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PurposeVaccine safety is a major issue in the world. Blockchain technology is the right solution to this worldwide problem. The impact of introducing blockchain technology on the operational efficiency of the vaccine supply chain is unclear. Therefore, from the perspective of game theory, this paper aims to construct a vaccine supply chain model consisting of a vaccine manufacturer, a vaccine traceability service platform based on blockchain technology and a vaccination unit to discuss its pricing and coordination.Design/methodology/approachThis study analyzes the pricing and coordination of the vaccine supply chain based on blockchain technology, compares the decision-making of fixed charge scenario and proportional charge scenario and reveals the impact of blockchain on the vaccine supply chain.FindingsResults demonstrate that the revenue-sharing contract can coordinate the vaccine supply chain when the proportion of revenue sharing meets certain conditions. The fixed charge scenario is more beneficial to the vaccine supply chain than the proportional charge scenario. The introduction of blockchain technology increases the total profit, consumer surplus and social welfare of the vaccine supply chain. Therefore, the operational efficiency of the vaccine supply chain is improved.Originality/valueThis study not only provides important support for enterprises to adopt blockchain technology but also provides some guidance for decision-makers to implement scientific and feasible vaccine supply chain management schemes.

With the changing business environment and the active participation of various stakeholders in the decision making process, it plays an increasingly important role to the weight of decision makers and the preference information given by decision makers. This paper presents a novel approach for group decision making under uncertainty with the involvement of the third-party evaluator in the decision making process. Recognizing the challenge in adequately determining the weight of decision makers in group decision making, the evidence theory is appropriately used with the involvement of the third-party evaluator. To effectively model the uncertainty and imprecision in the decision making process, fuzzy preference relations are used for better representing the subjective assessment of individual decision makers. To adequately determine the ranking of available alternatives, the logarithmic least square method is applied for appropriately aggregating the fuzzy preference relation of individual decision makers. A group consensus index is developed for facilitating consensus building in group decision making. This leads to better group decisions being made. A real-world application is presented that shows the proposed approach is effective in solving group decision making problems under uncertainty.

The challenge of complex multi-attribute large group decision-making (CMALGDM) is reflected from three perspectives: interrelated attributes, large group decision makers (DMs) and dynamic decision environments. However, there are few decision techniques that can address the three perspectives simultaneously. This paper proposes a random intuitionistic fuzzy factor analysis model, aiming to address the challenge of CMALGDM from the three perspectives. The proposed method effectively reduces the dimensionality of the original data and takes into account the underlying random environmental factors which may affect the performances of alternatives. The development of this method follows three steps. First, the random intuitionistic fuzzy variables are developed to deal with a hybrid uncertain situation where fuzziness and randomness co-exist. Second, a novel factor analysis model for random intuitionistic fuzzy variables is proposed. This model uses specific mappings or functions to define the way in which evaluations are affected by the dynamic environment vector through data learning or prior distributions. Third, multiple correlated attribute variables and DM variables are transformed into fewer independent factors by a two-step procedure using the proposed model. In addition, the objective classifications and weights for attributes and DMs are obtained from the results of orthogonal rotated factor loading. An illustrative case and detailed comparisons of decision results in different environmental conditions are demonstrated to test the feasibility and validity of the proposed method.

In real bargaining problems, players care not only about their own shares, but also about others’ shares. In addition, a player’ attitude toward others depends on how this player feels he is being treated. To model such preferences, the Rubinstein bargaining game is reconsidered, where players’ preferences is characterized as altruism and spite. First, a subgame perfect equilibrium (SPE) is constructed, where player’s strategy depends on the opponent’s share through altruistic and spiteful preferences. The uniqueness of SPE is shown if it shares with SPE in the classical Rubinstein case: no delay and stationarity. Then, a comparative statics analysis with respect to players’ altruism and spite is performed. It is shown that the equilibrium share of a player is negatively related to the opponent’s global spite and his own global altruism, and positively to global altruism of the other one and the global spite of himself. It is also found that the impact of the intrinsically altruistic and spiteful levels of a player on equilibrium share depends on this player’s attitudes towards the opponent. Furthermore, it is found that a more positive attitude towards the opponent leads to the increase (decrease) of this player’s share if this player is more (less) intrinsically altruistic than the opponent. Finally, we establish a relationship with asymmetric two-person Nash bargaining game. It is found that bargaining power of a player decreases with the globally altruistic and spiteful preferences of himself, and increases with the opponent’s. It is further found that the effects of players’ attitudes towards the opponent on their own bargaining power depend on the gap between the intrinsic altruistic and spiteful levels of players.

Bimatrix games are reconsidered under assumption that players are loss averse and payoffs are fuzzy, where reference points are given exogenously. The impact of loss aversion on bimatrix game is investigated by applying credibility theory. Three solution concepts of credibilistic loss aversion Nash equilibria (i.e., expected loss aversion Nash equilibrium, optimistic loss aversion Nash equilibrium and pessimistic loss aversion Nash equilibrium) and their existence theorems are proposed. The sufficient and necessary conditions are presented to find three equilibria. It is found that three credibilistic loss aversion Nash equilibria are equivalent if confidence level is equal to 0.5. Furthermore, an analysis on credibilistic loss aversion equilibria with respect to loss aversion is performed in a 2 × 2 bimatrix game with triangular fuzzy payoffs. It is found that with a higher probability a more loss-averse player receives a preferred payoff in the mixed strategy Nash equilibrium in some situations, but receives the second highest payoff in other situations. Finally, a case study is shown to illustrate the validity of the bimatrix game with triangular fuzzy payoffs developed in this paper.

The Rubinstein alternating-offers bargaining game is reconsidered, where players show fairness concerns and their fairness references are characterized by the Nash bargaining solution. The objective of this paper is to explore the impact of fairness concerns in the alternating-offer bargaining game. Alternating-offer bargaining with fairness concerns is developed. We construct a subgame perfect equilibrium and show its uniqueness. Then, it is shown that players’ payoffs in the subgame perfect equilibrium are positively related to their own fairness concern coefficient and bargaining power and negatively to the opponents’ fairness concern coefficient. Moreover, it is shown that the limited equilibrium partition depends on the ratio of discount rates of the two players when the time lapse between two offers goes to zero. Finally, the proposed model is applied to the bilateral monopoly market of professional basketball players, and some properties of equilibrium price are shown. Our result provides the implication that players should carefully weigh their own fairness concerns, bargaining power and fairness concerns of their opponents, and then make proposals, rather than simply follow the suggestion that the proposal at the current stage is higher than that at the past stages.

This paper investigates a two-echelon green supply chain (GSC) with a single loss-averse manufacturer and a single loss-averse retailer. Since the Nash bargaining solution exactly characterizes endogenous power and the contribution of the GSC members, it is introduced as the loss-averse reference point for the GSC members. Based on this, a decision model of the two-echelon GSC with loss aversion is formulated. The optimal strategies of price and product green degree are derived in four scenarios: (a) the centralized decision scenario with rational GSC members, namely the CD scenario; (b) the decentralized decision scenario with rational GSC members, namely the DD scenario; (c) the decentralized decision scenario with the GSC members loss-averse, where the manufacturer’s share is below its own loss-averse reference point, namely the DD(∆m ≥ πm) scenario; (d) the decentralized decision scenario with the GSC members loss-averse, where the retailer’s share is below its own loss-averse reference point, namely the DD(∆r ≥ πr) scenario. Then, a comparative analysis of the optimal strategies and profits in these four scenarios is conducted, and the impacts of loss aversion and green efficiency coefficient of products (GECP) on the GSC are also performed. The results show that (i) GECP has a critical influence on the retail price and the wholesale price; (ii) the GSC with loss aversion provide green products with the lowest green degree; (iii) the retail price, the wholesale price and product green degree are decreasing monotonically with the loss aversion level of the GSC member without incurring loss; (iv) furthermore, the effect of the loss aversion level of the GSC member with incurring loss on the optimal strategies is related to GECP and the gap between the GSC members’ loss aversion levels.

The palm oil industry faces significant pressure because of the environmental problems from the plantation process and the palm oil milling process in their supply chain, which is due to the constraints of natural resources and the growing ecological awareness among customers. Reverse logistics (RL) has been considered as a systematic approach for the palm oil industry to improve the environmental impact. However, there are more barriers which cannot be detected in the RL. Therefore, this study proposes robust and flexible strategies for overcoming such barriers by focusing on identifying and ranking the solutions on RL adoption in Thailand’s palm oil industry. We use a fuzzy multi-criteria decision-making (MCDM) methods based on fuzzy analytical network process (ANP) and Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) to prioritize related solutions and strategies. Firstly, fuzzy ANP is applied to identify the weighting of each barrier using pairwise comparison, while the final ranking of the solution on RL adoption is obtained through VIKOR. This model will help business analysis and supply chain managers formulate both short-term and long-term, flexible decision strategies for successfully managing and implementing RL adoption in the supply chain scenarios. In addition, sensitivity analysis is used to illustrate the method, and comparisons with other existing methods is also presented in this study.

Recognizing that strategic consumers have become increasingly common in the perishable products market, we develop a two-stage pricing model for a monopolistic firm with two classes of inventory strategies: non-replenishment and replenishment. First, the retailer mapping out his pricing policy, and then consumers determining their buying behavior given the retailers policy. Our results indicate that the game equilibrium exists between retailers and consumers in both cases. For a given realized price and inventory policy, the consumer's space is split into several areas by the optimal threshold functions. Inventory replenishment decisions are affected by market demand and a decline factor of consumers reservation value. The retailers profit loss is not necessarily related to the consumers waiting behavior but results from the ignorance of this behavior when pricing.

(1) Background: With the development of blockchain technology and fierce competition between tourism platforms, tourism platforms can adopt blockchain technology to disclose product information to enhance their core competitiveness. As for a tourism O2O, i.e., online to offline, supply chain, the tourism platform sells the product online, and the tour operator provides services offline. (2) Methods: We establish a game theory model and study the optimal strategies of supply chain members in two scenarios (decentralized and centralized) when the online platform does not adopt or adopts blockchain technology. Then, we introduce a two-part tariff contract for coordination. Furthermore, we discuss the impact of the cost of adopting blockchain technology, disclosing information and the proportion of information-sensitive consumers on the optimal strategies. (3) Conclusions: When the costs of adopting blockchain technology and information disclosure are low, if the proportion of information-sensitive consumers is large, adopting blockchain technology is beneficial to supply chain members. Compared with a wholesale price contract, a two-part tariff contract can encourage the platform to improve information disclosure quality, so the tour operator can adjust their cooperation contract to achieve Pareto improvements. Under a two-part tariff contract, the tourism platforms are more likely to disclose information and can effectively regulate the operational performance of the tourism O2O supply chain.

By using Moore&rsquo, s subtraction operator and a total order on the set of closed intervals, we introduce a new variation of the Banzhaf value for cooperative interval games called the interval Banzhaf-like value which may accommodate the shortcomings of the interval Banzhaf value. We first reveal the relation between this introduced value and the interval Banzhaf value. Then, we present two sets of properties that may be used to determine whether an interval value is median-indifferent to the interval Banzhaf-like value. Finally, in order to overcome the disadvantages of the interval Banzhaf-like value, we propose the contracted interval Banzhaf-like value and give an axiomatization of this proposed value.

In real multi-attribute decision-making problems, attributes are usually correlated and performances of alternatives are affected by random environmental factors. This paper proposes an intuitionis...

As an extension of the classical averaging operators, Choquet integral has been shown a powerful tool for decision theory. In this paper, a method based on the generalized interval-valued intuitionistic fuzzy Choquet integrals w.r.t. the generalized interaction indices is proposed for multiattribute group decision making problems, where the importance of the elements is considered, and their interactions are reflected. Based on the given operational laws on interval-valued intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy Choquet integrals with respect to the generalized Shapley and Banzhaf indices are defined. Moreover, some of their properties are studied, such as idempotency, boundary, comonotonic linearity and μ–linearity. Furthermore, a decision procedure based on the proposed operators is developed for solving multi-attribute group decision making under interval-valued intuitionistic fuzzy environment. Finally, a numerical example is provided to illustrate the developed procedure.

Triangular fuzzy reciprocal preference relations (TFRPRs) are good choices to denote the decision makers' fuzzy preferences. Consistency analysis is a very important topic to preference relations that can avoid the illogical ranking order. However, all previous multiplicative consistency concepts for TFRPRs cannot well address this type of preference relations. To address this issue, this paper introduces a new multiplicative consistency concept for TFRPRs, which can be seen as a natural extension of Tanino's multiplicative consistency concept for reciprocal preference relations. Based on the new consistency concept, 0–1 mixed programming models for judging the multiplicative consistency of TFRPRs are constructed, and an approach for deriving multiplicative consistent TFRPRs is provided. Considering the incomplete case, programming models to determine missing values are constructed. Subsequently, a multiplicative consistency based method for decision making with TFRPRs is presented that can address the inconsistent and incomplete cases. Meanwhile, illustrative examples are provided to show the concrete application of the proposed procedure, and comparison analysis is also made.

To examine the multiplicative consistency of interval fuzzy preference relations (IFPRs), this paper first analyzes the limitations associated with the previous consistency concepts. Accordingly, a new consistency concept is defined that is an extension of the crisp case and overcomes limitations in the previous concepts. Next, a linear programming model to judge the consistency of IFPRs is constructed, and an approach to derive multiplicative consistent IFPRs is introduced. Furthermore, goal-programming models to determine missing values in an incomplete IFPR are constructed that have the highest consistent level with respect to known values. Moreover, a multiplicative consistency and consensus based method for group decision making with IFPRs is developed that can address incomplete and inconsistent cases. Finally, two practical decision-making problems are offered to demonstrate the feasibility and efficiency of the new method, and an analysis of a numerical and theoretical comparison with several related methods is performed.

Display Omitted A new consistency concept for IMPRs is defined.It is a natural extension of Saatys consistency concept for crisp case.It is robust to the permutation of the object labels.Models to address inconsistent and incomplete IMPRs are built.An algorithm to IMPRs is presented. Consistency analysis is very important to ensure the reasonable ranking order. However, all previous consistency concepts for interval multiplicative preference relations (IMPRs) are insufficient to address this type of preference relations. This paper introduces a new consistency concept for IMPRs that is a natural extension of the Saatys consistency concept for multiplicative preference relations. Several desirable properties are discussed, and the relationship between the new concept and two previous ones is studied. Then, a method to judge the consistency of IMPRs is proposed. Considering the inconsistent case, a 01 mixed programming model to derive consistent IMPRs from inconsistent ones is established. To determine missing values in incomplete HFPRs, 01 mixed programming models are constructed that can address the situation where ignore objects exist. Meanwhile, illustrative examples are offered to show the feasibility and efficiency of the developed theoretical results, and comparison analysis is provided. Finally, a consistency analysis based algorithm to decision making with IMPRs is developed that can address inconsistent and incomplete cases.

The increase of environmental pollution has led to the rise of sustainable awareness in recent years. This trend has motivated various industries to recognize the importance of implementing sustainable supply chain practices to seek economic, environmental and social advantages. From a sustainability perspective, selecting a suitable supplier is the main component of modern enterprises. It is also a challenging problem since several criteria concerning supplier selection are interdependent with a complex character. Therefore, the contribution of this paper is a new extension to multi-criteria decision-making model (MCDM) under an intuitionistic fuzzy environment for sustainable supplier selection (SSS) based on sustainable supply chain management SSCM practices. It consists of intuitionistic fuzzy set theory (IFS) with a decision making trial and evaluation laboratory (DEMATEL) combined with an analytic network process (ANP) to identify uncertainties and interdependencies among criteria as well as analyzing the criteria weights. We modified Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) to evaluate and rank the desired level of sustainable supplier performance. The suggested approach is conducted by a case study from the Thailand palm oil industry. Results show that the proposed model not only can find the most suitable sustainable supplier, but also the enterprises can aid their suppliers in improving sustainability by using the proposed method and can improve enterprises&rsquo, socio-environmental performance, which is key to achieving sustainable development.

The consumer environmental awareness promotes green manufacturing and the behavioral preferences of members become prevailing in supply chain management. To promote further development of green supply chains, a two-echelon green supply chain with a manufacturer and a retailer is considered, where the manufacturer is loss-averse and the retailer is risk-neutral. We use a Stackelberg game to investigate the impacts of loss aversion and green efficiency coefficient on retail price, wholesale price, green degree, profits of members, and profit of the green supply chain under the assumption that manufacturer&rsquo, s reference point of loss aversion is equal to the subgame perfect equilibrium partition. It is shown that, in the centralized decision-making setting (CDS), green degree and profit of the green supply chain are higher than those in the decentralized decision-making setting (DDS), while in the decentralized decision-making setting with a loss-averse manufacturer (DDS-LAM) loss aversion of manufacturer further decreases green degree and profit of green supply chain. It is also found that profits of the manufacturer and the retailer decrease with levels of loss aversion of manufacturer. Furthermore, it is also shown that wholesale price and retail price in the three decision-making settings depend on the green efficiency coefficient. Wholesale price and retail price in DDS-LAM are always the lowest (highest) if the green efficiency coefficient is sufficiently high (low). Finally, executing a greening cost-sharing contract can improve chain members&rsquo, profits if the retailer shares an appropriate proportion with the loss-averse manufacturer.

The classical Bertrand game is assumed that players are perfectly rational. However, many empirical researches indicate that people have bounded rational behavior with fairness concern, which is important in the two-person game and has attracted much attention. In this paper, fairness concern is incorporated into the Bertrand game with two homogeneous products and the effect of fairness concern on this extended Bertrand game is explored. Nash bargaining solution of player is applied to be his own fairness reference point. Then, a Bertrand game model with fairness concern is established, and its equilibrium price is also derived and analyzed. It is shown from some numerical examples that fairness concern and bargaining power of players have a significant influence on their equilibrium price, expected profits, and utilities. As a player gets more fair-minded, if the other player has a less focus on fairness, the price competition between them will be intensified and both of them suffer loss. Thus, fairness concern may be advantageous or disadvantageous for players. In most situations, the fairness concern behavior is not beneficial for players. Additionally, the effect of bargaining power is relative to fairness concern. A player who manufactures a low-cost product should have a weak bargaining power if he terribly focuses on fairness and should have a strong bargaining power if he pays little attention to fairness. However, a player who manufactures a high-cost product should have a weak bargaining power if he is rarely concerned about fairness. Anyway, the same bargaining power is the best for two players.

Rubinstein bargaining game is extended to incorporate loss aversion, where the initial reference points are not zero. Under the assumption that the highest rejected proposal of the opponent last periods is regarded as the associated reference point, we investigate the effect of loss aversion and initial reference points on subgame perfect equilibrium. Firstly, a subgame perfect equilibrium is constructed. And its uniqueness is shown. Furthermore, we analyze this equilibrium with respect to initial reference points, loss aversion coefficients, and discount factor. It is shown that one benefits from his opponent’s loss aversion coefficient and his own initial reference point and is hurt by loss aversion coefficient of himself and the opponent’s initial reference point. Moreover, it is found that, for a player who has a higher level of loss aversion than the other, although this player has a higher initial reference point than the opponent, this player can(not) obtain a high share of the pie if the level of loss aversion of this player is sufficiently low (high). Finally, a relation with asymmetric Nash bargaining is established, where player’s bargaining power is negatively related to his own loss aversion and the initial reference point of the other and positively related to loss aversion of the opponent and his own initial reference point.

Aggregation operators play a key role in multiple criteria decision-making (MCDM). Extensions of aggregation operators to intuitionistic fuzzy sets (IFSs) usually involve replacing the standard arithmetic operations with those defined over the membership and nonmembership of IFS, which is essentially a pair of special Archimedean triangular norm (t-norm) and triangular conorm (t-conorm), called probabilistic sum t-conorm and product t-norm, on the membership and nonmembership of IFS, respectively. In this paper, we first introduce some operations on IFSs by means of Archimedean t-norm and t-conorm. Then some generalized Archimedean intuitionistic fuzzy aggregation operators are proposed, such as generalized Archimedean intuitionistic fuzzy weighted averaging operator, generalized Archimedean intuitionistic fuzzy ordered weighted averaging (GAIFOWA) operator, and generalized Archimedean intuitionistic fuzzy hybird averaging operator. Some desirable properties of these operators are investigated. The relations between these operators and the existing intuitionistic fuzzy aggregation operators are discussed. Finally, applying these proposed operators, we develop an approach for multi-criteria decision-making with intuitionistic fuzzy information, an illustrative example is used to verify the developed approach and to demonstrate its practicality and effectiveness.

In most existing literatures on Cournot game, game behaviour between players is based on the hypothesis that people are complete rationality. However, players’ decisions are often affected by their behavioural characteristic and psychology preference. Traditional Cournot model also doesn’t deal with ambiguous information. Based on rank-dependent utility theory, this paper develops an incomplete information Cournot game in an ambiguous decision environment, where the form of ambiguity is described by a set of fuzzy parameters, and behavioural pattern is reflected by means of emotional function in rank-dependent utility. Further, we investigate the Nash equilibrium quantity of each manufacture in this kind of fuzzy Cournot game with incomplete information. Finally, the proposed Cournot model is applied to a case study, and dynamic variation and sensitivity analysis of optimal quantity with respect to decision-maker’s behaviour pattern are discussed in detailed, which illustrates that the proposed Cournot mo...

Inspired by Shalev’s model of loss aversion, we investigate the effect of loss aversion on a bimatrix game where the payoffs in the bimatrix game are characterized by triangular fuzzy variables. First, we define three solution concepts of credibilistic loss aversion Nash equilibria, and their existence theorems are presented. Then, three sufficient and necessary conditions are given to find the credibilistic loss aversion Nash equilibria. Moreover, the relationship among the three credibilistic loss aversion Nash equilibria is discussed in detail. Finally, for2×2bimatix game with triangular fuzzy payoffs, we investigate the effect of loss aversion coefficients and confidence levels on the three credibilistic loss aversion Nash equilibria. It is found that an increase of loss aversion levels of a player leads to a decrease of his/her own payoff. We also find that the equilibrium utilities of players are decreasing (increasing) as their own confidence levels when players employ the optimistic (pessimistic) value criterion.

In this paper, we extend the generalized weighted geometric and generalized ordered weighted geometric operators to intuitionistic fuzzy environments, that is, we develop a series of generalized intuitionistic fuzzy geometric operators to aggregate input arguments that are expressed by intuitionistic fuzzy values based on Archimedean t-conorm and t-norm. Then some desired properties of these aggregation operators are investigated. The relations between these operators and some existing intuitionistic fuzzy geometric aggregation operators are discussed in detail. Furthermore, applying these proposed operators, we develop an approach for multi-criteria decision making with intuitionistic fuzzy information. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

In this paper, a generalized form of fuzzy games with interval characteristic functions is proposed, which can be seen as an extension of games with crisp characteristic functions. Based on the extended Hukuhara difference, the interval Shapley function for interval fuzzy games is studied. Then, the concept of interval population monotonic allocation function (IPMAF) is defined. When interval fuzzy games are convex, we prove that the interval Shapley function is an IPMAF. Furthermore, two special types of interval fuzzy games are researched, and the associated interval Shapley function is studied.

Although many researchers have realized that the trade determination problem in one-shot multi-attribute exchanges is an important decision problem, few studies can be really applied to deal with this issue under a fuzzy environment. This paper proposes a multi-objective matching approach for one-shot multi-attribute exchanges with fuzzy information. First, we use fuzzy set theory to represent the traders’ orders with fuzzy information and then give a framework for the proposed multi-objective matching approach. Second, we present a novel calculation method of the matching degree based on the improved fuzzy information axiom. According to the matching degree, we build a fuzzy multi-objective optimization model (FMOM) for the trade determination problem, where two criteria, i.e., profits and satisfactions, are considered simultaneously. Afterward, in order to solve the FMOM, the fuzzy chance constrained programming technique based on credibility measures and the fuzzy goal programming method are introduced to convert it into a crisp single objective one. Finally, we conduct the numerical study and analysis on a practical example to illustrate the application and effectiveness of the proposed multi-objective matching approach.

We research a series of new aggregation operators based on Hamacher t-norm and t-conorm for hesitant fuzzy information.Some Hamacher operational rules of hesitant fuzzy sets are developed.A wide range of new hesitant fuzzy aggregation operators is proposed.We investigate their desirable properties and discuss the relationships between them.The proposed aggregation operators have more flexible for multicriteria decision making under hesitant fuzzy information environment. As a fuzzy set extension, the hesitant set is effectively used to model situations where it is allowable to determine several possible membership degrees of an element to a set due to the ambiguity between different values. We first introduce some new operational rules of hesitant fuzzy sets based on the Hamacher t-norm and t-conorm, in which a family of hesitant fuzzy Hamacher operators is proposed for aggregating hesitant fuzzy information. Some basic properties of these proposed operators are given, and the relationships between them are shown in detail. We further discuss the interrelations between the proposed aggregation operators and the existing hesitant fuzzy aggregation operators. Applying the proposed hesitant fuzzy operators, we develop a new technique for hesitant fuzzy multicriteria decision making problems. Finally, the effectiveness of the proposed technique is illustrated by mean of a practical example.

In real game situations, the players are often lack of the information about their opponents’ or even their own payoffs. The existing literature on non-cooperative games with uncertain payoffs just focused on two-person zero-sum games or bimatrix games. In this paper, we consider a n-person non-cooperative game with fuzzy payoffs. First, based on credibility theory, three credibilistic criteria are introduced to define the behavior preferences of players in different game situations. Then, three solution concepts of credibilistic equilibria and their existence theorems are proposed. Finally, three sufficient and necessary conditions are presented for finding the credibilistic equilibrium strategies to illustrate the usefulness of the theory developed in this paper.

In this paper, another important solution for fuzzy games, called the Banzhaf function, is investigated. First, a sim- plified expression for the Banzhaf function for games with fuzzy coalition is proposed. The relationship between this simplified ex- pression and two kinds of particular Banzhaf functions are dis- cussed in detail. Furthermore, in the framework of games with fuzzy coalitions, we give a definition of the potential function of fuzzy games, and prove that the marginal values of the potential function are the components of the Banzhaf function. Further- more, a new axiomatic characterization of the Banzhaf function for games with fuzzy coalitions is provided.

In order to solve a problem of a discrete stochastic multiple-criteria decision making (MCDM) with aspiration levels, a method on the basis of prospect stochastic dominance is proposed in this paper. The psychological behavior of decision maker, for instance, judgmental distortion, reference dependence and loss aversion, are considered. Based on the concept of prospect theory, aspiration levels are initially took to be the reference points. Definition and related analysis of prospect stochastic dominance degree (PSDD) is given to describe the degree that one alternative dominates another when the prospect stochastic dominance relation for each pair of alternatives with respect to aspiration level is determined. On the basis of the PSDD matrix of alternative pairwise comparisons regarding the aspiration level of every criterion, an overall PSDD matrix is constructed using Choquet integral. Further, according to the concept of the PROMETHEE II, an outramking method is designed to collect the alternatives ranking result. Finally, the effectiveness and applicability of the method proposed are illustrated by two given numerical examples.

In this paper, by combining the Archimedean t-conorm and t-norm and Quasi-Choquet averaging operator, we develop an extended Atanassov's intuitionistic fuzzy Quasi-Choquet geometric operator to aggregate input arguments that are Atanassov's intuitionistic fuzzy values, where the inter-dependent or interactive characteristics among input arguments are taken into account. Some of the desirable properties and some special cases are investigated in detail. It is worth pointing out that most of the existing Atanassov's intuitionistic fuzzy geometric aggregation operators are special cases of this proposed aggregation operator. Furthermore, a decision procedure based on the proposed aggregation operator is developed for solving the multicriteria decision making problem in which all decision information is represented by Atanassov's intuitionistic fuzzy values. An illustrative example is given for demonstrating the applicability of the proposed decision procedure.

With respect to multichoice games with a coalition structure, a coalitional value named the generalized symmetric coalitional Banzhaf value is defined, which is an extension of the Shapley value for multichoice games and the symmetric coalitional Banzhaf value for traditional games with a coalition structure. Two axiomatic systems are established: One is enlightened by the characterizations for the symmetric coalitional Banzhaf value, and the other is inspired by the characterizations for the Banzhaf value.

Two interval-valued intuitionistic uncertain linguistic hybrid operators called the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley averaging (I-IIULHSA) operator and the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley geometric (I-IIULHSG) operator are defined. These operators not only reflect the importance of elements and their ordered positions, but also consider the correlations among elements and their ordered positions. Since the fuzzy measures are defined on the power set, it makes the problem exponentially complex. In order to simplify the complexity of solving a fuzzy measure, we further define the induced interval-valued intuitionistic uncertain linguistic hybrid ?-Shapley averaging (I-IIULH?SA) operator and the induced interval-valued intuitionistic uncertain linguistic hybrid ?-Shapley geometric (I-IIULH?SG) operator. Moreover, an approach for multi-attribute group decision making under the interval-valued intuitionistic uncertain linguistic environment is developed. Finally, a numerical example is provided to verify the developed procedure and demonstrate its practicality and feasibility.

Fuzziness is inherent in decision data and decision making process. In this paper, interval-valued intuitionistic fuzzy set is used to capture fuzziness in multi-criteria decision making problems. The purpose of this paper is to develop a new method for solving multi-criteria decision making problem in interval-valued intuitionistic fuzzy environments. First, we introduce and discuss the concept of interval-valued intuitionistic fuzzy point operators. Using the interval-valued intuitionistic fuzzy point operators, we can reduce the degree of uncertainty of the elements in a universe corresponding to an interval-valued intuitionistic fuzzy set. Then, we define an evaluation function for the decision-making problem to measure the degrees to which alternatives satisfy and do not satisfy the decision-maker's requirement. Furthermore, a series of new score functions are defined for multi-criteria decision making problem based on the interval-valued intuitionistic fuzzy point operators and the evaluation function and their effectiveness and advantage are illustrated by examples.

In this study, we first define the uncertain linguistic Choquet averaging ULCA operator and the generalized Shapley uncertain linguistic Choquet averaging GS-ULCA operator. Especially, the GS-ULCA operator does not only globally consider the importance of the elements and their ordered positions, but also overall reflect the correlations among them and their ordered positions. Meantime, some desirable properties are studied. Furthermore, an approach to multi-attribute group decision making under uncertain linguistic environment is developed, where the interactions among experts and attributes are respectively considered. Moreover, if the information about the weights of experts and attributes is incompletely known, the models for the optimal fuzzy measures on expert set and attribute set are respectively established, which are based on gray relational analysis GRA method. Finally, a practical application of the developed approach to the problem of evaluating university faculty for tenure and promotion is provided.

Environmental concerns have globally driven the encouragement of green supply chain management. Accordingly, business and industrial organizations try to seek green supply chain strategies to respond to market pressure regarding corporate social responsibility. Green supplier selection is one of the practical strategies for modern enterprises. With the large-scale development of the palm oil products industry, green supplier selection technique is the key for decision making when dealing with mass information and possible risks of biased data. For instance, the preference of decision makers possibly causes a misleading decision, thus leading to unnecessary waste of resources. Therefore, the contribution of this paper is to apply the integrated multi-criteria decision method using the &lsquo, fuzzy decision-making trial and evaluation laboratory&rsquo, (fuzzy DEMATEL) method to consider the cause and effect relationship and then using fuzzy analytic network process (fuzzy ANP) to assign the weight of each relevant criteria. The initial results are useful for strategic procurement planning. In the final step, we adopt the prospect theory to synthesize procurement&rsquo, s psychological and behavioral factors when selecting green suppliers. The final result refers to the comprehensive prospect value to rank the eligible suppliers into orders. Moreover, the results of both sensitivity analysis and comparison method confirm that the proposed model is adequately realistic and robust.

Evaluating and selecting information systems projects for development in an organization are a multicriteria group decision-making problem in which multiple, often conflicting criteria have to be considered by several decision makers whose preferences in the decision making process are often inter-dependent. To effectively solve this problem, this study presents an intuitionistic fuzzy approach with the use of intuitionistic fuzzy values for adequately modeling the subjectiveness and imprecision of the decision making process. The inter-dependence of the preferences of the decision makers are properly represented by the use of fuzzy measure. An intuitionistic fuzzy group decision making method with Choquet integral-based TOPSIS is utilized for determining the overall performance of alternative information systems projects across all the criteria, leading to effective decisions being made in evaluating and selecting information systems projects. An example is presented for demonstrating the applicability of the proposed approach for solving the information systems project evaluation and selection problem in the real world setting.

This paper presents a critical analysis of conventional operations on intuitionistic fuzzy values (IFVs), and some limitations of the conventional aggregation operator on IFVs are analyzed in detail. In order to overcome these limitations, according to new operation laws on IFVs based on Achimedean t-norm and t-conorm, we propose a new quasi-intuitionistic fuzzy OWA (QIFOWA) operator. Some corresponding specific QIFOWA operators are given to show a consistent result. Our revisions will undoubtedly result in the improvement of both the theoretic development and the practical application in aggregation operator for decision making problems.