Zeng-Tai Gong’s research while affiliated with Northwest Normal University and other places

The knowledge of key network members is generally known to be critical to fuzzy social network analysis. Thus far, most studies aiming to identify critical members have taken network structural centrality measures. Since fuzzy graph cannot effectively depict the multidimensional relationships between the nodes of fuzzy social networks, a fuzzy social network model is developed complying with a mathematical theory of fuzzy hypergraph, allowing fuzzy social network to be represented more intuitively and visually. A fuzzy hypergraph model of fuzzy social network refers to a structure, vertex set acts as an object set, and the fuzzy relation in fuzzy relation structure is expressed by membership function and fuzzy relation matrix. With the fuzzy hypergraph model of fuzzy social networks, the definitions of structural centrality are given (i.e., degree centrality, relative degree centrality, closeness centrality, relative closeness centrality, betweenness centrality and relative betweenness centrality). Lastly, by analyzing examples, the process of building fuzzy social network with fuzzy hypergraph and the calculation method of centrality are illustrated.

In this paper, the concept of fuzzy share functions of cooperative fuzzy games with fuzzy characteristic functions is proposed. Players in the proposed cooperative fuzzy game do not need to know precise information about the payoff value. We generalize the axiom of additivity by introducing a positive fuzzy value function (mu) over tilde on the class of cooperative fuzzy games in fuzzy characteristic function form. The so-called axiom of (mu) over tilde -additivity generalizes the classical axiom of additivity by putting the weight (mu) over tilde((v) over tilde) on the value of the game O. We show that any additive function determines a unique fuzzy share function satisfying the axioms of efficient shares, null player property, symmetry and (mu) over tilde -additivity on the subclass of games on which (mu) over tilde is positive and which contains all positively scaled unanimity games. Finally, we introduce the fuzzy Shapley share functions and fuzzy Banzhaf share functions for the cooperative fuzzy games with fuzzy characteristic functions.

The purpose of this paper is to introduce the concepts of alpha beta-statistical convergence of order gamma and strong alpha beta-convergence of order gamma for a sequence of fuzzy numbers. At the same time, some connections between alpha beta-statistical convergence of order gamma and strong alpha beta-convergence of order 7 for a sequence of fuzzy numbers are established. It also shows that if a sequence of fuzzy numbers is strongly alpha beta-convergent of order gamma then it is alpha beta-statistically convergent of order gamma.

In this paper, we shall characterize McShane integral and Henstock integral of fuzzy-number-valued functions by Riemann-type integral of fuzzy-number-valued functions with a small Riemann sum on a small set, and the results show that McShane integral (Benstock integrals) of fuzzy-number-valued functions could be represented by Riemann integral (McShane integral) with a small Riemann sum on a small set, respectively.

The purpose of this paper is to introduce the concepts of almost ideal lacunary statistical convergence (almost ideal statistical convergence) and strongly almost ideal lacunary convergence (strongly almost ideal convergence), we give some relations betweeen these concepts. At the same time, some connections between strongly almost ideal lacunary statistical convergence and almost ideal lacunary statistical convergence of sequences of fuzzy numbers are established. It also shows that if a sequence of fuzzy numbers is strongly almost ideal lacunary statistical convergence with respect to an Orlicz function then it is almost ideal lacunary statistical convergent.

In order to value the non-market goods, we consider the uncertain preference of the respondents for non-market goods, individual often have trouble trading off the good or amenity against a monetary measure. Valuation in these situations can best be described as fuzzy in terms of the amenity being valued.We move away from a probabilistic representation of uncertainty and propose the use of intuitionistic fuzzy contingent valuation. That is to say we could apply intuitionistic fuzzy logic to contingent valuation. Since intuitionistic fuzzy sets could provide the information of the membership degree and the nonmembership degree, it has more expression and flexibility better than traditional fuzzy sets in processing uncertain information data. In this paper, we apply intuitionistic fuzzy logic to contingent, developing an intuitionistic fuzzy clustering and interval intuitionistic fuzzy clustering approach for combining preference uncertainty.We develop an intuitionistic fuzzy random utility maximization framework where the perceived utility of each individual is intuitionistic fuzzy in the sense that an individual’s utility belong to each cluster to some degree. Both the willingness to pay (WTP) and willingness not to pay (WNTP) measures we obtain using intuitionistic fuzzy approach are below those using standard probability methods.

Based on the concepts of the pseudo-differentiability and the pseudo-integrability proposed in this paper, the transformation theorems for them are given. Newton-Leibniz formula is also obtained. As applications, the results can be applied directly to the discussion of nonlinear differential equations.