Young Chel Kwun

Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problems

In this paper, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFN), and the information about attribute weights is partially known. First, we use the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and then we use the obtained attribute weights and the interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator to fuse the interval-valued intuitionistic fuzzy information in the collective interval-valued intuitionistic fuzzy decision matrix to get the overall interval-valued intuitionistic fuzzy values of alternatives, and then rank the alternatives according to the correlation coefficients between IVIFNs and select the most desirable one(s). Finally, a numerical example is used to illustrate the applicability of the proposed approach.

Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information

The aim of this paper is to extend the VIKOR method for multiple attribute group decision making in interval-valued intuitionistic fuzzy environment, in which all the preference information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number, and the information about attribute weights is partially known, which is an important research field in decision science and operation research. First, we use the interval-valued intuitionistic fuzzy hybrid geometric operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and then determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution. We use the different distances to calculate the particular measure of closeness of each alternative to the interval-valued intuitionistic positive-ideal solution. According to values of the particular measure, we rank the alternatives and then select the most desirable one(s). Finally, a numerical example is used to illustrate the applicability of the proposed approach.

Extension of the VIKOR method to dynamic intuitionistic fuzzy multiple attribute decision making

The aim of this paper is to extend the VIKOR method for dynamic intuitionistic fuzzy multiple attribute decision making (DIF-MADM). Two new aggregation operators called dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator and uncertain dynamic intuitionistic fuzzy weighted geometric (UDIFWG) operator are presented. A procedure based on the DIFWG operator is developed to solve the dynamic intuitionistic fuzzy multiple attribute decision making (DIF-MADM) problems where all the decision information about values takes the form of intuitionistic fuzzy numbers collected at different periods, a procedure based on the UDIFWG operator is developed for DIF-MADM under interval uncertainty in which all the decision information about attribute values takes the form of interval-valued intuitionistic fuzzy numbers collected at different periods. Finally, a numerical example is used to illustrate the applicability of the proposed approach.

Uncertain linguistic harmonic mean operators and their applications to multiple attribute group decision making

In this paper, some uncertain linguistic aggregation operators called uncertain linguistic weighted harmonic mean (ULWHM) operator, uncertain linguistic ordered weighted harmonic mean operator and uncertain linguistic hybrid harmonic mean (ULHHM) operator are proposed. An approach to multiple attribute group decision making (MAGDM) with uncertain linguistic information is developed based on the ULWHM and the ULHHM operators. Finally, a practical application of the developed approach to MAGDM problem with uncertain linguistic information is given.

Controllability for the semilinear fuzzy integrodifferential equations with nonlocal conditions

In this paper, we study the controllability for the semilinear fuzzy integrodifferential control system with nonlocal condition in EN by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in EN.

2-Tuple linguistic harmonic operators and their applications in group decision making

Harmonic mean is reciprocal of arithmetic mean of reciprocal, which is a conservative average to be used to provide for aggregation lying between max and min operators. In this paper, we develop some new linguistic aggregation operators such as 2-tuple linguistic harmonic (2TLH) operator, 2-tuple linguistic weighted harmonic (2TLWH) operator, 2-tuple linguistic ordered weighted harmonic (2TLOWH) operator, and 2-tuple linguistic hybrid harmonic (2TLHH) operator, which can be utilized to aggregate preference information taking the form of linguistic variables, and then study some desirable properties of the operators. Based on the 2TLWH and 2TLHH operators, we present an approach to multiple attribute decision making with 2-tuple linguistic information. Finally, illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness by comparing with the existing approaches.

Controllability of second-order neutral functional differential inclusions in Banach spaces

In this paper, we prove the controllability of second-order neutral functional differential inclusions in Banach spaces. The result are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for condensing maps due to Martelli.

Some properties of equivalence soft set relations

The soft set theory is a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. Babitha and Sunil [Soft set relations and function, Computers and Mathematics with Applications 60 (2010) 1840-1849] introduced the notion of soft set relations as a soft subset of the Cartesian product of soft sets and discussed many related concepts such as equivalence soft set relations, partitions and functions. In this paper, we further study the equivalence soft set relations and obtain soft analogues of many results concerning ordinary equivalence relations and partitions. Furthermore, we introduce and discuss the transitive closure of a soft set relation and prove that the poset of the equivalence soft set relations on a given soft set is a complete lattice with the least element and greatest element.

On Some Results for Five Mappings using Compatibility of Type(α) in Intuitionistic Fuzzy Metric Space

The object of this paper is to introduce the notion of compatible mapping of type(α) in intuitionistic fuzzy metric space, and to establish common fixed point theorem for five mappings in intuitionistic fuzzy metric space. Our research are an extension for the results of [1] and [7].

Existence of Solutions for the Semilinear Fuzzy Integrodifferential Equations using by Successive Iteration

This paper is to investigate the existence theorem for the semilinear fuzzy integrodifferential equation in E N by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in E N . Main tool is successive iteration method.