Translations of Intuitionistic Fuzzy B-algebrasSenapati, Tapan
2015 Fuzzy Information and Engineering
doi: 10.1016/j.fiae.2015.11.001
AbstractIn this paper, the concept of intuitionistic fuzzy translation to intuitionistic fuzzy subalgebras and ideals in -algebras are introduced with several related properties investigated. Examples are also given to illustrate results. The notion of intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy subalgebras and ideals are introduced. Relationships are investigated between intuitionistic fuzzy translations, intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy subalgebras and ideals.
Fuzzy k-Primary Decomposition of Fuzzy k-Ideal in a SemiringKar, S.; Purkait, S.; Davvaz, B.
2015 Fuzzy Information and Engineering
doi: 10.1016/j.fiae.2015.11.002
AbstractIn this paper, we establish that the Lasker–Noether theorem for a commutative ring may be generalized for a commutative semiring. We produce an example of an ideal in a Noetherian semiring which cannot be expressed as finite intersection of primary ideals of that semiring. But we manifest that if we consider an arbitrary -ideal of a commutative Noetherian semiring, then it can be decomposed as finite intersection of primary -ideals. Focus mainly on the fuzzy version of the above result, we are able to prove that in a commutative Noetherian semiring, every fuzzy -ideal can be decomposed uniquely as finite intersection of fuzzy -primary ideals of that semiring.
Operations on Soft GraphsAkram, Muhammad; Nawaz, Saira
2015 Fuzzy Information and Engineering
doi: 10.1016/j.fiae.2015.11.003
AbstractMathematical modelling, analysis and computing of problems with uncertainty is one of the hottest areas in interdisciplinary research involving applied mathematics, computational intelligence and decision sciences. It is worth noting that uncertainty arises from various domains has very different nature and cannot be captured within a single mathematical framework. Molodtsov’s soft sets provide us a new way of coping with uncertainty from the viewpoint of parameterization. In this paper, we introduce the concepts of soft graphs, vertex-induced soft graphs, edge-induced soft graphs and describe some operations on soft graphs by presenting several examples to demonstrate these new concepts. Finally, we investigate some fundamental properties of soft graphs.
Multi-item Supplier Selection Model with Fuzzy Risk Analysis Studied by Possibility and Necessity ConstraintsPatra, Kartik; Mondal, Shyamal Kumar
2015 Fuzzy Information and Engineering
doi: 10.1016/j.fiae.2015.11.004
AbstractThree different supplier selection models have been developed in crisp and fuzzy environments. Here two objective functions have been considered, profit and risk. In this paper, profit has been maximized and risk has been minimized with some constraints. Each supplier has an limited capacity. The purchasing cost of each item from different supplier as well as associative risk is known. The total space and budget of a retailer are constant. In Model I, all the parameters are considered as crisp. In Model II, the demand has been considered as fuzzy. In Model III, the risk values and demand have been considered as fuzzy. To defuzzyfy the fuzzy constraints, necessity and possibility have been introduced. To defuzzyfy the fuzzy objective, two different methods, credibility measure and -cut method have been introduced. All the models have been illustrated numerically using multi-objective genetic algorithm (MOGA). Also a sensitivity analysis has been done taking different sets of risk values and a comparison result has been shown for credibility measure and -cut method for Model III.
A Type-2 Approach in Emotion Recognition and an Extended Type-2 Approach for Emotion DetectionGhosh, S.; Paul, G.
2015 Fuzzy Information and Engineering
doi: 10.1016/j.fiae.2015.11.005
AbstractThis paper aims at a fuzzy relational approach to similar emotions expressed by different subjects by facial expressions and predefined parameters. Facial attributes represents a wide variety subjected to different circumstances. The fuzzification and mapping of facial features like eye-opening, mouth-opening and length of eye-brow constriction from localized areas is done into emotion space by employing relational models. Uncertainty can be adeptly dealt with fuzzy logic where type-2 approach reigns supreme, which is developed on the basis of various patterns of facial features of various emotions of subjects. The fuzzy free space employs two type-2 fuzzy sets namely interval type-2 fuzzy set (IT2FS) and majority general type-2 fuzzy set (MGT2FS). The former (IT2FS) considers only primary membership functions for facial features extracted from subjects which exhibits instantaneous facial expression for a particular emotion. But the latter (MGT2FS) combines the function of IT2FS by introducing primary membership function and implementing secondary memberships for each primary membership curve, thus achieving the desired solution by minimization and optimization. Two other schemes namely average general type-2 approach (AGT-2) and centroidal general type-2 approach (CGT-2) are implied. Experimental results and computer simulation indicates that the proposed theory for emotion recognition and control is robust, easier to implement and possesses higher degree of accuracy.
A New Generalized Fuzzy Divergence Measure and ApplicationsOhlan, Anshu
2015 Fuzzy Information and Engineering
doi: 10.1016/j.fiae.2015.11.007
AbstractThis paper introduces a new parametric generalized measure of fuzzy divergence with the proof of its validity. The particular cases are proved in the proposed generalized fuzzy divergence measure. In addition, the elegant properties are studied on the new generalized fuzzy divergence measure. A method to solve multi-criteria decision making problem is developed by using the proposed generalized fuzzy divergence measure. Finally, the applications of this fuzzy divergence measure to pattern recognition and multi-criteria decision making are shown using numerical examples for each.