Iranian journal of fuzzy systems
Volume:16 Issue: 1, Jan-Feb 2019

In this paper, the separable programming problem subject to Fuzzy Relation Equation (FRE) constraints is studied. It is decomposed to two subproblems with decreasing and increasing objective functions with the same constraints. They are solved by the maximum solution and one of minimal solutions of its feasible domain, respectively. Their combination produces the original optimal solution. The detection of the optimal solution of the second subproblem by finding all the minimal solutions will be very time-consuming because of its NP-hardness. To overcome such difficulty, two types of sufficient conditions are proposed to find some of its optimal components or all of them. Under the first type sufficient conditions, some procedures are given to simplify the original problem. Also, a value matrix is defined and an algorithm is proposed to compute an initial upper bound on its optimal objective value using the matrix. Then, a branch-and-bound method is extended using the matrix and initial upper bound to solve the simplified problem without finding all the minimal solutions.

In this research paper, we use a normalized graph cut measure as a thresholding principle to separate an object from the background based on the standard S membership function. The implementation of the proposed algorithm known as fuzzy normalized graph cut method. This proposed algorithm compared with the fuzzy entropy method [25], Kittler [11], Rosin [21], Sauvola [23] and Wolf [33] method. Moreover, we examine that in most cases, our algorithm gives the lowest absolute error that improves the segmentation process of gray images. Finally, we change different parameter values in fuzzy normalized graph cut and the effect of the substitutes is studied. Also, we analyze the computational complexity of fuzzy weight matrix (fuzzification) results with a weight matrix (classical) results.

The objective of image fusion for medical images is to combine multiple images obtained from various sources into a single image suitable for better diagnosis. Most of the state-of-the-art image fusing technique is based on nonfuzzy sets, and the fused image so obtained lags with complementary information. Intuitionistic fuzzy sets (IFS) are determined to be more suitable for civilian, and medical image processing as more uncertainties are considered compared with fuzzy set theory. In this paper, an algorithm for effectively fusing multimodal medical images is presented. In the proposed method, images are initially converted into Yager’s intuitionistic fuzzy complement images (YIFCIs), and a new objective function called intuitionistic fuzzy entropy (IFE) is employed to obtain the optimum value of the parameter in membership and non-membership functions. Next, the YIFCIs are compared using contrast visibility (CV) to construct a decision map (DM). DM is refined with consistency verification to create a fused image. Simulations on several pairs of multimodal medical images are performed and compared with the existing fusion methods, such as simple average, discrete cosine transform (DCT), redundant wavelet transform (RWT), intuitionistic fuzzy set, fuzzy transform and interval-valued intuitionistic fuzzy set (IVIFS). The superiority of the proposed method is presented and is justified. Fused image quality is also verified with various quality metrics, such as spatial frequency (SF), average gradient (AG), fusion symmetry (FS), edge information preservation (QAB/F), entropy (E) and computation time (CoT).

In this paper, we improve some previous definitions of fuzzy-type Turing machines to obtain degrees of accepting and rejecting in a computational manner. We apply a BFS-based search method and some level’s upper bounds to propose a computational process in calculating degrees of accepting and rejecting. Next, we introduce the class of Extended Fuzzy Turing Machines equipped with indeterminacy states. These states are used to characterize the loops of classical Turing machines in a mathematical sense. In the sequel, as well as the notions of acceptable and decidable languages, we define the new notion of indeterminable language. An indeterminable language corresponds to non-halting runs of a machine. Afterwards, we show that there is not any universal extended machine; which concludes that these machines cannot solve the halting problem. Also, we show that our extended machines and classical Turing machines have the same computational power. Then, we define the new notion of semi-universality and prove that there exists a semi-universal extended machine. This machine can indeterminate the complement of classical halting problem. Moreover, to each r.e or co-r.e language, we correspond a language that is related to some extended fuzzy Turing machines.

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrated into a partial ordering set, a semi-ring and a complete non-separable metric space. Again, through two isomorphism theorem, the relationship between generalized fuzzy number space and fuzzy number space is established. Finally, as an application of generalized fuzzy numbers, the concept of continuous generalized fuzzy number-valued functions is introduced. And it is pointed out that many results of trapezoidal generalized fuzzy numbers can also be extended to generalized fuzzy numbers.

A finite switchboard state machine is a specialized finite state machine. It is built by binding the concepts of switching state machines and commutative state machines. The main purpose of this paper is to give a specific algorithm for fuzzy finite switchboard state machine and also, investigates the concepts of switching relation, covering, restricted cascade products and wreath products of fuzzy finite switchboard state machines. More precisely, we study that the direct products/Cartesian compositions of two such fuzzy finite switchboard state machines is again a fuzzy finite switchboard state machine. In addition, we introduce the perfect switchboard machine and establish its Cartesian composition. The relations among the products also been examined. Finally, we introduce asynchronous fuzzy finite switchboard state machine and study the switching homomorphic image of asynchronous fuzzy finite switchboard state machine. We illustrate the definition of a restricted product of fuzzy finite switchboard state machine with the single pattern example.

A multiobjective security game problem with fuzzy payoffs is studied in this paper. The problem is formulated as a bilevel programming problem with fuzzy coefficients. Using the idea of nearest interval approximation of fuzzy numbers, the problem is transformed into a bilevel programming problem with interval coefficients. The Karush-Kuhn-Tucker conditions is applied then to reduce the problem to an interval multiobjective single-level problem. It is shown that the solutions of this problem are obtained by solving a single-objective programming problem. Validity and applicability of the method are illustrated by a practical example.

Let X be a dcpo and let L be a complete lattice. The family σL(X) of all Scott continuous mappings from X to L is a complete lattice under pointwise order, we call it the L-fuzzy Scott structure on X. Let E be a dcpo. A mapping g : σL(E) −> M is called an LM-fuzzy possibility valuation of E if it preserves arbitrary unions. Denote by πLM(E) the set of all LM-fuzzy possibility valuations of E. The denotational semantics assigning to an LM-fuzzy possibility computation from a dcpo D to another one E is a Scott continuous mapping from D to πLM(E), which is a model of non-determinism computation in Domain Theory. A healthy LM-fuzzy predicate transformer from D to E is a sup-preserving mapping from σL(E) to σM(D), which is always interpreted as the logical semantics from D to E. In this paper, we establish a duality between an LM-fuzzy possibility computation and its LM-fuzzy logical semantics.

In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches.

Since the inception of intuitionistic fuzzy sets in 1986, many authors have proposed different methods for ranking intuitionistic fuzzy numbers (IFNs). How ever, due to the complexity of the problem, a method which gives a satisfactory result to all situations is a challenging task. Most of them contained some shortcomings, such as requirement of complicated calculations, inconsistency with human intuition and indiscrimination and some produce different rankings for the same situation and some methods cannot rank crisp numbers. For overcoming the above problems, in this paper, a new parametric ranking method for IFNs is proposed. It is developed based on the concept α-cuts and β-cuts and area on left side of IFNs. The proposed ranking method is applied to solve partner selection problem in which the rating of partner on attributes are expressed by using triangular IFNs. The proposed method is much simpler and more efficient than other methods in the literature. Some comparative examples are also given to illustrate the advantages of the proposed method.

The concepts of covering and matching in fuzzy graphs using strong arcs are introduced and obtained the relationship between them analogous to Gallai’s results in graphs. The notion of paired domination in fuzzy graphs using strong arcs is also studied. The strong paired domination number γspr of complete fuzzy graph and complete bipartite fuzzy graph is determined and obtained bounds for the strong paired domination number of fuzzy graphs. An upper bound for the strong paired domination number of fuzzy graphs in terms of strong independence number is also obtained.

In this paper, we introduce a notion of generalized states from an EQ-algebra E1 to another EQ-algebra E2, which is a generalization of internal states (or state operators) on an EQ-algebra E. Also we give a type of special generalized state from an EQ-algebra E1 to E1, called generalized internal states (or GI-state). Then we give some examples and basic properties of generalized (internal) states on EQ-algebras. Moreover we discuss the relations between generalized states on EQ-algebras and internal states on other algebras, respectively. We obtain the following (1) Every state-morphism on a good EQ-algebra E is a G-state from E to the EQ-algebra E0 = ([0,1],∧0,⊙0,∼0,1). (2) Every state operator µ satisfying µ(x)⊙µ(y) ∈ µ(E) on a good EQ-algebra E is a GI-state on E. (3) Every state operator τ on a residuated lattice (L,∧,∨,⊙,→,0,1) can be seen a GI-state on the EQ-algebra (L,∧,⊙,∼,1), where x ∼ y := (x → y) ∧ (y → x). (4) Every GI-state σ on a good EQ-algebra (L,∧,⊙,∼,1) is a internal state on equality algebra (L,∧,∼,1). (5) Every GI-state σ on a good EQ-algebra (L,∧,⊙,∼,1) is a left state operator on BCK-algebra (L,∧,→,1), where x → y = x ∼ x∧y.

Inthispaper, (L,M)-fuzzy domain finiteness and (L,M)-fuzzy restricted hull spaces are introduced, and several characterizations of the category (L,M)-CS of (L,M)-fuzzy convex spaces are obtained. Then, (L,M)-fuzzy stratified (resp. weakly induced, induced) convex spaces are introduced. It is proved that both categories, the category (L,M)-SCS of (L,M)-fuzzy stratified convex spaces and the category (L,M)-WICS of (L,M)-fuzzy weakly induced convex spaces, are coreflective subcategories of (L,M)-CS. It is also proved that three isomorphic categories, namely, the category MCS of M-fuzzifying convex spaces, the category (L,M)-CGCS of (L,M)-fuzzy convex spaces induced by M-fuzzifying convex spaces and the category (L,M)-ICS of (L,M)-fuzzy induced convex spaces, are coreflective subcategories of both (L,M)-SCS and (L,M)-WICS.

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completely distributive L-ordered set, the fuzzy S-upper topology has a special base such that it looks like the usual upper topology on the set of real numbers. For every complete L-ordered set, the fuzzy S-upper topology coincides the fuzzy Scott topology.