International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

We consider optimal multiagent cooperative decision making in stochastic environments. The focus is on simultaneous decision making, during which agents cooperate by limited communication. We model the multiagent system as a collaborative decision network (CDN). Several techniques are developed to improve efficiency for decision making with CDNs. We present an equivalent transformation of CDN subnets to facilitate model manipulation. We propose partial evaluation to allow action profiles evaluated with reduced computation. We decompose a CDN subnet, based on clustering of utility variables. A general simultaneous decision making algorithm suite is developed that embeds these techniques. We show that the new algorithm suite improves efficiency by a combination of a linear factor and an exponential factor.

The elements of the truth value algebra of type-2 fuzzy sets are the mappings of the unit interval into itself, with operations given by various convolutions of the pointwise operations. This algebra can be specialized and generalized in various interesting ways. First, we consider the more general case of all mappings of a bounded chain with an involution into a complete chain, and delimit some of the properties of the resulting algebra. These include two binary operations each of which give a partial order on the elements of that algebra. These partial orders and their intersection are the principal objects of interest. We specialize this situation in two cases: (1) all mappings of the unit interval into itself, the original version of the truth value algebra of type-2 fuzzy sets introduced by Zadeh, and (2) all mappings of a finite chain into another finite chain. Again, each of these two cases yields two partial orders on the elements of the resulting algebras, and in each case, our principal interest is in these partial orders and their intersection.

Decision makers often express their evaluations on decision problems with multi-granular linguistic terms. This fact leads to the unification of the multi-granular linguistic terms into a single linguistic set in the literature. However, this unification process increases the complexity of computation and the subjectivity in the determination of transformation functions. To overcome this deficiency, this paper aims to develop a normalized numerical scaling method for determining the semantics of multi-granular linguistic terms in the same domain. We first introduce a class of numerical scaling functions to generate several balanced or unbalanced linguistic sets. Since these scaled linguistic sets have different domains, we then develop a normalized numerical scaling method to form them into the unique interval [0,1]. As a result of this development, two classes of normalized scaling functions are derived from the priori scale information and applications of piecewise linear interpolation and piecewise arc interpolation. Finally, an example is given to illustrate how the method works.

Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we study the relations between implications and left (right) semi-uninorms on a complete lattice. We firstly investigate the left (right) semi-uninorms induced by implications, give some conditions such that the operations induced by implications constitute left or right semi-uninorms, and demonstrate that the operations induced by a right infinitely ∧-distributive implication, which satisfies the order property, are left (right) infinitely ∨-distributive left (right) semi-uninorms. Then, we discuss the residual operations of left (right) semi-uninorms and show that left (right) residual operators of strict left (right)-conjunctive left (right) infinitely ∨-distributive left (right) semi-uninorms are right infinitely ∧-distributive implications that satisfy the order property. Finally, we reveal the relationships between strict left (right)-conjunctive left (right) infinitely ∨-distributive left (right) semi-uninorms and right infinitely ∧-distributive implications which satisfy the order property.

In this paper, we first give the formula of possibility degree to rank the Atanassov's intuitionistic fuzzy numbers. Two methods called Atanassov's intuitionistic fuzzy weighted average (IFWA) and Atanassov's intuitionistic fuzzy weighted geometric mean (IFWGM) are developed to solve the multiple attribute decision making problems under Atanassov's intuitionistic fuzzy environment, in which the performance ratings of alternatives and relative importance of attributes are expressed with Atanassov's intuitionistic fuzzy sets. The IFWA and IFWGM methods, respectively, are treated as an auxiliary pair of fractional programming models and two linear programming (LP) solution procedures are proposed simultaneously by using Charnes and Cooper transformation. Furthermore, two algorithms which are based on the IFWA and IFWGM models, respectively, are developed to solve Atanassov's intuitionistic fuzzy decision making problems where attribute values and weights of attributes are all in Atanassov's intuitionistic fuzzy numbers. The order relationship between IFWA and IFWGM are investigated. Finally, a numerical example is illustrated to show the feasibility and effectiveness of the proposed methods.

The geometric Bonferroni mean (GBM) can capture the interrelationships between input arguments, which is an important generalization of Bonferroni mean (BM). In this paper, we combine geometric Bonferroni mean (GBM) with the power geometric average (PGA) operator under intuitionistic fuzzy environment and present the intuitionistic fuzzy geometric power Bonferroni mean (IFPGBM) and the weighted intuitionistic fuzzy power geometric Bonferroni mean (WIFPGBM). The desirable properties of these new extensions of Bonferroni mean and their special cases are investigated. We list the detailed steps of multiple attribute group decision making with the developed IFPGBM or WIFPGBM, and give a comparison of the new extensions of Bonferroni mean by this paper with the corresponding existing intuitionistic fuzzy Bonferroni means. Finally, examples are illustrated to show the validity and feasibility of the new approaches.