Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory

The first step of this study is to recall the definition and basic theorems for convex fuzzy metric space (Z, M). Then, the definition of the convex fuzzy distance between two sets F and Y as well as the convex fuzzy distance from a point z to a set Y are introduced. Furthermore, the set of all nonempty convex fuzzy compact sets CFC(Z) are proved as a convex fuzzy complete when the convex fuzzy metric space (Z, M) is convex fuzzy complete.

This paper presents a fuzzy goal programming (FGP) approach for modeling and solving multiobjective fractional programming problems (MOFPPs) with fuzzy numbers parameter sets. In the proposed approach, first the notion of α-cut in fuzzy sets (FSs) is used to transform a problem into conventional MOFPP by using the tolerance membership functions in FSs. In model formulation, membership functions are converted into fuzzy goals for measuring the degree of satisfaction of decision maker (DM) with the solution for achievement of fuzzily described objectives of the problem. In the solution process, an iterative parametric method is addressed within the framework of minsum FGP model to reach the highest membership value (unity) to the extent possible in the decision making environment. The efficiency of the proposed approach is illustrated by a numerical example. The model solution is also compared with the solution obtained by using other approaches studied previously.

In this paper, we present about the fuzzy mathematical modelling and lexicographical solution concept in fuzzy games. By introducing the concept of topological game over an ideal of Hausdorff space, a game over some special product space is played. Fuzzy set theory has been applied to fuzzify some of the results obtained.

This paper introduces repeated theory on the base of fuzzy cooperative game by Aubin etal in 1974 and then constructs repeated fuzzy games theory. It gives the conception of repeated convex fuzzy cooperative games and studies the property of repeated convex fuzzy games.

Cardinality, quantifiers, and the aggregation of fuzzy criteria

On fuzzy goals and maximizing decisions in stochastic optimal control

In this paper we first consider the problem of extending fuzzy (weak and strict) preference relations, represented by fuzzy preorders on a set to a fuzzy preferences on subsets, and we characterise different possibilities. Based on their properties, we then semantically define and axiomatize several two-tiered graded modal logics to reason about the corresponding different notions of fuzzy preferences.

In fuzzy set theory, fuzzy convex structures are important mathematical structures. In this paper, we focus on separation axioms in fuzzy convex spaces. Concretely, we introduce S0, S1 and S2 separation axioms in fuzzy convex spaces and establish their relationships. Furthermore, we investigate their hereditary and productive properties.

This paper considers the consensual analysis in decision-making (CDM) processes based on fuzzy logic (FL) and interval-valued fuzzy logic (IVFL), providing a CDM-strategy, by exploring the axiomatic properties of fuzzy consensus measures (FCM) via penalty functions. Thus, two models are formalized, FS-FCM and IVFS-FCM. In the former, the fuzzy-valued lattice enables the analysis of fuzzy information for linguistic variables (LV), which is obtained by the aggregation of penalty functions. And, in the latter, the consensus measures of fuzzy sets are aggregated to build a new consensual analysis modeling. Thus, e.g., the cohesion of several terms related to the same LV can be analyzed, and also the coherence between fuzzy sets referring to the lowest and highest projections. Such models decide based on relevance criteria and qualitative assessments, via the selection of alternatives, supporting the corresponding algorithmic strategies: FS-FCM strategy, applied to fuzzy values, and IVFS-FCM strategy, covering fuzzy sets. The Intf-HybridMem approach explores the access patterns to volatile and non-volatile memories related to decision-making in two steps: (i) the FS-FCM strategy explores consensus measures of fuzzy values from membership functions; and (ii) the IVFS-FCM strategy, modeling inaccuracy inherent in input variables, as read/write frequency and access recency, also including the migration recommendation as output, which is validated by evaluations carried out in both proposed strategies.

The inductive learning methodology known as decision trees, concerns the ability to classify objects based on their attributes values, using a tree like structure from which decision rules can be accrued. In this article, a description of decision trees is given, with the main emphasis on their operation in a fuzzy environment. A first reference to decision trees is made in Hunt et al. (1966), who proposed the Concept learning system to construct a decision tree that attempts to minimize the score of classifying chess endgames. The example problem concerning chess offers early evidence supporting the view that decision trees are closely associated with artificial intelligence (AI). It is over ten years later that Quinlan (1979) developed the early work on decision trees, to introduced the Interactive Dichotomizer 3 (ID3). The important feature with their development was the use of an entropy measure to aid the decision tree construction process (using again the chess game as the considered problem). It is ID3, and techniques like it, that defines the hierarchical structure commonly associated with decision trees, see for example the recent theoretical and application studies of Pal and Chakraborty (2001), Bhatt and Gopal (2005) and Armand et al. (2007). Moreover, starting from an identified root node, paths are constructed down to leaf nodes, where the attributes associated with the intermediate nodes are identified through the use of an entropy measure to preferentially gauge the classification certainty down that path. Each path down to a leaf node forms an ‘if .. then ..’ decision rule used to classify the objects. The introduction of fuzzy set theory in Zadeh (1965), offered a general methodology that allows notions of vagueness and imprecision to be considered. Moreover, Zadeh’s work allowed the possibility for previously defined techniques to be considered with a fuzzy environment. It was over ten years later that the area of decision trees benefited from this fuzzy environment opportunity (see Chang and Pavlidis, 1977). Since then there has been a steady stream of research studies that have developed or applied fuzzy decision trees (FDTs) (see recently for example Li et al., 2006 and Wang et al., 2007). The expectations that come with the utilisation of FDTs are succinctly stated by Li et al. (2006, p. 655); “Decision trees based on fuzzy set theory combines the advantages of good comprehensibility of decision trees and the ability of fuzzy representation to deal with inexact and uncertain information.” Chiang and Hsu (2002) highlight that decision trees has been successfully applied to problems in artificial intelligence, pattern recognition and statistics. They go onto outline a positive development the FDTs offer, namely that it is better placed to have an estimate of the degree that an object is associated with each class, often desirable in areas like medical diagnosis (see Quinlan (1987) for the alternative view with respect to crisp decision trees). The remains of this article look in more details at FDTs, including a tutorial example showing the rudiments of how an FDT can be constructed.

Background: A Fuzzy Cubic Set (FCS) is composed of a Fuzzy Set (FS) (certain fuzzy numbers) and an Interval-Valued Fuzzy Set (IVFS) (uncertain fuzzy numbers) to describe the hybrid information of both. To enhance the credibility of both, they should be closely related to the measures/degrees of credibility owing to the vagueness and uncertainty of humans’ cognitions regarding the real world. Objective: This paper presents the notions of a Fuzzy Cubic Credibility Set (FCCS) and a Fuzzy Cubic Credibility Number (FCCN) as the new generalization of the FCS notion to enhance the credibility level of FCS by means of the credibility degrees of both FS and IVFS. Next, we define operations of FCCNs, an expected value of FCCN, and the FCCN Weighted Arithmetic Averaging (FCCNWAA) and FCCN Weighted Geometric Averaging (FCCNWGA) operators for Decision Making (DM) strategy. Method: A DM strategy using the FCCNWAA or FCCNWGA operator is proposed to solve multicriteria DM problems in the environment of FCCNs. Then, the proposed DM strategy is applied to a DM example of slope design schemes for an open-pit mine in the environment of FCCNs to reflect the feasibility of the proposed DM strategy. Result: By comparison with the fuzzy cubic DM strategy, the DM results with and without the degrees of credibility, can impact on the ranking of alternatives in the DM example to reflect the effectiveness of the proposed DM strategy. Conclusion: However, the highlighting advantage of this study is that the proposed DM strategy not only indicates the degrees of credibility regarding the assessed values of FCNs in the DM process but also enhances the DM reliability in the environment of FCCNs. Hence, the proposed DM strategy is superior to the fuzzy cubic DM strategy in the environment of FCCNs.

In this paper we consider a bi-matrix game with fuzzy payoffs. To compare a fuzzy numbers, some different ordering operators can be used. We define Nash equilibrium in fuzzy game using the ordering op erator. The game with crisp payoffs is associated with the original game. Here, crisp payoffs are the operator’s value on a fuzzy payoff. We propose the following statement: if the ordering operator is linear, then the game with payoffs has same Nash equilibrium strategy profile as the crisp game. We present an algorithm for constructing a Nash equilibrium in a bi-matrix game with fuzzy payoffs and we are using this fact. We use such ordering operators, and construct the Nash equilibrium in examples of bi-matrix games. Key Word: Fuzzy set, bi-matrix, membership function, cooperative game

Length functions and fuzzy groups

Fuzzy predictive control integrates conventional model-based predictive control with techniques from fuzzy multicriteria decision making, and translates the goals and the constraints to predictive control in a transparent way. The information regarding the (fuzzy) goals and the (fuzzy) constraints of the control problem is combined by using a decision function from the fuzzy set theory. This paper investigates the use of fuzzy decision making in predictive control and compares the results to those obtained from conventional model-based predictive control. Experiments on a nonminimum phase, unstable linear system and air conditioning system with nonlinear dynamics are studied. It is shown that the performance of the model-based predictive controller can be improved by the use of fuzzy goals and criteria with fuzzy decision-making techniques.

WASPAS-based decision making methodology with unknown weight information under uncertain evaluations