Journal of Intelligent & Fuzzy Systems - Volume 32, issue 3

Authors: Zhou, Shenghai | Xu, Xuanhua | Li, Zhaohui | Zhang, Faming

Article Type: Research Article

Abstract: Aiming at the Multiple Attribute Decision Making (MADM) problem that each attribute value is a stochastic variable instead of a real number, this paper develops a probability approximation method to deal with the randomness of the stochastic attribute values. We consider two general cases: (1) the distributions of all stochastic attribute values are known to decision-maker, and (2) the distributions of all stochastic attribute values are unknown, but decision-maker knows the possible value set of each stochastic attribute value. As for each case, firstly, we introduce the probability approach to approximate the stochastic attribute value. Through this approximation, we make …sure that the larger the transformed attribute value of one alternative is, the better it is than others. Secondly, a new method is proposed to calculate the weights of stochastic attribute values under the uncertain environment. With this method, we derive the attribute weights from two parts differences: the intra-attributes differences, which denote the weights affected by the uncertainty of the stochastic attributes themselves, and inter-attributes differences which represent the weighted affected by the different attribute differences, and then calculate the two types of attribute weights. Finally, a numerical analysis is used to illustrate the effectiveness of the method proposed. Show more

Keywords: Multi-attribute decision-making, stochastic attribute values, weights determination under stochastic environment

DOI: 10.3233/JIFS-16511

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2537-2548, 2017

Authors: Zhang, Qinghua | Zhang, Pei | Wang, Guoyin

Article Type: Research Article

Abstract: Rough set characterizes an uncertain set with two crisp boundaries, i.e., lower and upper-approximation sets, and it has successfully been applied into artificial intelligence fields. However, there is little discuss on how to establish a crisp set as approximation set of a target set instead of only giving out two boundary lines. Although many uncertain decision rules can be acquired from the information system based on lower-approximation set by keeping the positive region unchanged, the accuracy of these rules depends on the similarity between a target set and its lower-approximation set. In order to solve this problem, an approximation set …model of rough set was proposed and applied into attribute reduction or uncertain image segmentation successfully in our previous research. In this paper, a kind of fuzzy similarity between a target set and its approximation set is presented based on Euclidean distance instead of the similarity based on cardinality of a finite set. Then many good properties of 0.5-approximation set of a rough set are presented, and the conclusion that 0.5-appoximation set is the best approximation set of a rough set in all definable sets is successfully proved with Euclidean similarity between two fuzzy sets. Finally, the change laws of fuzzy similarity between a target set and its 0.5-approximation set in different granularity spaces is analyzed in detail. Show more

Keywords: Rough set, fuzzy set, 0.5-approximation set, fuzzy similarity, granularity

DOI: 10.3233/JIFS-16533

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2549-2562, 2017

Authors: Chu, Junfeng | Chin, Kwai-Sang | Liu, Xinwang | Wang, Yingming

Article Type: Research Article

Abstract: The decision maker’s attitudinal character towards risk and the psychological aspects are critical factors of the multiple attribute decision making (MADM) problems. In this paper, we consider the attitudinal character during the whole decision making procedure. The reference points associated with prospect theory are in the form of interval-valued intuitionistic fuzzy number (IVIFN) and we assume the membership degree and non-membership degree of the IVIFN obey normal distribution according to the central limit theorem. We combine the properties of normal distribution and the attitudinal character associated with the ordered weighted averaging (OWA) operator to convert all the reference points into …crisp numbers. We construct one feasible multiple objective optimization programming to obtain the optimal weight vector of the attributes by minimizing the deviation between the alternative and the reference point corresponding to each alternative. The hybrid weighted averaging (HWA) operator is applied to aggregate the prospect values for each alternative. Especially, we directly reorder the weighted prospect values considering their plus or minus, which reflects the decision-maker’s attitudinal character towards risk as well. Finally, an illustrative example about group-buying is provided to show the feasibility of the proposed method. Show more

Keywords: Prospect theory, attitudinal character, interval-valued intuitionistic fuzzy set (IVIFS), hybrid weighted averaging (HWA) operator, multiple attribute decision making (MADM)

DOI: 10.3233/JIFS-16543

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2563-2578, 2017

Authors: Liu, Yang | Ban, Xiaojun | Wu, Fen | Lam, H.K.

Article Type: Research Article

Abstract: This paper presents a gain-scheduling output feedback control design method for T-S fuzzy systems with actuator saturation. Different from existing control design methods for T-S fuzzy systems, the basic idea of the proposed approach is to transform the T-S fuzzy model with saturation nonlinearity into the form of linear fractional transformation (LFT). Instead of commonly used fuzzy controllers, a gain-scheduled output feedback controller in the LFT form is introduced to stabilize the saturated T-S fuzzy system with guaranteed H ∞ performance. The problem of establishing regional stability and performance of the closed-loop nonlinear system are tackled by using robust …control techniques. As a result, the conservatism introduced by dealing with the quadratic terms of normalized fuzzy weighting functions can be avoided. The proposed controller synthesis problem is cast as a convex optimization in terms of linear matrix inequalities (LMIs) and can be solved efficiently. An example of balancing the inverted pendulum with bounded actuation is provided to illustrate the effectiveness of the proposed design method. Show more

Keywords: T-S fuzzy systems, actuator saturation, gain-scheduling control, linear fractional transformation

DOI: 10.3233/JIFS-16546

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2579-2589, 2017

Authors: Xin, Xiaolong | Cheng, Xiaoyun | Zhang, Xiaohong

Article Type: Research Article

Abstract: In this paper, we introduce the notion of a generalized state operator by extending the codomain of a state operator to a more general algebraic structure, that is, from a BCI-algebra X to an arbitrary BCI-algebra Y . Also we give some special types of generalized state operators according to the structures of Y such as GD-states, GK-states and state operators. We get that generalized state operators are the generalization of state-morphisms and state-morphism operators on BCK/BCI-algebras. Then we focus on studying state operators on BCI-algebras and obtain some important results: (1) State BCI-algebras are a genuine generation …of state MV-algebras. (2) There is a bijection between all state congruences and all closed state ideals on a state BCI-algebra. (3) If (X , σ ) is a nontrivial subdirectly irreducible state BCI-algebra with Ker  (σ ) =0, then σ  (X ) is a nontrivial subdirectly irreducible subalgebra of X . Moreover we give some characterizations of several special types of BCI-algebras by use of state operators and differential states. Show more

Keywords: BCI-algebra, generalized state operator, state operator, state ideal, differential state

DOI: 10.3233/JIFS-16550

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2591-2602, 2017

Authors: Xu, Changjin | Li, Peiluan

Article Type: Research Article

Abstract: In this paper, fuzzy cellular neural networks with distributed delays and variable coefficients are studied. Applying Gaines and Mawhin, s continuation theorem of coincidence degree theory, the method of Lyapunov function and the elementary inequality 2xy  ≤ x 2  + y 2 , we establish some sufficient conditions which ensure the existence and global exponential stability of periodic solution of such fuzzy cellular neural networks with distributed delays and variable coefficients. These sufficient conditions, which are easily checked in practice by simple algebra methods, have a wide range of application. An example with its numerical simulations is given to show the feasibility …of the obtained theoretical predictions. The results obtained in this article are completely new and complement the previously known studies. Show more

Keywords: Fuzzy cellular neural networks, exponential stability, periodic solution, distributed delay, topological degree theory, variable coefficient

DOI: 10.3233/JIFS-16939

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2603-2615, 2017

Authors: Talo, Özer | Bayazit, Funda

Article Type: Research Article

Abstract: In this paper, we introduce slow oscillation and Hardy’s two-sided Tauberian conditions for double sequences in n -dimensional fuzzy number space E n . Besides, slow decrease and Landau’s one-sided Tauberian conditions for double sequences in E 1 are presented. Under these conditions we also prove Tauberian theorems for statistically convergent double sequences of fuzzy numbers.

Keywords: Double sequence, statistical convergence, fuzzy number, Tauberian conditions

DOI: 10.3233/JIFS-16573

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2617-2624, 2017

Authors: Zhang, Huan

Article Type: Research Article

Abstract: Along with the development of human being, the environmental problems have attracted more and more attention, “The Green” will become the main trend in the 21th century, and “The Green Action” will be an important department and a decisive factor to any country and enterprise which take part in the competition of the world market. Based on the above analysis, it is an important mode for the modern enterprise. We propose “The Green Idea” to the management of supply system, and then construct “The Green Supply Management” to reduce the resource cost and the environmental affect. In the study of …“The Green Supply”, how to estimate the performance with high accuracy is of great importance. Furthermore, high quality performance evaluation may let the enterprise to answer the questions, to discover the solutions, and then to enhance the quality of the operation and improvement of “The Green Supply”. Therefore, it is very crucial to enhance “The Green Supply” by making the performance evaluation with high accuracy. In this paper, we study on the multiple attribute decision making problems to estimate the performance in green supply chain based on environmental economics with fuzzy information. Then, we have developed the fuzzy Hamacher correlated averaging (FHCA) operator. We have exploited the FHCA operator to multiple attribute decision making to estimate the wireless network security with fuzzy information. In the end, an example to estimate the performance in green supply chain based on environmental economics has been proposed to prove the effectiveness of the proposed approach. Show more

Keywords: Multiple attribute decision making, triangular fuzzy number, performance in green supply chain, environmental economics

DOI: 10.3233/JIFS-16576

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2625-2631, 2017

Authors: Zhu, Li-Cai | Hou, Jin-Long | Wang, Lv

Article Type: Research Article

Abstract: Sports ground for the construction of public sports service system, services, and improving the livelihood of the people plays an important role, which is the material base to carry out the national fitness activities and improve the competitive sports achievement, it plays an indispensable role of meeting people’s spiritual and cultural life as well as the growing fitness demand. There is the reference value to comprehensively understand the current situation of sports development of new technology development zone, and it’s important to carry out the national fitness activities, increase participate in regular physical exercise population, develop sports undertakings, enhance the …level of sports services, improve the sports people’s livelihood. In this paper, we investigate the multiple attribute decision making problems for sports grounds’ management performance evaluation with triangular fuzzy information. Motivated by the ideal of geometric Bonferroni mean and dependent aggregating operators, we develop the dependent triangular fuzzy geometric Bonferroni mean (DTFGBM) operator for aggregating the triangular fuzzy information. Finally, a practical example for sports grounds’ management performance evaluation is given to verify the developed approach. Show more

Keywords: Performance evaluation, triangular fuzzy numbers, geometric Bonferroni mean, dependent triangular fuzzy geometric Bonferroni mean (DTFGBM) operator, sports grounds, management performance

DOI: 10.3233/JIFS-16582

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2633-2640, 2017

Authors: Yu, Guangji | Wu, Xiaoyun | Xia, Guoen

Article Type: Research Article

Abstract: This paper studies T -similarity of L -fuzzy relations and its algebraic structures where L is a complete residuated lattice. L -fuzzy topologies induced by L -fuzzy rough approximation operators are investigated and T -similarity of L -fuzzy relations is first introduced. Next, a characteristic condition for L -fuzzy relations to be T -transitive is established. Finally, algebraic structures on T -similarity of L -fuzzy relations are obtained and an example is given in order to illustrate the practical significance and possible applications of the proposed concepts.

Keywords: Complete residuated lattice, L-fuzzy approximate space, L-fuzzy relation, L-fuzzy topology, T-similarity, algebraic structure

DOI: 10.3233/JIFS-16606

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2641-2653, 2017

Authors: Wang, Xiao | Ning, Yufu

Article Type: Research Article

Abstract: Uncertain delay differential equation is a type of differential equations driven by a canonical Liu process. This paper mainly focuses on the stability of uncertain delay differential equations. At first, the concept of stability in measure, stability in mean and stability in moment for uncertain delay differential equations will be presented. In addition, the sufficient condition for uncertain delay differential equations being stable in measure, in mean and in moment will be derived. Finally, this paper will discuss the relationship among stability in measure, stability in mean and stability in moment.

Keywords: Uncertain delay differential equation, stability, uncertainty theory

DOI: 10.3233/JIFS-16639

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2655-2664, 2017

Authors: Hazarika, Bipan

Article Type: Research Article

Abstract: In this paper we introduce the concepts of ideal convergence, pointwise ideal convergence, and uniformly ideal convergence of sequences of fuzzy valued functions based on the concept of convergence of sequences of fuzzy numbers and obtain the relationship among pointwise ideal convergence and uniformly ideal convergence of sequences of fuzzy valued functions, and study their representations of sequences of α-level cuts.

Keywords: Fuzzy number, fuzzy valued function, ideal convergence, pointwise ideal convergence, uniformly ideal convergence

DOI: 10.3233/JIFS-16662

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2665-2677, 2017

Authors: Zhang, Yao | Guan, Xin

Article Type: Research Article

Abstract: Successful new product launches are significant for company survival in intense competition environments. Companies generally divide customers into different marketing segments to increase profits due to the growing focus on customer relationship management (CRM). For new product launches, developing marketing strategies towards customers in different segments is a critical issue faced by companies. To address this issue, this paper proposes a fuzzy optimization method to select marketing strategies for new products based on similar cases. In the proposed method, a case database and a target case are constructed that consist of relevant data about historical products and a new product, …respectively. Then, historical similar cases are retrieved based on similarities and adapted according to the current situation. Next, triangular fuzzy numbers are used to describe customers’ responses to the marketing strategies. Finally, a fuzzy integer linear model is constructed. By solving this model, marketing strategies for the new product towards customers in different segments can be obtained. A case study is provided to illustrate the potential for the practical application of the proposed methodology and several managerial implications are also noted. Show more

Keywords: Fuzzy integer linear programming, similar cases, marketing strategy, new product launch, customer segment

DOI: 10.3233/JIFS-16723

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2679-2695, 2017

Authors: Cui, Jia

Article Type: Research Article

Abstract: Wireless networks, which can be tasked with a target monitoring or tracking mission in various complicated environments, are guiding a revolution of sensing and gathering information, and have a bright future in a wide range of fields. Wireless networks are vulnerable to various types of security threats and pose unique challenges to security techniques due to many factors such as deployment in unattended environments, broadcast nature of the unreliable wireless channel, larger scale and multi-hop networking property in an ad hoc fashion, special data-centric traffic flow model, inter-node unconditional collaborative and trust relationship, and severe resource constraints etc. Therefore, the …key issue in further widely application of wireless sensor networks is how to give consideration to both availability and security for wireless networks. In this paper, we investigate the multiple attribute decision making problems with fuzzy linguistic information. Motivated by the ideal of generalized Bonferroni mean, we develop the generalized fuzzy linguistic Bonferroni Mean (GFLBM) operator for aggregating the fuzzy linguistic information. For the situations where the input arguments have different importance, we then define the generalized fuzzy linguistic weighted Bonferroni Mean(GFLWBM) operator, based on which we develop the procedure for multiple attribute decision making under the fuzzy linguistic environments. Finally, we give an illustrative example for evaluating the security of wireless network with fuzzy linguistic information to verify the developed approach and to demonstrate its feasibility and practicality. Show more

Keywords: Multiple attribute decision making, fuzzy linguistic variables, generalized fuzzy linguistic Bonferroni Mean(GFLBM) operator, generalized fuzzy linguistic weighted Bonferroni Mean(GFLWBM) operator, wireless network

DOI: 10.3233/JIFS-16744

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2697-2704, 2017

Authors: Li, Chengdong | Zhang, Guiqing | Yi, Jianqiang | Shang, Fang | Gao, Junlong

Article Type: Research Article

Abstract: In this study, we propose a novel fast learning data-driven method for the design of interval type-2 fuzzy logic system (IT2FLS). In order to accelerate the learning speed, we present a parallel mechanism to generate the antecedents of the IT2FLS and the least square method based learning algorithm to optimize the consequents. Firstly, driven by different sub-data sets, corresponding type-1 fuzzy logic systems (T1FLSs) which have the same initial fuzzy partition (thus the same initial fuzzy rule base) are parallelly obtained through the popular ANFIS method. Then, an ensembling strategy is proposed to form the type-2 fuzzy partition for each …input variable through merging corresponding type-1 fuzzy sets (T1FSs) in the type-1 fuzzy partitions of the learned T1FLSs. By this strategy, the antecedents of the IT2FLS are determined and then fixed, however, the consequent parameters still need to be optimized. To achieve both excellent performance and fast training speed, a least square method based learning algorithm is provided for the optimization of the consequent parameters. Finally, three benchmark problems and one real-world application are given, and detailed comparisons with some well performed methods are made. Simulation and comparison results have verified the effectiveness and superiorities of the proposed method. Show more

Keywords: Data-driven method, fast learning, fuzzy logic system, ANFIS, type-2 fuzzy

DOI: 10.3233/JIFS-16799

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2705-2715, 2017

Authors: Tong, Yun

Article Type: Research Article

Abstract: Today, with the development of economic globalization, the quality competition between enterprises has extended to the supply chain. If the enterprises want to get sustainable development, the traditional closed “Vertical Integration” mode needs to be changed; “Horizontal Integration” has become the inevitable choice of enterprises. With the development of performance management and supply chain technology, the combination of the two and focusing on the green supply chain quality management under low-carbon agricultural economy environment have become the hot topics in both academic area and practical area. In this paper, we study on the multiple attribute decision making problems to estimate …the green supply chain performance under low-carbon agricultural economy environment with 2-tuple linguistic information. Then, we propose the 2-tuple power Einstein weighted geometric (2TPEWG) operator for aggregating 2-tuple linguistic information, and then apply 2TPEWG operator for evaluating the green supply chain performance under low-carbon agricultural economy environment with 2-tuple linguistic information. In the end, we propose an example to test the effectiveness of our proposed method. Show more

Keywords: Multiple attribute decision making, 2-tuple linguistic information, power geometric operator, 2-tuple power Einstein weighted geometric (2TPEWG) operator, performance evaluation, green supply chain

DOI: 10.3233/JIFS-16802

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2717-2723, 2017

Authors: Altinok, Hifsi | Yağdiran, Damla

Article Type: Research Article

Abstract: In the present paper, we introduce the concept of strongly N θ β ( p , F , Δ m , M ) - summable with respect to the Orlicz function M and examine the notions S θ β ( F , Δ m ) - statistical convergence and strong N θ β ( p , F , Δ m , M ) - summability for different two lacunary sequences and β  ∈ (0, 1] . Moreover, we show that a sequence is S θ β …( F , Δ m ) - statistically convergent if it is strongly N θ ∣ γ ( p , F , Δ m , M ) - summable, where θ  ={ k r  } and θ ′ ={ s r  } are two lacunary sequences and give some inclusion relations between them. Show more

Keywords: Sequence of fuzzy numbers, statistical convergence, lacunary sequence, difference sequence, Orlicz function

DOI: 10.3233/JIFS-16842

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2725-2731, 2017

Authors: He, Xingxing | Li, Yingfang | Qin, Keyun | Meng, Dan

Article Type: Research Article

Abstract: The fuzzy XNOR connective, as the dual construction of the fuzzy symmetric difference operator, has been defined and discussed by Li, Qin and He [18 ]. The aim of this paper is to give a systematic investigation of properties and structures of fuzzy XNOR connectives. The main results are: (1) It is proved that the biresiduation of a t-norm is indeed a fuzzy XNOR connective. (2) The structures and properties for biresiduations and two canonical constructions of fuzzy XNOR connectives given in [18 ] are examined. The associativity of fuzzy XNOR connectives is specially investigated. (3) Three additional ways of …constructing fuzzy XNOR connectives are proposed. Show more

Keywords: Symmetric difference operator, equivalence operator, fuzzy XNOR connective, t-Norm, t-Conorm, fuzzy negation

DOI: 10.3233/JIFS-16845

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2733-2745, 2017

Authors: Akram, Muhammad | Sarwar, Musavarah

Article Type: Research Article

Abstract: A hypergraph is one of the most developing tool for modeling various practical problems in different fields, including computer science, biological sciences, social networks and psychology. Sometimes information in a network model is based on multi-object, multi-polar information or uncertainty rather than a single bit. Our aim in this research paper is to apply the powerful methodology of m -polar fuzzy sets to generalize the theory of hypergraphs. We introduce the notion of m -polar fuzzy hypergraphs, dual m -polar fuzzy hypergraphs, m -polar fuzzy line graphs and 2-section of m -polar fuzzy hypergraphs. We develop certain algorithms to construct …dual m -polar fuzzy hypergraphs and m -polar fuzzy line graphs. We also present some applications of m -polar fuzzy hypergraphs in planet surface networks, social networks and grouping of incompatible chemical substances. Show more

Keywords: m-Polar fuzzy hypergraph, m-Polar fuzzy line graph, Dual m-polar fuzzy hypergraph, Applications

DOI: 10.3233/JIFS-16859

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2747-2762, 2017

Authors: Jin, Huan

Article Type: Research Article

Abstract: Vehicle stability performance, as an important performance of automobile evaluation, it affected the performance of the vehicle and the people’s subjective feeling aspect, it is also the modern car driver that paid more and more attention to the stability performance, it is directly impacted the ride safety of the vehicle. In terms of the vehicle, stability performance affects the service life of the car, and even endanger the occupant safety; secondly, in terms of crew, people’s subjective feeling is one of the most important performance, stability performance will be evaluated by the people’s subjective feeling, the good or bad of …stability performance will be relation with each occupant comfort level, and it also make the each occupant do the correct and effective response, at the same time, it also influence the stability of the car. In this paper, we investigate the multiple attribute decision making problems for evaluating the vehicle stability performance with hesitant fuzzy information. Then, we propose the dependent hesitant fuzzy weighted Bonferroni mean (DHFWBM) operator, in which the associated weights only depend on the aggregated hesitant fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results and then apply DHFWBM operator to solve the vehicle stability performance with hesitant fuzzy information. Finally, an illustrative example for evaluating the vehicle stability performance is given to verify the developed approach. Show more

Keywords: Hesitant fuzzy information, operational laws, dependent hesitant fuzzy weighted Bonferroni mean (DHFWBM) operator, vehicle stability performance

DOI: 10.3233/JIFS-16868

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2763-2769, 2017

Authors: Guo, Xiaobin | Zhang, Ke

Article Type: Research Article

Abstract: In paper a general fuzzy matrix equation X ˜ A = B ˜ is investigated by using the embedding approach. A numerical procedure for calculating the solution is designed and a sufficient condition for the existence of fuzzy solution is derived. Two examples are given to illustrate the proposed method.

Keywords: Fuzzy numbers, matrix analysis, fuzzy matrix systems, fuzzy approximate solutions

DOI: 10.3233/JIFS-16895

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2771-2778, 2017

Authors: Liu, Zhengmin | Liu, Peide | Liu, Weilong | Pang, Jinyan

Article Type: Research Article

Abstract: In this paper, a new extension of linguistic term sets called Pythagorean uncertain linguistic sets (PULSs) is defined, which is based on uncertain linguistic term sets and Pythagorean fuzzy sets (PFSs) originally introduced by Yager [41 ]. This new fuzzy linguistic set has a greater membership representation space and a more powerful expression ability than the intuitionistic uncertain linguistic sets (IULSs) proposed by Liu [18 ]. Based on the defined operations of PULSs, the Pythagorean uncertain linguistic Bonferroni mean (PULBM) operator and its weighted form are developed to capture the interrelationship among attributes. Taking into account that the classical BM …operator is based on the assumption that all attributes are interrelated, and such assumption does not always exist in most of the practical decision-making situations, we further present a Pythagorean uncertain linguistic Partitioned Bonferroni mean (PULPBM) operator and its weighted form (WPULPBM) to solve such situations where all attributes may be divided into several different categories based on specific correlation characteristics and members in the same category are interrelated while no correlation exists among different categories. Then, based on the WPULPBM operator, an approach for MADM problems with Pythagorean uncertain linguistic information is proposed. Finally, a practical example is given to illustrate the application of the proposed approach and comparison analysis is investigated with other existing methods to show the effectiveness of the proposed approach. Show more

Keywords: Multi-attribute decision making, pythagorean uncertain linguistic set, bonferroni mean, partitioned Bonferroni mean

DOI: 10.3233/JIFS-16920

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2779-2790, 2017