A multi-objective decision-making model with fuzzy rough coefficients and its application to the inventory problem

In this paper, we concentrate on developing a fuzzy rough multi-objective decision-making model according to uncertainty theory. We present some equivalent models and a traditional algorithm based on an interactive fuzzy satisfying method, which is similar to the interactive fuzzy rough satisfying method, in order to obtain a satisfying solution for the decision maker. In addition, the technique of fuzzy rough simulation is applied to deal with general fuzzy rough objective functions and fuzzy rough constraints which are usually difficult to convert into their equivalents. Furthermore, combined with the techniques of fuzzy rough simulation, a genetic algorithm using the compromise approach is designed for solving a fuzzy rough multi-objective programming problem. Finally, a model is applied to an inventory problem to illustrate the usefulness of the proposed model and algorithm, and then a sensitivity analysis is made.     

A class of multi-objective supply chain networks optimal model under random fuzzy environment and its application to the industry of Chinese liquor

An important issue, when shipping cost and customers demand are random fuzzy variables in supply chain network (SCN) design problem, is to find the network strategy that can simultaneously achieve the objectives of minimization total cost comprised of fixed costs of plants and distribution centers (DCs), inbound and outbound distribution costs, and maximization customer services that can be rendered to customers in terms of acceptable delivery time. In this paper, we propose a random fuzzy multi-objective mixed-integer non-linear programming model for the SCN design problem of Luzhou Co., Ltd. which is representative in the industry of Chinese liquor. By the expected value operator and chance constraint operator, the model has been transformed into a deterministic multi-objective mixed-integer non-linear programming model. Then, we use spanning tree-based genetic algorithms (st-GA) by the Prüfer number representation to find the SCN to satisfy the demand imposed by customers with minimum total cost and maximum customer services for multi-objective SCN design problem of this company under condition of random fuzzy customers demand and transportation cost between facilities. Furthermore, the efficacy and the efficiency of this method are demonstrated by the comparison between its numerical experiment results and those of tradition matrix-based genetic algorithm.     

A multiple attributes decision making method using individual and collaborative attribute data in a fuzzy environment

Although multiple attribute decision making (MADM) problems with both individual attribute data of a single alternative and collaborative attribute data of pairwise alternatives exist in the real world, they have seldom been a focus of research. This paper proposes a MADM method using individual and collaborative attribute data in a fuzzy environment, in which experts use linguistic variables to express their opinions. In the method, first, the evaluation matrix of individual attributes date and the judgment matrix of collaborative attributes data are constructed. Then, the central dominance of one alternative outranking other all alternatives is defined for aggregating the collaborative data. From this, an integrated decision matrix incorporating individual and collaborative attribute data is constructed. Further, based on an extended TOPSIS, the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS) are determined, and the relative closeness of each alternative to the FPIS and FNIS is calculated to determine the ranking order of all alternatives. Finally, two examples are used to illustrate the applicability of the proposed method.     

Characterizations of regular ordered semigroups in terms of (α, β)-fuzzy generalized bi-ideals

In this paper, the concept of an (α, β)-fuzzy generalized bi-ideal in an ordered semigroup is introduced, which is a generalization of the concept of a fuzzy generalized bi-ideal in an ordered semigroup. Using this concept, some characterization theorems are provided. The upper/lower parts of an (∈, ∈ ∨ q)-fuzzy generalized bi-ideal are introduced and some characterizations of regular ordered semigroups are given. Also, we consider the concept of implication-based fuzzy generalized bi-ideals in an ordered semigroup. In particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed.     

Second order (F, α, ρ, d)-convexity and duality in multiobjective programming

A class of second order (F, α, ρ, d)-convex functions and their generalizations is introduced. Using the assumptions on the functions involved, weak, strong and strict converse duality theorems are established for a second order Mond-Weir type multiobjective dual.     

Pricing and inventory management in a system with multiple competing retailers under (r, Q) policies

We consider a multi-retailer system operated on an infinite horizon, in which each retailer faces stochastic demand following a Poisson process and adopts a continuous-review (r, Q) policy for replenishing inventory to satisfy customer demand. The system involves decisions of pricing and inventory management with the goal of maximizing profit, which equals the sales revenue minus the purchase and inventory costs. Taking Cournot competition into account, models are formulated to optimize simultaneously the expected sales volumes and (r, Q) policies of all retailers. An efficient approach is proposed to calculate the approximate inventory cost. Based on this approach, solution methods for centralized and decentralized scenarios are developed. A great number of numerical computations are provided to evaluate the efficiency of the solution methods, and their performance in the two scenarios. Moreover, system performance under sequential decisions (first pricing and then inventory management) is also investigated.     

A new distance measure for interval valued intuitionistic fuzzy sets and its application to group decision making problems with incomplete weights information

The aim of this study is to introduce a novel generalized distance measure for interval valued intuitionistic fuzzy sets and to illustrate the applicability of the proposed distance measure to group decision making problems. Firstly, a generalized distance measure is proposed along with proofs satisfying its axioms. Then, a comparison between the proposed distance measure and well-known distance measures is performed in terms of counter-intuitive cases. Subsequently, the extension of TOPSIS method, in which the proposed distance measure is used to calculate separation measures, to an interval valued intuitionistic fuzzy (IVIF) environment is demonstrated to solve multi-criteria group decision making (MCGDM) problems using optimal criteria weights determined with linear programming model based on the concept of maximizing relative closeness coefficient. Finally, two illustrative examples are provided for proof-of-concept purposes and to demonstrate benefits of using the proposed distance measure over the existing ones in IVIF TOPSIS method for MCGDM problems.     

On a new class of fuzzy implications: h-Implications and generalizations

A new class of fuzzy implications called the h-implications is introduced. They are implications generated from an additive generator of a representable uninorm in a similar way of Yager’s f- and g-implications which are generated from additive generators of continuous Archimedean t-norms and t-conorms. Basic properties of these implications are studied in detail. Modifications and generalizations of the initial definition are presented and their properties studied and compared between them. One of the modifications, called (h, e)-implications, is another example of a fuzzy implication satisfying the exchange principle but not the law of importation for any t-norm, in fact for any function F : [0, 1]² → [0, 1].     

(?, T)-fuzzy rough approximation operators and the TL-fuzzy rough ideals on a ring

In this paper, we consider a ring as a universal set and study (?, T)-fuzzy rough approximation operators with respect to a TL-fuzzy ideal of a ring. First, some new properties of generalized (?, T)-fuzzy rough approximation operators are obtained. Then, a new fuzzy algebraic structure - TL-fuzzy rough ideal is defined and its properties investigated. And finally, the homomorphism of (?, T)-fuzzy rough approximation operators is studied.     

Necessary optimality conditions for fuzzy variational problems

The main aims of this study are to derive the fuzzy Euler-Lagrange conditions for both fuzzy unconstrained and constrained variational problems based on the concepts of differentiability and integrability of a fuzzy mapping that may be parameterized by the left and right-hand functions of its α-level sets.     

Fuzzy random renewal reward process and its applications

This paper studies a renewal reward process with fuzzy random interarrival times and rewards under the ?-independence associated with any continuous Archimedean t-norm ?. The interarrival times and rewards of the renewal reward process are assumed to be positive fuzzy random variables whose fuzzy realizations are ?-independent fuzzy variables. Under these conditions, some limit theorems in mean chance measure are derived for fuzzy random renewal rewards. In the sequel, a fuzzy random renewal reward theorem is proved for the long-run expected reward per unit time of the renewal reward process. The renewal reward theorem obtained in this paper can degenerate to that of stochastic renewal theory. Finally, some application examples are provided to illustrate the utility of the result.     

Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings

A new kind of generalized fuzzy h-ideals of a hemiring, namely, the (∈,∈∨q)-fuzzy h-bi-ideal (resp., h-quasi-ideal) is studied and the relationships between these generalized fuzzy h-ideals are described. Some characterization theorems of prime and semiprime (∈,∈∨q)-fuzzy h-bi-ideals (resp., h-quasi-ideals) of a hemiring are also given. In particular, we show that the h-hemiregular hemirings and h-intra-hemiregular hemirings can be described by using some of their generalized fuzzy h-ideals. Finally, the implication-based fuzzy h-bi-ideals (resp., h-quasi-ideals) of a hemiring are considered.     

A new view of fuzzy hypernear-rings

In this survey article, we first introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. This concept is a generalized concept of quasi-coincidence of a fuzzy point within a fuzzy set. By using this new idea, we consider the interval valued (∈,∈∨q)-fuzzy sub-hypernear-rings (hyperideals) of a hypernear-ring, and hence, a generalization of a fuzzy sub-near-ring (ideal) is given. Some related properties of fuzzy hypernear-rings are described. Finally, we consider the concept of implication-based interval valued fuzzy sub-hypernear-rings (hyperideals) in a hypernear-ring, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed.     

Self-learning fuzzy logic controllers for pursuit-evasion differential games

This paper addresses the problem of tuning the input and the output parameters of a fuzzy logic controller. The system learns autonomously without supervision or a priori training data. Two novel techniques are proposed. The first technique combines Q(λ)-learning with function approximation (fuzzy inference system) to tune the parameters of a fuzzy logic controller operating in continuous state and action spaces. The second technique combines Q(λ)-learning with genetic algorithms to tune the parameters of a fuzzy logic controller in the discrete state and action spaces. The proposed techniques are applied to different pursuit-evasion differential games. The proposed techniques are compared with the classical control strategy, Q(λ)-learning only, reward-based genetic algorithms learning, and with the technique proposed by Dai et al. (2005) [19] in which a neural network is used as a function approximation for Q-learning. Computer simulations show the usefulness of the proposed techniques.     

Bootstrap approach to the multi-sample test of means with imprecise data

A bootstrap approach to the multi-sample test of means for imprecisely valued sample data is introduced. For this purpose imprecise data are modelled in terms of fuzzy values. Populations are identified with fuzzy-valued random elements, often referred to in the literature as fuzzy random variables. An example illustrates the use of the suggested method. Finally, the adequacy of the bootstrap approach to test the multi-sample hypothesis of means is discussed through a simulation comparative study.     

Linguistic truth-valued lattice-valued propositional logic system ?P(X) based on linguistic truth-valued lattice implication algebra

In the semantics of natural language, quantification may have received more attention than any other subject, and syllogistic reasoning is one of the main topics in many-valued logic studies on inference. Particularly, lattice-valued logic, a kind of important non-classical logic, can be applied to describe and treat incomparability by the incomparable elements in its truth-valued set. In this paper, we first focus on some properties of linguistic truth-valued lattice implication algebra. Secondly, we introduce some concepts of linguistic truth-valued lattice-valued propositional logic system ?P(X), whose truth-valued domain is a linguistic truth-valued lattice implication algebra. Then we investigate the semantic problem of ?P(X). Finally, we further probe into the syntax of linguistic truth-valued lattice-valued propositional logic system ?P(X), and prove the soundness theorem, deduction theorem and consistency theorem.