Journal of Intelligent & Fuzzy Systems - Volume 33, issue 1

Authors: Adillon, Romà | Jorba, Lambert

Article Type: Research Article

Abstract: The aim of this work is to construct quantified trapezoidal fuzzy numbers as an extension of trapezoidal fuzzy numbers, by using modal intervals and accepting the possibility that the α-cuts of a trapezoidal fuzzy number may also be improper intervals. In addition, this paper addresses the inclusion relationship which is deduced from the inclusion of modal intervals and is related to the classical set-inclusion relationship between trapezoidal fuzzy numbers. Moreover, in this paper we also study the extensions of real continuous functions over the set of quantified trapezoidal fuzzy numbers. Using the semantic interpretation of the calculations over modal …intervals will enable us to interpret the meaning of the calculus accurately over quantified trapezoidal fuzzy numbers. With quantified trapezoidal fuzzy numbers, we will be able to overcome some operational limitations that are usually faced when working with trapezoidal fuzzy numbers from a classical point of view. In order to show the applicability of quantified trapezoidal fuzzy numbers, we propose fuzzy equations which have no solution in the set of proper fuzzy numbers yet do have solutions that are improper fuzzy numbers. We also propose two applications of quantified trapezoidal fuzzy numbers, one of them about financial calculations and the other one in an optical problem. Show more

Keywords: Fuzzy numbers, modal intervals, semantic interpretation

DOI: 10.3233/JIFS-16631

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 1, pp. 601-611, 2017

Authors: Xiu, Zhen-Yu | Pang, Bin

Article Type: Research Article

Abstract: In this paper, the relations between M -fuzzifying cotopologies and M -fuzzifying closure systems, and the relations between M -fuzzifying convex structures and M -fuzzifying closure systems are studied, respectively. A categorical approach is provided to present these relations. It is shown that the category of M -fuzzifying cotopological spaces and the category of M -fuzzifying convex spaces are both bicoreflective subcategories of the category of M -fuzzifying closure spaces.

Keywords: M-fuzzifying cotopology, M-fuzzifying convex structure, M-fuzzifying closure system, Bicoreflective subcategory

DOI: 10.3233/JIFS-16661

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 1, pp. 613-620, 2017

Authors: Liu, Xiaolan | Yi, Miao | Han, Le | Deng, Xue

Article Type: Research Article

Abstract: Sparse subspace clustering (SSC) and low-rank representation (LRR) are the state-of-the-art methods for subspace clustering, which force the representation matrix to be sparse and low-rank, respectively. Considering that sparsity and low rankness are of complementarity and the clean data matrix can be expressed as the combination of itself, in this paper, a new algorithm, named sparse and low-rank subspace clustering (SSC_LRR for short), was proposed. SSC_LRR decomposes the data matrix as the sum of a self-express clean dictionary and an error matrix, and forces the linear representation coefficient matrix to be simultaneously sparse and low-rank. An alternating direction method of …multipliers (ADMM) based algorithm was developed to solve the SSC_LRR problem. Experimental results on synthetic data, motion segmentation and face clustering tasks demonstrate the effectiveness of our approach. Show more

Keywords: Subspace clustering, sparse representation, low-rank representation, motion segmentation, face clustering

DOI: 10.3233/JIFS-16771

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 1, pp. 621-633, 2017

Authors: Rahman, Khaista | Abdullah, Saleem | Ahmed, Rehan | Ullah, Murad

Article Type: Research Article

Abstract: There are many aggregation operators and its applications have been developed up to date, but Pythagorean fuzzy Einstein weighted geometric (PFEWG) operator was not introduced. Therefore in this paper, we introduce Pythagorean fuzzy Einstein weighted geometric (PFEWG) operator. We also discuss some basic properties of the proposed operator, including idempotency, boundedness, and monotonicity. Finally, we apply the PFEWG operator to deal with multiple attribute group decision making problem under Pythagorean fuzzy information. For Pythagorean fuzzy Einstein weighted geometric (PFEWG) operator, we construct an algorithm for multiple attribute group decision making problem also. In the last we construct a numerical example …also for multiple attribute group decision making problem Show more

Keywords: Pythagorean fuzzy set, Pythagorean fuzzy Einstein weighted geometric aggregation operator, multiple attribute group decision making

DOI: 10.3233/JIFS-16797

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 1, pp. 635-647, 2017

Authors: Kundu, Anindita | Guchhait, Partha | Panigrahi, Goutam | Maiti, Manoranjan

Article Type: Research Article

Abstract: In this paper, a multi-item economic production quantity (EPQ) model for deteriorating seasonal products is developed with stock and promotional effort dependent demand in an imperfect production process. The promotional efforts are advertising, delivery facilities, better services, etc. The production process produces some imperfect quality units which are instantly reworked at a cost to bring back its quality to the perfect ones. Here, the rate of production is time dependent. Unit production cost is a function of production rate including the defective ones and the deterioration rate is considered as constant. The model is formulated as a profit maximization problem …with space and budget constraints in the form of an optimal control problem. The total profit function with the effect of inflation and time-value of money is expressed as a finite integral over a finite planning horizon. The problem is solved using variational calculus to determine the minimum defective rates of the production process for which the total profit is maximum. Another three models are developed considering the constraints as uncertain (fuzzy, random and rough) in nature. For fuzzy model, three types of fuzzy numbers are considered. To deal with the fuzzy constraints, fuzzy possibility measure is used. Also, stochastic and rough constraints are reduced to the approximate crisp ones following chance constrained approach and rough expectation respectively. Numerical experiments are performed to illustrate the models. Also, some sensitivity analyses are performed and presented. Show more

Keywords: Economic production quantity, imperfect production process, time-dependent demand, euler-lagrange function, defective rate, promotional effort

DOI: 10.3233/JIFS-16875

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 1, pp. 649-666, 2017

Authors: Imdad, Mohammad | Ahmed, M.A. | Nafadi, H.A.

Article Type: Research Article

Abstract: In this paper, we adopt the notion of CLR property for hybrid pairs of L -fuzzy mappings in non-Archimedean modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems for L -fuzzy mappings in non-Archimedean modified intuitionistic fuzzy metric spaces. Our results generalize and improve several earlier relevant known results. We also substantiate our results using illustrative examples.

Keywords: Modified IFMS, hybrid pairs of mappings, common fixed point

DOI: 10.3233/JIFS-16966

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 1, pp. 667-677, 2017