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

Authors: Bica, Alexandru Mihai | Popescu, Constantin

Article Type: Research Article

Abstract: In this paper we develop an iterative numerical method for solving nonlinear fuzzy Volterra integral equations. The convergence of the method is proved and the obtained theoretical results are tested on some numerical examples.

Keywords: Fuzzy numerical analysis, fuzzy-number-valued functions, fuzzy Hammerstein-Volterra nonlinear integral equations, iterative numerical method

DOI: 10.3233/IFS-152032

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 1639-1648, 2017

Authors: Parchami, Abbas | Sadeghpour Gildeh, Bahram | Taheri, S. Mahmoud | Mashinchi, Mashaallah

Article Type: Research Article

Abstract: In testing the capability of industrial processes, the researcher considers and tests the vague hypothesis “the capability index is low” against the vague hypothesis “the capability index is high”. But, two fuzzy concepts low and high are usually formulated by two crisp hypotheses in traditional quality tests. In this paper, we formulate these two fuzzy concepts by considering two complement fuzzy sets. Afterwords, a new p -value-based approach is considered for testing the mentioned fuzzy hypotheses which is constructed on the basis of two capability indices C p and C pm . This new approach …has several advantages over the common p -value methods for testing fuzzy hypotheses. The main one is depending the result of this new approach on both null and alternative fuzzy hypotheses, while the common p -value-based methods are according to only the null fuzzy hypothesis. To clarify the potential of the proposed approach in the process of capability analyses, two applied examples are given based on two real-world data set. Show more

Keywords: Boundary of fuzzy hypothesis, weighted density, Taguchi capability index, maximum likelihood estimator

DOI: 10.3233/JIFS-141680

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 1649-1658, 2017

Authors: Kahraman, Cengiz | Parchami, Abbas | Cevik Onar, Sezi | Oztaysi, Basar

Article Type: Research Article

Abstract: The process capability analysis aims at measuring the capability degree of the process distribution in meeting the specification limits. Process capability indices are used to indicate the capability degree of a process. A process whose distribution falls inside the specification limits is a capable process and its capability indices are at least 1. In case of vague and imprecise information, process capability analyses have been extended by using ordinary fuzzy sets in the literature. In this paper we extend the fuzzy process capability analysis from ordinary fuzzy sets to intuitionistic fuzzy sets. We realize this extension by using both intuitionistic …fuzzy numbers and interval-valued intuitionistic fuzzy sets. We also propose defuzzification methods for intuitionistic fuzzy numbers and interval-valued intuitionistic fuzzy sets. Numerical examples show the applications of the proposed analyses and help the readers understand them. Show more

Keywords: Process capability, intuitionistic, fuzzy set, fuzzy number, interval-valued, defuzzification

DOI: 10.3233/JIFS-141877

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 1659-1671, 2017

Authors: Li, Junhong | Zeng, Wenyi

Article Type: Research Article

Abstract: In this paper, we propose a new similarity measure between generalized trapezoidal fuzzy numbers (GTFN), which can ensure the effectiveness of similarity measure, reduce the complexity of computation, and improve its distinguish ability and application scope. Meanwhile, we introduce two indexes to evaluate the performance of different similarity measures, and use numerical examples to compare our proposed similarity measure with some existing similarity measures. Finally, we apply our proposed similarity measure in fuzzy risk analysis, and the results show that our proposed similarity measure is reasonable and effective.

Keywords: Similarity measure, fuzzy risk analysis, distinguish ability, evaluation index, generalized trapezoidal fuzzy number

DOI: 10.3233/JIFS-141907

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 1673-1683, 2017

Authors: Zareizadeh, Zahra | Helfroush, Mohammad Sadegh | Kazemi, Kamran

Article Type: Research Article

Abstract: In this paper a new multi-objective clonal selection algorithm (θ -MCSA) is presented to solve multi-objective problems with multimodal and non-continuous functions. The concept of clonal selection algorithm (CSA) is based on the immune system and white blood cells behavior that select the antibodies similar to antigen for cloning. Although the clonal selection is a robust optimization method, however, as a shortcoming, it takes long time to find optimal Pareto front especially in problems with large search space. To overcome this problem, the proposed method replaces the large search space with the θ -search based on the phase angles. To …avoid trapping into local optima in mutation step, two strong mutation methods are implemented according to the iteration number and algorithm efficiency. For converging to uniformly Pareto front in less iterations, the proposed multi-objective algorithm handles the size of the repository and a new population updating mechanism is iteratively applied to select the non-dominate, one-dominate and two-dominate solutions of prior iteration. The experimental results show the efficiency of the proposed θ -MCSA algorithm compared to other methods. Show more

Keywords: Clonal selection, multi-objective optimization problem, θ-search method, niching, non-dominate solution

DOI: 10.3233/JIFS-151459

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 1685-1696, 2017

Authors: Roy, Sankar Kumar | Maity, Gurupada

Article Type: Research Article

Abstract: This paper explores the study of Transportation Problem (TP) under the light of multi-choice environment with interval analysis. The parameters of TP follow multi-choice interval-valued type so this form of TP is called Multi-Choice Interval Transportation Problem (MCITP). Introduction of time is an important notion in TP of this paper. Transportation time and cost, both are minimized through single objective function of TP, which is the main aim of this paper. A procedure is shown for converting from MCITP to deterministic TP and then solve it. A case study is included to illustrate the usefulness of the paper. Finally, concluding …remarks and an outlook for future study are presented to this paper. Show more

Keywords: Transportation problem, multi-choice programming, interval number, transformation technique, binary variable

DOI: 10.3233/JIFS-151656

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 1697-1709, 2017

Authors: Norouzi, Morteza | Cristea, Irina

Article Type: Research Article

Abstract: In this paper, combining the notions of “belongingness” and “quasi coincidence” of fuzzy points and fuzzy subsets, a new type of fuzzy subsemihypermodules, namely (∝, ⋐k )-fuzzy subsemihypermodules of general hypermodules, is introduced and characterized, using the “max” operator. Their properties and connections with other (α, β)-fuzzy subsemihypermodules are investigated.

Keywords: General hypermodule, (∝, ⋐k)-fuzzy subsemihypermodule, (∝, ∝)-fuzzy subsemihypermodule, (∝, qk)-fuzzy subsemihypermodule

DOI: 10.3233/JIFS-151867

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 1711-1717, 2017

Authors: Sun, Bingzhen | Ma, Weimin

Article Type: Research Article

Abstract: This paper presents a general framework for the study of rough approximation of a fuzzy (crisp) concept in multi-universes environment, which is an extension of the original Pawlak rough set theory. The Pawlak rough set is mainly concerned with the approximation of objects confined on the same universe by an arbitrary binary relation. However, the objects (concept) may be related with three or more different universes in reality of the decision-making. This paper presents the rough set model over multi-universes, where the concept approximations are defined by using a multiple relation on the multi-universes. We firstly present the rough approximation …of a fuzzy concept over multi-universes by using the multiple fuzzy relation defined on the multi-universes, i.e., the fuzzy rough set over multi-universes. Then, a number of important properties of fuzzy rough set over multi-universes are obtained. It is shown that some of the properties of the fuzzy rough set on the same universe are special instances of those of fuzzy rough set over multi-universes. Furthermore, several special rough set models over multi-universes are derived from the fuzzy rough set over multi-universes. Subsequently, we give a new approach to multiple attribute decision making (MADM) with the characteristic of uncertainty, incomplete and inaccurate available information based on fuzzy rough set over multi-universes by combing the idea of uncertainty risk decision making. The decision steps and the algorithm of the decision method are also given. The proposed approach can obtain an objectively decision result with the data information owned by the decision problem only. Finally, the validity of the decision methods is tested by a numerical example with the background of clinical medical diagnosis decision making. The main contribution of this paper is twofold. One is to present a new perspective of the universe-oriented extension for classical rough set and then establish a new generalized rough set model under the framework of multiple different universes, i.e., fuzzy rough set model over multi-universes. Another is to present an approach to multiple attribute decision making problems based on fuzzy rough set over multi-universes. Show more

Keywords: Rough set theory, multiple relation, uncertainty decision making, multiple attribute decision making (MADM), fuzzy rough set over multi-universes

DOI: 10.3233/JIFS-151977

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 1719-1734, 2017

Authors: Huang, Xiaokun | Li, Qingguo

Article Type: Research Article

Abstract: This paper addresses the strongly convex lattice-valued fuzzy (L -fuzzy) subsets of an ordered semigroup. It is shown that the set of all strongly convex L -fuzzy subsets of an ordered semigroup S forms a quantale and that S can be embedded into the quantale. The properties of L -fuzzy ideals of an ordered semigroup, a special class of strongly convex L -fuzzy subsets, are discussed. Specially, two approaches are developed to construct an L -fuzzy (left) ideal by an arbitrary L -fuzzy subset of an ordered semigroup.

Keywords: Ordered semigroup, strongly convex L-fuzzy subset, quantale, embedding mapping, L-fuzzy ideal

DOI: 10.3233/JIFS-152042

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 1735-1744, 2017

Authors: Sun, Xi-Ping

Article Type: Research Article

Abstract: With the dramatic economic increases and irreversible increases of China’s population, and declines of arable land, the feasible way to increase food production is to increase the grain yield per unit area. These result in the huge increases of nitrogen fertilizer application, and reducing nitrogen-use efficiency, lower economic profit, poor grain quality and environmental contamination by nitrogen. Selection of rice genotype with high nitrogen use efficiency is one feasible way of methods to improve nitrogen use efficiency. In this paper, we first introduce some operations on the intuitionistic fuzzy sets, and further develop the intuitionistic fuzzy Hamacher power weighted average …(IFHPWA) operator. We also establish some desirable properties of this operator, such as idempotency, Boundedness and monotonicity. Then, we apply the intuitionistic fuzzy Hamacher power weighted average (IFHPWA) to deal with multiple attribute decision making with Intuitionistic fuzzy information. Finally, an illustrative example for Nitrogen use efficiency evaluation of different rice genotypes is given to verify the developed approach. Show more

Keywords: Intuitionistic fuzzy numbers, operational laws, intuitionistic fuzzy Hamacher power weighted average (IFHPWA) operator, nitrogen use efficiency evaluation, different rice genotypes

DOI: 10.3233/JIFS-152242

Citation: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 1745-1751, 2017