Constrained fuzzy arithmetic approach to fuzzy transportation problems with fuzzy decision variables

Most of the existing methods for solving fully fuzzy mathematical programs are based on the standard fuzzy arithmetic operations and/or Zadeh's extension principle. These methods may produce questionable results for many real-life applications. Due to this fact, this paper presents a novel method based on the constrained fuzzy arithmetic concept to solve fully fuzzy balanced/unbalanced transportation problems in which all of the parameters (source capacities, demands of destinations, transportation costs etc.) as well as the decision variables (transportation quantities) are considered as fuzzy numbers. In the proposed method, the requisite crisp and/or fuzzy constraints between the base variables of the fuzzy components are provided from the decision maker according to his/her exact or vague judgments. Thereafter, fuzzy arithmetic operations are performed under these requisite constraints by taking into account the additional information while transforming the fuzzy transportation model into crisp equivalent form. Therefore, various fuzzy efficient solutions can be generated by making use of the proposed method according to the decision maker's risk attitude. In order to present the efficiency/applicability of the proposed method, different types of fully fuzzy transportation problems are generated and solved as illustrative examples. A detailed comparative study is also performed with other methods available in the literature. The computational analysis have shown that relatively more precise solutions are obtained from the proposed method for “risk-averse” and “partially risk-averse” decision makers. The proposed method also successfully provided fuzzy acceptable solutions for “risk seekers” with high degree of uncertainty similar to the other existing methods in the literature.     

Application of a fuzzy TOPSIS method base on modified preference ratio and fuzzy distance measurement in assessment of traffic police centers performance

In this paper we have presented a TOPSIS approach based on preference ratio and an efficient fuzzy distance measurement for a Fuzzy Multiple Criteria Group Decision-Making Problem (FMCGDMP). Preference ratio with a moderate modification for negative fuzzy numbers was used as an efficient ranking method for fuzzy numbers in a relative manner. As human reasoning persuades that distances between two fuzzy numbers should be a fuzzy measure, so all distances between fuzzy numbers (i.e. distances between alternatives, Fuzzy Positive Ideal solutions, and Fuzzy Negative Ideal solutions) have been calculated as fuzzy numbers using an efficient fuzzy distance measurement. The aforementioned arguments make the proposed algorithm unique and well posed for real-life problem modeling. Moreover, the main novelties of the proposed procedure (i.e. the fuzzy distance measurement and Preference Ratio) have been developed for Generalized Fuzzy Numbers (GFNs). The proposed algorithm has efficiently been applied in assessment of traffic police centers which is treated as a FMCGDMP.     

An epsilon-constraint method for fully fuzzy multiobjective linear programming

Linear ranking functions are often used to transform fuzzy multiobjective linear programming (MOLP) problems into crisp ones. The crisp MOLP problems are then solved by using classical methods (eg, weighted sum, epsilon-constraint, etc), or fuzzy ones based on Bellman and Zadeh's decision-making model. In this paper, we show that this transformation does not guarantee Pareto optimal fuzzy solutions for the original fuzzy problems. By using lexicographic ranking criteria, we propose a fuzzy epsilon-constraint method that yields Pareto optimal fuzzy solutions of fuzzy variable and fully fuzzy MOLP problems, in which all parameters and decision variables take on LR fuzzy numbers. The proposed method is illustrated by means of three numerical examples, including a fully fuzzy multiobjective project crashing problem.     

Multicriteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets

In this paper, we present a new method for multicriteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets, where interval-valued intuitionistic fuzzy values are used to represent evaluating values of the decision-maker with respect to alternatives. First, we propose a new method for ranking interval-valued intuitionistic fuzzy values. Based on the proposed fuzzy ranking method of interval-valued intuitionistic fuzzy values, we propose a new method for multicriteria fuzzy decision making. The proposed multicriteria fuzzy decision making method outperforms Ye’s method (2009) due to the fact that the proposed method can overcome the drawback of Ye’s method (2009), where the drawback of Ye’s method is that it can not distinguish the ranking order between alternatives in some situations. The proposed method provides us with a useful way for dealing with multicriteria fuzzy decision making problems based on interval-valued intuitionistic fuzzy sets.     

Soft computing based on new interval-valued fuzzy modified multi-criteria decision-making method

In this paper, a new interval-valued fuzzy modified TOPSIS (IVFM-TOPSIS) method is proposed that can reflect both subjective judgment and objective information in real life situations. This proposed method is based on concepts of the positive ideal and negative ideal solutions for solving multi-criteria decision-making (MCDM) problems in a fuzzy environment. The performance rating values and weights of criteria are linguistic variables expressed as triangular interval-valued fuzzy numbers. Furthermore, we appraise the performance of alternatives against both subjective and objective criteria with multi-judges for decision-making problems. Finally, for the purpose of proving the validity of the proposed method a numerical example is presented for a robot selection problem.     

A novel criterion for nonlinear time-delay systems using LMI fuzzy Lyapunov method

This study presents a kind of fuzzy robustness design for nonlinear time-delay systems based on the fuzzy Lyapunov method, which is defined in terms of fuzzy blending quadratic Lyapunov functions. The basic idea of the proposed approach is to construct a fuzzy controller for nonlinear dynamic systems with disturbances in which the delay-independent robust stability criterion is derived in terms of the fuzzy Lyapunov method. Based on the robustness design and parallel distributed compensation (PDC) scheme, the problems of modeling errors between nonlinear dynamic systems and Takagi–Sugeno (T–S) fuzzy models are solved. Furthermore, the presented delay-independent condition is transformed into linear matrix inequalities (LMIs) so that the fuzzy state feedback gain and common solutions are numerically feasible with swarm intelligence algorithms. The proposed method is illustrated on a nonlinear inverted pendulum system and the simulation results show that the robustness controller cannot only stabilize the nonlinear inverted pendulum system, but has the robustness against external disturbance.     

Exact fuzzy optimal solution of fully fuzzy linear programming problems with unrestricted fuzzy variables

Kumar et al. (Appl. Math. Model. 35:817?C823, 2011) pointed out that there is no method in literature to find the exact fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems and proposed a new method to find the fuzzy optimal solution of FFLP problems with equality constraints having non-negative fuzzy variables and unrestricted fuzzy coefficients. There may exist several FFLP problems with equality constraints in which no restriction can be applied on all or some of the fuzzy variables but due to the limitation of the existing method these types of problems can not be solved by using the existing method. In this paper a new method is proposed to find the exact fuzzy optimal solution of FFLP problems with equality constraints having non-negative fuzzy coefficients and unrestricted fuzzy variables. The proposed method can also be used to solve the FFLP problems with equality constraints having non-negative fuzzy variables and unrestricted fuzzy coefficients. To show the advantage of the proposed method over existing method the results of some FFLP problems with equality constraints, obtained by using the existing and proposed method, are compared. Also, to show the application of proposed method a real life problem is solved by using the proposed method.     

Application of practical fuzzy arithmetic to fuzzy internal model control

This paper applies a new fuzzy arithmetic of interval calculus and fuzzy quantities to automatic control. Practical results are obtained which overcome those based on the extension principle or α-cuts. The proposed approach is based on a different representation of fuzzy numbers, though most common arithmetic operators cannot be directly applied for designing a fuzzy controller due to the unjustified overestimation effect. To avoid this phenomenon, a procedure based on an “exact” resolution calculus is proposed, whose solutions allow creating a fuzzy internal model control scheme. The validity of the new method is illustrated by a real-time educational engineering application on classical control design: a coupled tanks system.     

Hierarchical semi-numeric method for pairwise fuzzy group decision making

Gradual improvements to a single-level semi-numeric method, i.e., linguistic labels preference representation by fuzzy sets computation for pairwise fuzzy group decision making are summarized. The method is extended to solve multiple criteria hierarchical structure pairwise fuzzy group decision-making problems. The problems are hierarchically structured into focus, criteria, and alternatives. Decision makers express their evaluations of criteria and alternatives based on each criterion by using linguistic labels. The labels are converted into and processed in triangular fuzzy numbers (TFNs). Evaluations of criteria yield relative criteria weights. Evaluations of the alternatives, based on each criterion, yield a degree of preference for each alternative or a degree of satisfaction for each preference value. By using a neat ordered weighted average (OWA) or a fuzzy weighted average operator, solutions obtained based on each criterion are aggregated into final solutions. The hierarchical semi-numeric method is suitable for solving a larger and more complex pairwise fuzzy group decision-making problem. The proposed method has been verified and applied to solve some real cases and is compared to Saaty's (1996) analytic hierarchy process (AHP) method.