or incomplete information or knowledge. In this paper, we study the aggregation methods of the dual hesitant fuzzy information. Several aggregation operators are proposed, such as the generalized dual hesitant fuzzy weighted averaging operator (GDHFWA), the generalized dual hesitant fuzzy ordered weighted averaging operator (GDHFOWA) and the generalized dual hesitant fuzzy hybrid averaging operator (GDHFHA) operator for aggregating the dual hesitant fuzzy elements and establish various properties of these operators. A method is also proposed for multi-criteria decision making under dual hesitant fuzzy environment and applied it to teaching quality assessment. [ABSTRACT FROM AUTHOR]

Highlights: [•] Construct new fuzzy multiobjective programming models with TrFNs. [•] Propose a new method for the derived fuzzy linear programming models with TrFNs. [•] A method is developed to heterogeneous MADM based on fuzzy alternative comparison. [•] Weights are obtained solving the derived fuzzy linear programming model with TrFNs. [ABSTRACT FROM AUTHOR]

Highlights: [•] Cu-containing NTC ceramics are prepared by co-precipitation and solid-state methods. [•] Co-precipitation way can reduce the oxidation of Cu+ ions. [•] Co-precipitation method can improve the electrical stability of ceramics. [ABSTRACT FROM AUTHOR]

Interval-valued intuitionistic fuzzy (IVIF) sets are a useful tool to deal with fuzziness inherent in decision data and decision making process. The aim of this paper is to develop a methodology for solving multiattribute decision making (MADM) with both ratings of alternatives on attributes and weights being expressed with IVIF sets. In this methodology, a weighted Euclidean distance between IF sets is defined using weights of IF sets. A pair of nonlinear programming models is constructed based on the concept of the relative closeness coefficients and the distance defined. Two simpler auxiliary nonlinear programming models are further derived to calculate the relative closeness coefficient intervals of alternatives to the IVIF positive ideal solution, which can be used to generate ranking order of alternatives based on the concept of likelihood of interval numbers. The method proposed in this paper is illustrated with a real example. [ABSTRACT FROM AUTHOR]

Triangular intuitionistic fuzzy numbers (TIFNs) are a special kind of intuitionistic fuzzy sets (IFSs) on the real number set. TIFNs are useful to deal with ill-known quantities in decision data and decision making problems themselves. How to measure the value and uncertainty of a TIFN is of great importance. In this paper, we introduce the concepts of the weighted possibility mean, variance and covariance of TIFNs. Furthermore, we show that the weighted possibility mean and the weighted possibility variance of linear combination of TIFNs can be computed in a similar manner to those in probability theory. The desirable properties for the possibility covariance of TIFNs are also investigated. The concepts of the weighted possibility mean, variance and covariance of TIFNs can be considered as a generalization of those of the triangular fuzzy numbers. [ABSTRACT FROM AUTHOR]

Triangular intuitionistic fuzzy numbers (TIFNs) are useful to deal with ill-known quantities in decision making problems. The focus of this paper is on multi-attribute decision making (MADM) problems in which the attribute values are expressed with TIFNs and the information on attribute weights is incomplete, which are solved by developing a new decision method based on possibility mean and variance of TIFNs. The notions of possibility mean and variance for TIFNs are introduced as well as the possibility standard deviation. A new ranking approach for TIFNs is developed according to the ratio of the possibility mean to the possibility standard deviation. Hereby we construct a bi-objective programming model, which maximizes the ratios of the possibility mean to the possibility standard deviation for membership and non-membership functions on alternative's overall attribute values. Using the lexicographic approach, the bi-objective programming model is transformed into two non-linear programming models, which are further transformed into the linear programming models by using the variable transformation. Thus, we can obtain the maximum ratios of the possibility mean to the possibility standard deviation, s are used to rank the alternatives. A numerical example is examined to demonstrate applicability and implementation process of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: Constrained matrix games with payoffs of triangular fuzzy numbers (TFNs) are a type of matrix games with payoffs expressed by TFNs and sets of players’ strategies which are constrained. So far as we know, no study have yet been attempted for constrained matrix games with payoffs of TFNs since there is no effective way to simultaneously incorporate the payoffs’ fuzziness and strategies’ constraints into classical and/or fuzzy matrix game methods. The aim of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of TFNs. In this methodology, we introduce the concepts of Alpha-constrained matrix games for constrained matrix games with payoffs of TFNs and the values. By the duality theorem of linear programming, it is proven that players’ gain-floor and loss-ceiling always have a common interval-type value and hereby any Alpha-constrained matrix game has an interval-type value. Moreover, using the representation theorem for the fuzzy set, it is proven that any constrained matrix game with payoffs of TFNs always has a TFN-type fuzzy value. The auxiliary linear programming models are derived to compute the lower and upper bounds of the interval-type value and optimal strategies of players for any Alpha-constrained matrix game. In particular, the mean and the lower and upper limits of the TFN-type fuzzy value of any constrained matrix game with payoffs of TFNs can be directly obtained through solving the derived three linear programming models with data taken from only 1-cut and 0-cut of payoffs. Hereby the TFN-type fuzzy value of any constrained matrix game with payoffs of TFNs are easily computed. The proposed method in this paper is compared with other methods and its validity and applicability are illustrated with a numerical example. [Copyright &y& Elsevier]

The aim of this paper is to study how to solve a type of matrix game with interval payoffs. In this paper, the interval inequality relations and the concept of solutions of the matrix game with interval payoffs are defined. Based on the fuzzy ranking index defined, the solution of the matrix game with interval payoffs can be obtained through solving a pair of bi-objective linear programming models derived from the constructed auxiliary interval programming models. It is shown that the models proposed in this paper extend those of the classical matrix game. The validity and applicability of the proposed methodology are illustrated with a numerical example. [ABSTRACT FROM PUBLISHER]

A method that constructs an MRA E-tight frame wavelet by using a generalized low pass E-filter is given, and it is showed that all of MRA E-tight frame wavelets can be obtained via the method, where the dilation matrix E is the quincunx matrix or the matrix consists of (0, 1)T and (2, 0)T. Furthermore, the properties of MRA E-tight frame wavelet multipliers as well as E-pseudoscaling function multipliers and generalized low pass E-filter multipliers are characterized. In addition, as an application of these multipliers, we discuss the connectivity of the set of all MRA E-tight frame wavelets in L2(R2). [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper is to develop a methodology for solving multiattribute decision making (MADM) problems in which weights of attributes and ratings of alternatives on qualitative and quantitative attributes are expressed with intuitionistic fuzzy sets (IFSs). In this methodology, relative membership/satisfaction and non-membership/non-satisfaction degrees are formulated to construct IFSs for numerical values of alternatives on quantitative attributes. Alternatives on qualitative attributes are evaluated using linguistic variables and semantics which are parameterized by IFSs. Hereby, weights and ratings of alternatives on both qualitative attributes and quantitative attributes may be expressed with IFSs in a unified way. The generalized ordered weighted averaging (GOWA) operator is further extended to the situations in which the argument values are IFSs and thus a methodology is developed to solve MADM problems using IFSs. Validity and applicability of the proposed methodology in this paper are illustrated with a real numerical example. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop a new methodology for solving group decision making problems in which preference comparisons between alternatives are expressed with Atanassov's intuitionistic fuzzy (IF) preference relations. In this methodology, the generalized ordered weighted averaging (GOWA) operator is extended to develop the Atanassov's IF set (IFS) generalized ordered weighted averaging (IFSGOWA) operator, which can aggregate vague or imprecise information expressed with the Atanassov's IFSs. The Atanassov's IFSGOWA operator based methodology is further developed to solve group decision making problems with Atanassov's IF preference relations. A real example of the agroecological region assessment problem is used to illustrate the implementation and applicability of the proposed methodology. It is also shown that the obtained decision results could be affected by the choice of the parameter lambda and the nature of the weights. [ABSTRACT FROM AUTHOR]

Abstract: The intuitionistic fuzzy (IF) set characterized by two functions was a generalization of the fuzzy set. In this paper, we investigate multiattribute decision making (MADM) problems with ratings of alternatives being expressed using IF sets and attribute weights given as real numbers. Firstly, the generalized ordered weighted averaging (GOWA) operators introduced by Yager [Yager, R. (2004). Generalized OWA aggregation operators. Fuzzy Optimization and Decision Making, 3, 93–107] are extended to aggregate IF sets. Secondly, MADM problems with IF sets are formulated through transforming the ratings of alternatives on both qualitative and quantitative attributes into IF sets in a unified way. The method and procedure based on the extended GOWA operators are developed to solve the MADM problems with IF sets. Finally, the effectiveness and practicability of the proposed method are illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop a nonlinear programming model and method for solving fuzzy multi-attribute group decision making (FMAGDM) problems with linguistic variables. In this methodology, alternatives are assessed on qualitative attributes using linguistic terms from the designated linguistic term set, which can be expressed with the triangular fuzzy number set designated a priori. Alternatives for decision makers are assessed on the basis of the distances between the ordered weighted averaging (OWA) comprehensive value and the group best alternative which is unknown a priori. The group best alternative is then estimated through solving an auxiliary nonlinear programming model based on the concept that the sum of the distances of alternatives from the group best alternative for the decision makers should be as small as possible. The obtained group best alternative can be expressed using the designated triangular fuzzy numbers, which are corresponding to the designated linguistic terms. A numerical example is examined to demonstrate the difference between the proposed method and the generalized induced OWA operator method. [ABSTRACT FROM AUTHOR]

Abstract: The structural and electronic properties of S- and Se-passivated GaP(001)(2×1) surfaces were studied using first-principles simulations. Our calculations showed that the most stable structure consists of a single chalcogen atom (S or Se) in the first crystal layer, which is bonded to two Ga atoms of the second layer, and the third P layer replaced by chalcogen atoms, similar to the passivation of GaAs(001)(2×1) surface by chalcogen atoms. The structural parameters were determined and the surface band characters and the local density of states were also analyzed. The results showed that the preferable structure has no surface states in the bulk band gap, but the energy band gaps of the S- and Se-adsorbed GaP(001) surfaces are 1.83 and 1.63eV, respectively. The passivation effects for the S- and Se-adsorbed surfaces are similar to each other. [Copyright &y& Elsevier]

Abstract: The concept of an intuitionistic fuzzy number (IFN) is of importance for quantifying an ill-known quantity, and the ranking of IFNs is a very difficult problem. The aim of this paper is to introduce the concept of a triangular IFN (TIFN) as a special case of the IFN and develop a new methodology for ranking TIFNs. Firstly the concepts of TIFNs and cut sets as well as arithmetical operations are introduced. Then the values and ambiguities of the membership function and the non-membership function for a TIFN are defined. A new ranking method is developed on the basis of the concept of a ratio of the value index to the ambiguity index and applied to multiattribute decision making problems in which the ratings of alternatives on attributes are expressed with TIFNs. The validity and applicability of the proposed method, as well as analysis of the comparison with other methods, are illustrated with a real example. [ABSTRACT FROM AUTHOR]

Abstract: Fuzziness is inherent in decision data and decision making process. In this paper, interval-valued intuitionistic fuzzy (IVIF) sets are used to capture fuzziness in multiattribute decision making (MADM) problems. The purpose of this paper is to develop a methodology for solving MADM problems with both ratings of alternatives on attributes and weights being expressed with IVIF sets. In this methodology, a weighted absolute distance between IF sets is defined using weights of IF sets. Based on the concept of the relative closeness coefficients, we construct a pair of nonlinear fractional programming models which can be transformed into two simpler auxiliary linear programming models being used to calculate the relative closeness coefficient intervals of alternatives to the IVIF positive ideal solution, which can be employed to generate ranking order of alternatives based on the concept of likelihood of interval numbers. The proposed method is illustrated with a real example. [Copyright &y& Elsevier]

Abstract: C-type lectins (CTLs) acting as pattern recognition receptors play essential roles in shrimp innate immune responses. Using WSSV envelope proteins (VP26, VP28, and VP281) to screen a phage display library of Marsupenaeus japonicus, three lectins (termed as MjLecA, MjLecB, and MjLecC) were found to interact with WSSV. Sequence analysis revealed that these MjLecs shared low similarities with each other. Phylogenetic analysis indicated MjLecA and MjLecB are likely to belong to the same lectin sub-family, while MjLecC belongs to another sub-family. These MjLecs showed broad, unique carbohydrate binding spectra. Also, the three MjLecs could interact with several envelope proteins of WSSV and could recognize a wide range of microorganisms. Moreover, binding of MjLecA or MjLecB to WSSV reduced the viral infection rate in vitro. These results suggest that various kinds of CTLs with structural and functional diversities may constitute a recognizing network against invading pathogens such as bacteria and virus, and play essential roles in the defence system of shrimp. [Copyright &y& Elsevier]

The aim of this paper is to use the concept of extended linguistic variables to develop a new methodology for solving multiattribute group decision making problems under linguistic assessments. In this methodology, using the generalized induced ordered weighted averaging operator and extended linguistic variables, linguistic ratings of each alternative on all attributes for each decision maker are aggregated into a comprehensive assessment, which is not always a linguistic term in the linguistic term set designated a priori. Comprehensive assessments of each alternative on all decision makers are similarly aggregated into a comprehensive assessment of the alternative for the group. An optimal linguistic term in the linguistic term set which approaches the comprehensive assessment of each alternative for the group as close as possible is computed and an extended 2-tuple fuzzy linguistic representation is obtained for the alternative. The ranking order of alternatives for the group is generated according to the extended 2-tuple fuzzy linguistic representations. A numerical example is examined to demonstrate applicability and implementation process of the methodology proposed in this paper. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to study how to solve a type of matrix games with payoffs of triangular fuzzy numbers. In this paper, the value of a matrix game with payoffs of triangular fuzzy numbers has been considered as a variable of the triangular fuzzy number. First, based on two auxiliary linear programming models of a classical matrix game and the operations of triangular fuzzy numbers, fuzzy optimization problems are established for two players. Then, based on the order relation of triangular fuzzy numbers the fuzzy optimization problems for players are decomposed into three-objective linear programming models. Finally, using the lexicographic method maximin and minimax strategies for players and the fuzzy value of the matrix game with payoffs of triangular fuzzy numbers can be obtained through solving two corresponding auxiliary linear programming problems, which are easily computed using the existing Simplex method for the linear programming problem. It has been shown that the models proposed in this paper extend the classical matrix game models. A numerical example is provided to illustrate the methodology. [ABSTRACT FROM AUTHOR]

Abstract: White Spot Syndrome Virus (WSSV) is a virulent and widespread dsDNA virus with a wide range of hosts. Although remarkable progress has been made on virus characterization, however, its mechanism of infection is poorly understood. In this study, by analyzing the phage display library of the WSSV genome, a WSSV envelope protein VP187 (wsv209) was found to interact with shrimp integrin. VP187 possesses the RGD motif. The interaction between integrin and VP187 was confirmed with coimmunoprecipitation. These results demonstrate for the first time an interaction between the WSSV envelope protein and a cell surface molecule. Soluble integrin, integrin-specific antibody and an RGD-containing peptide were found to block the WSSV infection in vivo and in vitro. Gene silencing using a sequence-specific dsRNA targeting β-integrin effectively inhibited the virus infection. These findings suggest that β-integrin may function as a cellular receptor for WSSV infection. [Copyright &y& Elsevier]

A new coupled-mode formulation based on scalar modes is developed for the anisotropic optical waveguide. In the new formulation, the birefringence property of the material is represented as additional coupling to the coupling due to the refractive-index perturbations. The theory is applied to the direction coupler made of parallel slab waveguides. The numerical results show that the numerical value of the birefringence coupling correction is around 10% as much as that of the refractive-index perturbation coupling for the special case. [ABSTRACT FROM AUTHOR]

Abstract: The Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) developed by Srinivasan and Shocker [V. Srinivasan, A.D. Shocker, Linear programming techniques for multidimensional analysis of preference, Psychometrika 38 (1973) 337–342] is one of the existing well-known methods for multiattribute decision making (MADM) problems. However, the LINMAP only can deal with MADM problems in crisp environments. Fuzziness is inherent in decision data and decision making processes, and linguistic variables are well suited to assessing an alternative on qualitative attributes using fuzzy ratings. The aim of this paper is further extending the LINMAP method to develop a new methodology for solving MADM problems under fuzzy environments. In this methodology, linguistic variables are used to capture fuzziness in decision information and decision making processes by means of a fuzzy decision matrix. A new vertex method is proposed to calculate the distance between trapezium fuzzy number scores. Consistency and inconsistency indices are defined on the basis of preferences between alternatives given by the decision maker. Each alternative is assessed on the basis of its distance to a fuzzy positive ideal solution (FPIS) which is unknown. The FPIS and the weights of attributes are then estimated using a new linear programming model based upon the consistency and inconsistency indices defined. Finally, the distance of each alternative to the FPIS can be calculated to determine the ranking order of all alternatives. A numerical example is examined to demonstrate the implementation process of this methodology. Also it has been proved that the methodology proposed in this paper can deal with MADM problems under not only fuzzy environments but also crisp environments. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to point out and correct some errors of properties of the four operators defined over the IFSs in Atanassov (Intuitionistic Fuzzy Sets, Springer, Heidelberg, 1999). [Copyright &y& Elsevier]

Abstract: The concept of intuitionistic fuzzy sets is the generalization of the concept of fuzzy sets. The theory of intuitionistic fuzzy sets is well suited to dealing with vagueness. Recently, intuitionistic fuzzy sets have been used to build soft decision making models that can accommodate imprecise information, and two solution concepts about the intuitionistic fuzzy core and the consensus winner for group decision-making have also been developed by other researchers using intuitionistic fuzzy sets. However, it seems that there is little investigation on multicriteria and/or group decision making using intuitionistic fuzzy sets with multiple criteria being explicitly taken into account. In this paper, multiattribute decision making using intuitionistic fuzzy sets is investigated, in which multiple criteria are explicitly considered, several linear programming models are constructed to generate optimal weights for attributes, and the corresponding decision-making methods have also been proposed. Feasibility and effectiveness of the proposed method are illustrated using a numerical example. [Copyright &y& Elsevier]

The concept of an intuitionistic fuzzy set introduced by K. Atanassov is a generalization of that of a fuzzy set. Many similarity/dissimilarity measures have been proposed for measuring the degree of similarity/dissimilarity between fuzzy sets. However, it seems that there is little investigation on dissimilarity measures for measuring the degree of dissimilarity between intuitionistic fuzzy sets. In this paper, two dissimilarity measures between intuitionistic fuzzy sets of a finite set are defined, and it is proved that both of the measures are metrical. The measures can also be generalized to intuitionistic fuzzy structures, such as intuitionistic fuzzy subgraphs, defined on a finite set. The generalization of intuitionistic fuzzy subgraph is of important to investigation on graph dissimilarity. [Copyright &y& Elsevier]

Polarization property characterization of the microwave (MW) field with high speed and resolution is vitally beneficial as the circularly-polarized MW field plays an important role in the development of quantum technologies and satellite communication technologies. In this work, we propose a scheme to detect the axial ratio of the MW field with optical diffraction limit resolution with a nitrogen vacancy (NV) center in diamond. Firstly, the idea of polarization selective detection of the MW magnetic field is carried out using a single NV center implanted in a type-IIa CVD diamond with a confocal microscope system achieving a sensitivity of 1.7 μ T/ Hz . Then, high speed wide-field characterization of the MW magnetic field at the submillimeter scale is realized by combining wide-field microscopy and ensemble NV centers inherent in a general CVD diamond. The precision axial ratio can be detected by measuring the magnitudes of two counter-rotating circularly-polarized MW magnetic fields. The wide-field detection of the axial ratio and strength parameters of microwave fields enables high speed testing of small-scale microwave devices. [ABSTRACT FROM AUTHOR]

Uncertainty provides an importance in decision making problems like game theory. Several types of uncertainties occur in the literature as fuzzy, soft, rough, interval, etc., and game theory is treated by these types of uncertainties and vagueness by game theorists and others in different aspects. Neutrosophic set and logic are emerged nowadays as another type of uncertainty. Single-valued triangular neutrosophic numbers liberally assume the indeterminacy in choice of elements based upon decision makers' intuition, assumption, judgement, behaviour, evaluation and decision. Here, a new ranking approach is based on the (α , β , γ) -cut of single-valued triangular neutrosophic number and is applied on bi-matrix game theory. We compare our derived results with some previously defined score and accuracy functions and put some interesting and comparatively good results without any plausible fiasco. In this paper, our principal purpose is to validate and approve the proposed contemplations by applying it on illuminating real-life problems in neutrosophic realm through bi-matrix game theory. [ABSTRACT FROM AUTHOR]

The giant Jianchaling Au (52 t Au) deposit is located in the Mian-Lue-Yang Terrane in the southern part of the Qinling Orogen of central China and is hosted by metamorphosed carbonate rocks of the Late Neoproterozoic Duantouya Formation. The deposit consists of multiple generations of mineralised quartz(-carbonate) veins in WNW-trending extensional ductile-brittle shear zones. Based on the mineral assemblages and cross-cutting relationships between the quartz(-carbonate) veins, the paragenesis is characterised by an early coarse-grained pyrite-pyrrhotite-pentlandite-dolomite-quartz assemblage (I), followed by pyrite-sphalerite-galena-carbonate-arsenopyrite-fuchsite-carbonate-quartz containing gold (II), and fine-grained pyrite-dolomite-calcite-quartz-realgar (As2S2)-orpiment (As2S3) (III). The H-O-C isotope systematics for the three vein sets indicate that the mineralising fluid is probably sourced from the metamorphic dehydration of carbonate rocks in the Duantouya Formation, and gradually mixed with meteoric water during the emplacement of the third vein set. The δ34S values for sulfides (6.3–16.6‰) from the second auriferous vein set are greater than zero, indicating sulfates reduction from the Neoproterozoic metamorphic rocks (Duantouya Fm). The (206Pb/204Pb)i ratios from pyrite (17.521–18.477) from each of the vein sets overlap those of the ultramafic rocks (18.324–18.717) and the Bikou Group (17.399–18.417), indicating that the units are possible sources for the sulfides in the mineralisation. Both εNd(t) and Isr(t) of sulfide overlap with the meta-ultramafic field and Duantouya formation and dominated with mature Sr-Nd character, which indicated that the Duantouya may play an important role during the ore formation and there may exist a minor ultramafic source that is involved in the ore fluid. The S-Pb-Sr-Nd isotopic ratios are closely related to those of the Bikou Group and Duantouya Formation, which indicates that the mineralised fluid has interacted with both units. Combining the previously published data with data from this study on the mineralised area, we surmise that Jianchaling is characteristic of an orogenic-type gold deposit related to the Triassic Qinling Orogeny associated with continental collision. [ABSTRACT FROM AUTHOR]