Iranian journal of fuzzy systems
Volume:17 Issue: 1, Jan-Feb 2020

Based on a new hesitant fuzzy partial ordering proposed by Garmendia et al.~cite{GaCa:Pohfs}, in this paper a fuzzy disjunction ${D}$ on the set ${H}$ of finite and nonempty subsets of the unit interval and a t-conorm ${S}$ on the set $bar{{B}}$ of equivalence class on the set of finite bags of unit interval based on this partial ordering are introduced respectively. Then, hesitant fuzzy negations $N_n$ on ${H}$ and $mu_n$ on $bar{{B}}$ are proposed. Particularly, their De Morgan's laws are investigated with respect to binary operations ${C}$  and ${D}$ on ${H}$, as well as ${T}$  and {S} on $bar{{B}}$ respectively, where ${C}$ is a commutative fuzzy conjunction on $({H},leq_H)$ and ${T}$ is a t-norm on $(bar{{B}},leq_B)$. Finally, the new hesitant fuzzy aggregation operators are presented on ${H}$ and $bar{{B}}$ and their more general forms are given. Moreover, the validity of the aggregation operations is illustrated by a numerical example on decision making.

In this study, the aim is to propose a new method for fuzzification of nested dummy variables. The fuzzification idea of dummy variables has been acquired from non-linear part of regime switching models in econometrics. In these models, the concept of transfer functions is like the notion of fuzzy membership functions, but no principle or linguistic sentence have been used for inputs. Consequently, for the non-linear part including transfer function, there is no reason why the different types of functions such as logistic are used. Therefore, in order to solve the aforementioned problem like the regime switching models, the transfer functions are considered for dummy variables. However, the presented transfer functions are proposed by fuzzy clustering membership function. Finally, using fuzzy logic, the membership functions of clusters are combined with each other and constitute the fuzzy nested regimes. The suggested model has been used in financial data of Iran's stock in order to examine the equity premium Puzzle. The results of using above model helped in modeling appropriate second-order moments in consumption capital asset pricing model.

In this research work, a wholesaler-retailer-customer supply chain model for a deteriorating item is considered, where the retailer's warehouse in the market place has a limited capacity. The retailer can rent an additional warehouse (rented warehouse) if needed, with a higher rent compared to the existing warehouse (own warehouse). The customers' demand of the item is linearly influenced by the stock level and in case of shortages the base demand is partially backlogged. Being the leader of the supply chain, the retailer introduces some promotional cost to boost the base demand of the item. To participate in joint marketing decision, the wholesaler shares a compromise part of this promotional cost. Goal of this research work is to maximize the individual profits (when the retailer is the leader and the wholesaler is the follower) as well as the channel profit (when the retailer and the wholesaler jointly make marketing decision) of the system. It is established that if the wholesaler shares a part of the promotional cost, then the channel profit as well as the individual profits increase. The supply chain model is also considered in imprecise environment, where different inventory parameters are fuzzy/rough in nature. In this case, the individual profits as well as the channel profit become fuzzy/rough in nature. As optimization of fuzzy/rough objective is not well defined, following credibility/trust measure of fuzzy/rough event, an approach is followed for comparison of fuzzy/rough objectives and a Particle Swarm Optimization algorithm is implemented to find the marketing decisions. Efficiency of the algorithm in solving the problem is statistically established. The existence of the joint marketing decision is established analytically and numerically (with illustration) in crisp as well as in imprecise environments.

The present paper studies fuzzy matroids in view of degree. First wegeneralize the notion of $(L,M)$-fuzzy independent structure byintroducing the degree of $M$-fuzzy family of independent $L$-fuzzysets with respect to a mapping from $L^X$ to $M$. Such kind ofdegrees is proved to satisfy some axioms similar to those satisfiedby $(L,M)$-fuzzy independent structure. Then we define and studysome special degrees (e.g. quotient degrees and isomorphism degrees)with respect to mappings between two $(L,M)$-fuzzy matroid-likespaces in details. Finally we give characterizations of thesedegrees and investigate relationships between them.

Particle Swarm Optimization (PSO) is a metaheuristic optimization algorithm that owes much of its allure to its simplicity and its high effectiveness in solving sophisticated optimization problems. However, since the performance of the standard PSO is prone to being trapped in local extrema, abundant variants of PSO have been proposed by far. For instance, Fuzzy Adaptive PSO (FAPSO) algorithms have been being studied extensively in recent years. In this study, a modified version of PSO algorithms is presented and is named as Adaptive Particularly Tunable Fuzzy Particle Swarm Optimization (APT-FPSO). In it, the global and personal learning coefficients of every single particle are tuned adaptively and particularly, at an individual extent, within each iteration with the aid of fuzzy logic concepts. Ample statistical evidence is provided indicating that the proposed algorithm further improves the potentialities and capabilities of the standard PSO.

In this paper, an interval Type-2 fuzzy logic based pitch angle controller is proposed for fixed speed wind energy system (WES) to maintain the aerodynamic power at its rated value. The pitch angle reference is generated by the proposed controller which can compensate the non-linear characteristics of the pitch angle to the wind speed. The presence of third dimension in the Type-2 fuzzy logic controller (FLC) membership function offers an additional degree-of-freedom in the design of the Type-2 FLC controller to improve the system performance. The applicability of the proposed controller is evaluated by considering a nonlinear simulation model of the WES which is developed and implemented using OPAL-RT real time digital simulator. The results show that the proposed controller offers better performance than the conventional PI and fuzzy logic controllers.

A novel ranking method based on multi-time information fusion is proposed for intuitionistic fuzzy sets (IFSs) and applied to the threat assessment problem, a multi-attribute decision making (MADM) one. This method integrates a designed intuitionistic fuzzy entropy (IFE), the closeness degree of technique for order preference by similarity to ideal solution (TOPSIS), the decision maker¡¯s (DM¡¯s) risk attitude and decision information from DMs in multiple times. Firstly, a novel IFE is designed in order to sufficiently express the fuzziness and the unknown of uncertainty conveyed by IFSs. Secondly, considering the distance from the positive ideal solution and the negative ideal solution simultaneously, the closeness degree of TOPSIS is utilized to characterize the amount of information conveyed by the IFS. The amount of information and the uncertainty of information are combined by the introduction of DMs¡¯ risk attitudes and then; a novel single time ranking method for IFSs is structured. Next, to reflect the subjective ranking intention on alternatives, the comprehensive preference model of DMs is established. The optimal attribute weights are derived from the linear programming model which incorporates the subjective ranking intension and the objective ranking result. Finally, the decision information from DMs in multiple times is aggregated to give the final ranking results. A threat assessment example and comparison analysis demonstrates the flexibility and effectiveness of the proposed method.

The competition among shopping malls is getting increasingly more intense.In order to enhance corporate competitiveness and profitability, how toretain key loyal customers has become an important issue for the managers ofshopping malls. Customer loyalty programs are a universal practice. Thisstudy proposes an analytical model for developing the strategic managementof customer loyalty programs. Based on quality function deployment, ourmodel constructs a fuzzy relational matrix to integrate the customerbenefits and the customer loyalty programs. The results contribute to abetter understanding of the different importance of customer benefits withrespect to ``Utilitarian benefits'', ``Hedonic benefits'' and ``Symbolicbenefits''. The study's findings provide prioritized customer loyaltyprograms, including ``Newest information transmissions,'' ``Communicationservice specialists,'' ``Exclusive free gift promotions,'' and ``VIP loungeservice,'' which can be used to determine the directions for the improvementof shopping malls. The study has implications for the theory andpractitioners. First, it allows the integration of customer benefits incustomer loyalty programs and the consideration of VIP customers inthe programs. Second, the requirement evaluation considering fuzzylinguistic preferences allows for prioritizing the customer loyalty programswhen dealing with uncertainty and vagueness. Finally, this approach helps toobtain more realistic results by integrating fuzzy decision-making into QFD.

The interval-valued intuitionistic fuzzy set (IVIFS) which is an extension of the Atanassov’s intuitionistic fuzzy set is a powerful tool for modeling real life decision making problems. In this paper, we propose the emph{generalized interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral} (GIVIFHGSCI) and the emph{interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral} (IVIFHGSCI) operators, which consider the importance of the ordered positions and correlations among the arguments with the assumption that the aggregated arguments are interrelated. Furthermore, some of the properties and special cases of these operators are discussed. An approach for multicriteria decision making based on these operators is developed. Finally an illustrative example follows.

This paper deals with fuzzy cellular neural networks (FCNNs) with leakage delays and proportional delays. Applying the differential inequality strategy, fixed point theorem and almost periodic function principle, some sufficient criteria which ensure the existence and global attractivity of a unique almost periodic solution for fuzzy cellular neuralnetworks with leakage delays and proportional delays are derived.Computer simulations are carried out to illustrate our theoreticalfindings. Our results are new and complement some previouspublished ones.

The present paper is an attempt to study the minimal BL-general fuzzy automata which realizes the given fuzzy behavior. Of two methods applied for construction of such automaton presented here, one has been based on Myhill-Nerode's theory while the other has been based on derivatives of the given fuzzy behavior. Meanwhile, the categories of BL-general fuzzy automata and fuzzy behavior, along with a functorial relationship between them, are introduced.

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactness and show that the indices of compactness of the quantale-valued metric space and of the hyperspaces equipped with the quantale-valued Hausdorff metric and with the quantale-valued Wijsman structure coincide.

Multivariate control chats are generally used in situations where the simultaneous monitoring or control of two or more related quality characteristics is necessary. In most processes in the real world, distribution of the process characteristics are unknown or at least non-normal, so the non-parametric or distribution-free charts are desirable. Most non-parametric statistical process-control techniques depend on ranks. In this survey, we apply the fuzzy set theory to deal with the circumstances thatthe values of each characteristic are presented in linguistic form, so we propose non-parametric multivariate control charts based on sign and Wilcoxon signed-rank tests.The performance of the proposed charts is investigated in a simulation study. Numerical examples are used to demonstrate the effectiveness and performance of the proposed charts.